53
Chapter 4 Displaying Quantitative Data
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Chapter 4
Displaying Quantitative Data
Quantitative variables
bull Quantitative variables- record measurements or amounts of something Must have units or a variable in which the numbers act as numerical values
Types of Displays
bull Histogram
bull Stem and Leaf Displays
bull Dotplots
Histogram
bull A histogram uses adjacent bars to show the distribution of values in a quantitative variable
bull Looks very similar to a bar graph but there are differences
bull The horizontal axis is continuous not just labeled
An example
bull The histogram shown below gives the number of children visited a particular zoo bull
Histogram
bull A histogram is more convenient than a dot-plot or a stem and leaf plot because you dont have to represent each data point However you dont get to see the value of each data point So a table of data and summary statistics would help people interpret the data
Be Careful
bull A histogram gives the number of data points that fall into equal intervals Care must be taken in choosing the intervals because it can affect the shape of the graph and misrepresent the true data
1st graph
bull The first graph is uses intervals of size 10 yielding the intervals 40-50 50-60 etc In this case Yemen had a life expectancy of 50 and was placed in the 50-60 column Usually borderline values are placed in the higher column
2nd Graph
bull In the second graph the intervals are 40-45 45-50 50-55 etc This affects the shape of the graph
Stem and Leaf Displays
bull Shows quantitative data values in a way that sketches the distribution of the data
bullThe stem-and-leaf plot below shows the number of students enrolledbull in a dance class in the past 12 yearsbull The number of students are 81 84 85 86 93 94 97 100 102 103 110 and 111
Dotplot
bull Graphs a dot for each case against a single axis
bull Graph the following number 5 5555551010101010 etc
Dotplot with two sets of data
Example
Shape
bull To describe the shape of a distribution look for
bull Symmetry versus skewness
bull Single versus multiple modes
Symmetrical
bull A distribution is symmetric if the two halves on either side of the center look approximately like the mirror images of each other
Symmetrical
bull Symmetrical Histogram
Dotplot
bull Dots are mirrored images
Stem and leaf
bull Example
Skewed
bull A distribution is skewed if it is not symmetric and one tail stretched out further than the other
bull Skewed left- when the longer tail stretches to the left
bull Skewed right-when the longer tail stretched to the right
Examples
bull Skewed right
Skewed left
bull Left
All three
bull Examples
Funny example
bull httpwwwherkimershideawayorgapstatisticsymmsum99ymm111htm
New seating chart
bull httpwwwrandomorgintegers
Stem-and-Leaf Revisited
1048708 Compare the histogram and stem-and-leafdisplay for the pulse rates of 24 women at ahealth clinic Which graphical display do youprefer
Think Before You Draw Again
bull 1048708 Remember the ldquoMake a picturerdquo rulebull 1048708 Now that we have options for data displays
youbull need to Think carefully about which type ofbull display to makebull 1048708 Before making a stem-and-leaf display abull histogram or a dotplot check thebull 1048708 Quantitative Data Condition The data arebull values of a quantitative variable whose unitsbull are known
Constructing a Stem-and-Leaf Display
bull 1048708 First cut each data value into leading digits
bull (ldquostemsrdquo) and trailing digits (ldquoleavesrdquo)bull 1048708 Use the stems to label the binsbull 1048708 Use only one digit for each leafmdasheither
round orbull truncate the data values to one decimal
placebull after the stem
Center
bull A value that attempts the impossible by summarizing the entire distribution with a single number a ldquotypicalrdquo value
bull Measures include the mean and median
Spread
bull A numerical summary of how tightly the values are clustered around the center
bull Measures of spread include the IQR and standard deviation
Mode
bull a hump or local high pint in the shape of the distribution of a variable is called the mode The apparent location of modes can change as the scale of a histogram is changed
Unimodal
bull Having one mode
Bimodal
bull Distribution with two modes
Example
Uniform
1048708 A histogram that doesnrsquot appear to have any mode andin which all the bars are approximately the same heightis called uniform
Anything Unusual
bull Do any unusual features stick outbull 1048708 Sometimes itrsquos the unusual features that tellbull us something interesting or exciting about thebull databull 1048708 You should always mention any stragglers orbull outliers that stand off away from the body ofbull the distributionbull 1048708 Are there any gaps in the distribution If sobull we might have data from more than onebull group
Outliers
The following histogram has outliersmdashthere arethree cities in the leftmost bar
Outliers
bull Are extreme values that do not appear to belong to the rest of the data They may be unusual values that deserve further investigation or they may be just mistakes therersquos no obvious way to tell Do not delete them Outliers can affect many statistical analyses so you should always be alert to them
Outliers
bull Away from the main portion of data
Where is the Center of the Distribution
bull 1048708 If you had to pick a single number to describe allbull the data what would you pickbull 1048708 Itrsquos easy to find the center when a histogram isbull unimodal and symmetricmdashitrsquos right in the middlebull 1048708 On the other hand itrsquos not so easy to find thebull center of a skewed histogram or a histogram withbull more than one modebull 1048708 For now we will ldquoeyeballrdquo the center of thebull distribution In the next chapter we will find thebull center numerically
How Spread Out is the Distribution
bull 1048708 Variation matters and Statistics is about
bull variation
bull 1048708 Are the values of the distribution tightly clustered
bull around the center or more spread out
bull 1048708 In the next two chapters we will talk about
bull spreadhellip
Comparing Distributions
bull 1048708 Often we would like to compare two or morebull distributions instead of looking at one distributionbull by itselfbull 1048708 When looking at two or more distributions it isbull very important that the histograms have been putbull on the same scale Otherwise we cannot reallybull compare the two distributionsbull 1048708 When we compare distributions we talk about thebull shape center and spread of each distribution
Example
Compare thefollowingdistributions ofages for femaleand male heartattack patients
Compare thefollowingdistributions ofages for femaleand male heartattack patients
HOMEWORK
Web Pages Used
bull httpwwwfaoorgwairdocsilrix5469ex5469e38gif
bull httpwwwsciencebuddiesorgscience-fair-projectsdescriptive_statistics_filesBimodalDistjpg
bull httpimagesabsoluteastronomycomimagesencyclopediaimagesbbibimodalpng
bull httpuploadwikimediaorgwikipediacommonsbbcBimodal_geologicalPNG
Web Pages Used
bull httpmathworldwolframcomimageseps-gifOutlierHistogram_1000gif
Timeplots Order Please
bull 1048708 For some data sets we are interested in how the
bull data behave over time In these cases we
bull construct timeplots of the data
Re-expressing Skewed Data toImprove Symmetry
Re-expressing Skewed Data toImprove Symmetry (cont)
One way to make a skeweddistribution more symmetric isto re-express or transform thedata by applying a simplefunction(eg logarithmic function)1048708 Note the change in skewnessfrom the raw data (Figure411) to the transformed data(Figure 412)
What Can Go Wrong
bull 1048708 Donrsquot make a histogram of a categorical variablemdash
bull bar charts or pie charts should be used for
bull categorical data
bull 1048708 Donrsquot look for shape
bull center and spread
bull of a bar chart
What Can Go Wrong (cont)
bull 1048708 Donrsquot use bars in every displaymdashsave them for
bull histograms and bar charts
bull 1048708 Below is a badly drawn timeplot and the proper
bull histogram for the number of eagles sighted in a
bull collection of weeks
What Can Go Wrong (cont)
What Can Go Wrong (cont)
Choose a bin width appropriate to the data1048708 Changing the bin width changes theappearance of the histogram
What Can Go Wrong (cont)
1048708 Avoid inconsistent scaleseither within the display orwhen comparing twodisplays1048708 Label clearly so a readerknows what the plotdisplays1048708 Good intentions badplot
What have we learned
bull 1048708 Wersquove learned how to make a picture for quantitative databull to help us see the story the data have to Tellbull 1048708 We can display the distribution of quantitative data with abull histogram stem-and-leaf display or dotplotbull 1048708 Tell about a distribution by talking about shape centerbull spread and any unusual featuresbull 1048708 We can compare two quantitative distributions by lookingbull at side-by-side displays (plotted on the same scale)bull 1048708 Trends in a quantitative variable can be displayed in abull timeplot
Quantitative variables
bull Quantitative variables- record measurements or amounts of something Must have units or a variable in which the numbers act as numerical values
Types of Displays
bull Histogram
bull Stem and Leaf Displays
bull Dotplots
Histogram
bull A histogram uses adjacent bars to show the distribution of values in a quantitative variable
bull Looks very similar to a bar graph but there are differences
bull The horizontal axis is continuous not just labeled
An example
bull The histogram shown below gives the number of children visited a particular zoo bull
Histogram
bull A histogram is more convenient than a dot-plot or a stem and leaf plot because you dont have to represent each data point However you dont get to see the value of each data point So a table of data and summary statistics would help people interpret the data
Be Careful
bull A histogram gives the number of data points that fall into equal intervals Care must be taken in choosing the intervals because it can affect the shape of the graph and misrepresent the true data
1st graph
bull The first graph is uses intervals of size 10 yielding the intervals 40-50 50-60 etc In this case Yemen had a life expectancy of 50 and was placed in the 50-60 column Usually borderline values are placed in the higher column
2nd Graph
bull In the second graph the intervals are 40-45 45-50 50-55 etc This affects the shape of the graph
Stem and Leaf Displays
bull Shows quantitative data values in a way that sketches the distribution of the data
bullThe stem-and-leaf plot below shows the number of students enrolledbull in a dance class in the past 12 yearsbull The number of students are 81 84 85 86 93 94 97 100 102 103 110 and 111
Dotplot
bull Graphs a dot for each case against a single axis
bull Graph the following number 5 5555551010101010 etc
Dotplot with two sets of data
Example
Shape
bull To describe the shape of a distribution look for
bull Symmetry versus skewness
bull Single versus multiple modes
Symmetrical
bull A distribution is symmetric if the two halves on either side of the center look approximately like the mirror images of each other
Symmetrical
bull Symmetrical Histogram
Dotplot
bull Dots are mirrored images
Stem and leaf
bull Example
Skewed
bull A distribution is skewed if it is not symmetric and one tail stretched out further than the other
bull Skewed left- when the longer tail stretches to the left
bull Skewed right-when the longer tail stretched to the right
Examples
bull Skewed right
Skewed left
bull Left
All three
bull Examples
Funny example
bull httpwwwherkimershideawayorgapstatisticsymmsum99ymm111htm
New seating chart
bull httpwwwrandomorgintegers
Stem-and-Leaf Revisited
1048708 Compare the histogram and stem-and-leafdisplay for the pulse rates of 24 women at ahealth clinic Which graphical display do youprefer
Think Before You Draw Again
bull 1048708 Remember the ldquoMake a picturerdquo rulebull 1048708 Now that we have options for data displays
youbull need to Think carefully about which type ofbull display to makebull 1048708 Before making a stem-and-leaf display abull histogram or a dotplot check thebull 1048708 Quantitative Data Condition The data arebull values of a quantitative variable whose unitsbull are known
Constructing a Stem-and-Leaf Display
bull 1048708 First cut each data value into leading digits
bull (ldquostemsrdquo) and trailing digits (ldquoleavesrdquo)bull 1048708 Use the stems to label the binsbull 1048708 Use only one digit for each leafmdasheither
round orbull truncate the data values to one decimal
placebull after the stem
Center
bull A value that attempts the impossible by summarizing the entire distribution with a single number a ldquotypicalrdquo value
bull Measures include the mean and median
Spread
bull A numerical summary of how tightly the values are clustered around the center
bull Measures of spread include the IQR and standard deviation
Mode
bull a hump or local high pint in the shape of the distribution of a variable is called the mode The apparent location of modes can change as the scale of a histogram is changed
Unimodal
bull Having one mode
Bimodal
bull Distribution with two modes
Example
Uniform
1048708 A histogram that doesnrsquot appear to have any mode andin which all the bars are approximately the same heightis called uniform
Anything Unusual
bull Do any unusual features stick outbull 1048708 Sometimes itrsquos the unusual features that tellbull us something interesting or exciting about thebull databull 1048708 You should always mention any stragglers orbull outliers that stand off away from the body ofbull the distributionbull 1048708 Are there any gaps in the distribution If sobull we might have data from more than onebull group
Outliers
The following histogram has outliersmdashthere arethree cities in the leftmost bar
Outliers
bull Are extreme values that do not appear to belong to the rest of the data They may be unusual values that deserve further investigation or they may be just mistakes therersquos no obvious way to tell Do not delete them Outliers can affect many statistical analyses so you should always be alert to them
Outliers
bull Away from the main portion of data
Where is the Center of the Distribution
bull 1048708 If you had to pick a single number to describe allbull the data what would you pickbull 1048708 Itrsquos easy to find the center when a histogram isbull unimodal and symmetricmdashitrsquos right in the middlebull 1048708 On the other hand itrsquos not so easy to find thebull center of a skewed histogram or a histogram withbull more than one modebull 1048708 For now we will ldquoeyeballrdquo the center of thebull distribution In the next chapter we will find thebull center numerically
How Spread Out is the Distribution
bull 1048708 Variation matters and Statistics is about
bull variation
bull 1048708 Are the values of the distribution tightly clustered
bull around the center or more spread out
bull 1048708 In the next two chapters we will talk about
bull spreadhellip
Comparing Distributions
bull 1048708 Often we would like to compare two or morebull distributions instead of looking at one distributionbull by itselfbull 1048708 When looking at two or more distributions it isbull very important that the histograms have been putbull on the same scale Otherwise we cannot reallybull compare the two distributionsbull 1048708 When we compare distributions we talk about thebull shape center and spread of each distribution
Example
Compare thefollowingdistributions ofages for femaleand male heartattack patients
Compare thefollowingdistributions ofages for femaleand male heartattack patients
HOMEWORK
Web Pages Used
bull httpwwwfaoorgwairdocsilrix5469ex5469e38gif
bull httpwwwsciencebuddiesorgscience-fair-projectsdescriptive_statistics_filesBimodalDistjpg
bull httpimagesabsoluteastronomycomimagesencyclopediaimagesbbibimodalpng
bull httpuploadwikimediaorgwikipediacommonsbbcBimodal_geologicalPNG
Web Pages Used
bull httpmathworldwolframcomimageseps-gifOutlierHistogram_1000gif
Timeplots Order Please
bull 1048708 For some data sets we are interested in how the
bull data behave over time In these cases we
bull construct timeplots of the data
Re-expressing Skewed Data toImprove Symmetry
Re-expressing Skewed Data toImprove Symmetry (cont)
One way to make a skeweddistribution more symmetric isto re-express or transform thedata by applying a simplefunction(eg logarithmic function)1048708 Note the change in skewnessfrom the raw data (Figure411) to the transformed data(Figure 412)
What Can Go Wrong
bull 1048708 Donrsquot make a histogram of a categorical variablemdash
bull bar charts or pie charts should be used for
bull categorical data
bull 1048708 Donrsquot look for shape
bull center and spread
bull of a bar chart
What Can Go Wrong (cont)
bull 1048708 Donrsquot use bars in every displaymdashsave them for
bull histograms and bar charts
bull 1048708 Below is a badly drawn timeplot and the proper
bull histogram for the number of eagles sighted in a
bull collection of weeks
What Can Go Wrong (cont)
What Can Go Wrong (cont)
Choose a bin width appropriate to the data1048708 Changing the bin width changes theappearance of the histogram
What Can Go Wrong (cont)
1048708 Avoid inconsistent scaleseither within the display orwhen comparing twodisplays1048708 Label clearly so a readerknows what the plotdisplays1048708 Good intentions badplot
What have we learned
bull 1048708 Wersquove learned how to make a picture for quantitative databull to help us see the story the data have to Tellbull 1048708 We can display the distribution of quantitative data with abull histogram stem-and-leaf display or dotplotbull 1048708 Tell about a distribution by talking about shape centerbull spread and any unusual featuresbull 1048708 We can compare two quantitative distributions by lookingbull at side-by-side displays (plotted on the same scale)bull 1048708 Trends in a quantitative variable can be displayed in abull timeplot
Types of Displays
bull Histogram
bull Stem and Leaf Displays
bull Dotplots
Histogram
bull A histogram uses adjacent bars to show the distribution of values in a quantitative variable
bull Looks very similar to a bar graph but there are differences
bull The horizontal axis is continuous not just labeled
An example
bull The histogram shown below gives the number of children visited a particular zoo bull
Histogram
bull A histogram is more convenient than a dot-plot or a stem and leaf plot because you dont have to represent each data point However you dont get to see the value of each data point So a table of data and summary statistics would help people interpret the data
Be Careful
bull A histogram gives the number of data points that fall into equal intervals Care must be taken in choosing the intervals because it can affect the shape of the graph and misrepresent the true data
1st graph
bull The first graph is uses intervals of size 10 yielding the intervals 40-50 50-60 etc In this case Yemen had a life expectancy of 50 and was placed in the 50-60 column Usually borderline values are placed in the higher column
2nd Graph
bull In the second graph the intervals are 40-45 45-50 50-55 etc This affects the shape of the graph
Stem and Leaf Displays
bull Shows quantitative data values in a way that sketches the distribution of the data
bullThe stem-and-leaf plot below shows the number of students enrolledbull in a dance class in the past 12 yearsbull The number of students are 81 84 85 86 93 94 97 100 102 103 110 and 111
Dotplot
bull Graphs a dot for each case against a single axis
bull Graph the following number 5 5555551010101010 etc
Dotplot with two sets of data
Example
Shape
bull To describe the shape of a distribution look for
bull Symmetry versus skewness
bull Single versus multiple modes
Symmetrical
bull A distribution is symmetric if the two halves on either side of the center look approximately like the mirror images of each other
Symmetrical
bull Symmetrical Histogram
Dotplot
bull Dots are mirrored images
Stem and leaf
bull Example
Skewed
bull A distribution is skewed if it is not symmetric and one tail stretched out further than the other
bull Skewed left- when the longer tail stretches to the left
bull Skewed right-when the longer tail stretched to the right
Examples
bull Skewed right
Skewed left
bull Left
All three
bull Examples
Funny example
bull httpwwwherkimershideawayorgapstatisticsymmsum99ymm111htm
New seating chart
bull httpwwwrandomorgintegers
Stem-and-Leaf Revisited
1048708 Compare the histogram and stem-and-leafdisplay for the pulse rates of 24 women at ahealth clinic Which graphical display do youprefer
Think Before You Draw Again
bull 1048708 Remember the ldquoMake a picturerdquo rulebull 1048708 Now that we have options for data displays
youbull need to Think carefully about which type ofbull display to makebull 1048708 Before making a stem-and-leaf display abull histogram or a dotplot check thebull 1048708 Quantitative Data Condition The data arebull values of a quantitative variable whose unitsbull are known
Constructing a Stem-and-Leaf Display
bull 1048708 First cut each data value into leading digits
bull (ldquostemsrdquo) and trailing digits (ldquoleavesrdquo)bull 1048708 Use the stems to label the binsbull 1048708 Use only one digit for each leafmdasheither
round orbull truncate the data values to one decimal
placebull after the stem
Center
bull A value that attempts the impossible by summarizing the entire distribution with a single number a ldquotypicalrdquo value
bull Measures include the mean and median
Spread
bull A numerical summary of how tightly the values are clustered around the center
bull Measures of spread include the IQR and standard deviation
Mode
bull a hump or local high pint in the shape of the distribution of a variable is called the mode The apparent location of modes can change as the scale of a histogram is changed
Unimodal
bull Having one mode
Bimodal
bull Distribution with two modes
Example
Uniform
1048708 A histogram that doesnrsquot appear to have any mode andin which all the bars are approximately the same heightis called uniform
Anything Unusual
bull Do any unusual features stick outbull 1048708 Sometimes itrsquos the unusual features that tellbull us something interesting or exciting about thebull databull 1048708 You should always mention any stragglers orbull outliers that stand off away from the body ofbull the distributionbull 1048708 Are there any gaps in the distribution If sobull we might have data from more than onebull group
Outliers
The following histogram has outliersmdashthere arethree cities in the leftmost bar
Outliers
bull Are extreme values that do not appear to belong to the rest of the data They may be unusual values that deserve further investigation or they may be just mistakes therersquos no obvious way to tell Do not delete them Outliers can affect many statistical analyses so you should always be alert to them
Outliers
bull Away from the main portion of data
Where is the Center of the Distribution
bull 1048708 If you had to pick a single number to describe allbull the data what would you pickbull 1048708 Itrsquos easy to find the center when a histogram isbull unimodal and symmetricmdashitrsquos right in the middlebull 1048708 On the other hand itrsquos not so easy to find thebull center of a skewed histogram or a histogram withbull more than one modebull 1048708 For now we will ldquoeyeballrdquo the center of thebull distribution In the next chapter we will find thebull center numerically
How Spread Out is the Distribution
bull 1048708 Variation matters and Statistics is about
bull variation
bull 1048708 Are the values of the distribution tightly clustered
bull around the center or more spread out
bull 1048708 In the next two chapters we will talk about
bull spreadhellip
Comparing Distributions
bull 1048708 Often we would like to compare two or morebull distributions instead of looking at one distributionbull by itselfbull 1048708 When looking at two or more distributions it isbull very important that the histograms have been putbull on the same scale Otherwise we cannot reallybull compare the two distributionsbull 1048708 When we compare distributions we talk about thebull shape center and spread of each distribution
Example
Compare thefollowingdistributions ofages for femaleand male heartattack patients
Compare thefollowingdistributions ofages for femaleand male heartattack patients
HOMEWORK
Web Pages Used
bull httpwwwfaoorgwairdocsilrix5469ex5469e38gif
bull httpwwwsciencebuddiesorgscience-fair-projectsdescriptive_statistics_filesBimodalDistjpg
bull httpimagesabsoluteastronomycomimagesencyclopediaimagesbbibimodalpng
bull httpuploadwikimediaorgwikipediacommonsbbcBimodal_geologicalPNG
Web Pages Used
bull httpmathworldwolframcomimageseps-gifOutlierHistogram_1000gif
Timeplots Order Please
bull 1048708 For some data sets we are interested in how the
bull data behave over time In these cases we
bull construct timeplots of the data
Re-expressing Skewed Data toImprove Symmetry
Re-expressing Skewed Data toImprove Symmetry (cont)
One way to make a skeweddistribution more symmetric isto re-express or transform thedata by applying a simplefunction(eg logarithmic function)1048708 Note the change in skewnessfrom the raw data (Figure411) to the transformed data(Figure 412)
What Can Go Wrong
bull 1048708 Donrsquot make a histogram of a categorical variablemdash
bull bar charts or pie charts should be used for
bull categorical data
bull 1048708 Donrsquot look for shape
bull center and spread
bull of a bar chart
What Can Go Wrong (cont)
bull 1048708 Donrsquot use bars in every displaymdashsave them for
bull histograms and bar charts
bull 1048708 Below is a badly drawn timeplot and the proper
bull histogram for the number of eagles sighted in a
bull collection of weeks
What Can Go Wrong (cont)
What Can Go Wrong (cont)
Choose a bin width appropriate to the data1048708 Changing the bin width changes theappearance of the histogram
What Can Go Wrong (cont)
1048708 Avoid inconsistent scaleseither within the display orwhen comparing twodisplays1048708 Label clearly so a readerknows what the plotdisplays1048708 Good intentions badplot
What have we learned
bull 1048708 Wersquove learned how to make a picture for quantitative databull to help us see the story the data have to Tellbull 1048708 We can display the distribution of quantitative data with abull histogram stem-and-leaf display or dotplotbull 1048708 Tell about a distribution by talking about shape centerbull spread and any unusual featuresbull 1048708 We can compare two quantitative distributions by lookingbull at side-by-side displays (plotted on the same scale)bull 1048708 Trends in a quantitative variable can be displayed in abull timeplot
Histogram
bull A histogram uses adjacent bars to show the distribution of values in a quantitative variable
bull Looks very similar to a bar graph but there are differences
bull The horizontal axis is continuous not just labeled
An example
bull The histogram shown below gives the number of children visited a particular zoo bull
Histogram
bull A histogram is more convenient than a dot-plot or a stem and leaf plot because you dont have to represent each data point However you dont get to see the value of each data point So a table of data and summary statistics would help people interpret the data
Be Careful
bull A histogram gives the number of data points that fall into equal intervals Care must be taken in choosing the intervals because it can affect the shape of the graph and misrepresent the true data
1st graph
bull The first graph is uses intervals of size 10 yielding the intervals 40-50 50-60 etc In this case Yemen had a life expectancy of 50 and was placed in the 50-60 column Usually borderline values are placed in the higher column
2nd Graph
bull In the second graph the intervals are 40-45 45-50 50-55 etc This affects the shape of the graph
Stem and Leaf Displays
bull Shows quantitative data values in a way that sketches the distribution of the data
bullThe stem-and-leaf plot below shows the number of students enrolledbull in a dance class in the past 12 yearsbull The number of students are 81 84 85 86 93 94 97 100 102 103 110 and 111
Dotplot
bull Graphs a dot for each case against a single axis
bull Graph the following number 5 5555551010101010 etc
Dotplot with two sets of data
Example
Shape
bull To describe the shape of a distribution look for
bull Symmetry versus skewness
bull Single versus multiple modes
Symmetrical
bull A distribution is symmetric if the two halves on either side of the center look approximately like the mirror images of each other
Symmetrical
bull Symmetrical Histogram
Dotplot
bull Dots are mirrored images
Stem and leaf
bull Example
Skewed
bull A distribution is skewed if it is not symmetric and one tail stretched out further than the other
bull Skewed left- when the longer tail stretches to the left
bull Skewed right-when the longer tail stretched to the right
Examples
bull Skewed right
Skewed left
bull Left
All three
bull Examples
Funny example
bull httpwwwherkimershideawayorgapstatisticsymmsum99ymm111htm
New seating chart
bull httpwwwrandomorgintegers
Stem-and-Leaf Revisited
1048708 Compare the histogram and stem-and-leafdisplay for the pulse rates of 24 women at ahealth clinic Which graphical display do youprefer
Think Before You Draw Again
bull 1048708 Remember the ldquoMake a picturerdquo rulebull 1048708 Now that we have options for data displays
youbull need to Think carefully about which type ofbull display to makebull 1048708 Before making a stem-and-leaf display abull histogram or a dotplot check thebull 1048708 Quantitative Data Condition The data arebull values of a quantitative variable whose unitsbull are known
Constructing a Stem-and-Leaf Display
bull 1048708 First cut each data value into leading digits
bull (ldquostemsrdquo) and trailing digits (ldquoleavesrdquo)bull 1048708 Use the stems to label the binsbull 1048708 Use only one digit for each leafmdasheither
round orbull truncate the data values to one decimal
placebull after the stem
Center
bull A value that attempts the impossible by summarizing the entire distribution with a single number a ldquotypicalrdquo value
bull Measures include the mean and median
Spread
bull A numerical summary of how tightly the values are clustered around the center
bull Measures of spread include the IQR and standard deviation
Mode
bull a hump or local high pint in the shape of the distribution of a variable is called the mode The apparent location of modes can change as the scale of a histogram is changed
Unimodal
bull Having one mode
Bimodal
bull Distribution with two modes
Example
Uniform
1048708 A histogram that doesnrsquot appear to have any mode andin which all the bars are approximately the same heightis called uniform
Anything Unusual
bull Do any unusual features stick outbull 1048708 Sometimes itrsquos the unusual features that tellbull us something interesting or exciting about thebull databull 1048708 You should always mention any stragglers orbull outliers that stand off away from the body ofbull the distributionbull 1048708 Are there any gaps in the distribution If sobull we might have data from more than onebull group
Outliers
The following histogram has outliersmdashthere arethree cities in the leftmost bar
Outliers
bull Are extreme values that do not appear to belong to the rest of the data They may be unusual values that deserve further investigation or they may be just mistakes therersquos no obvious way to tell Do not delete them Outliers can affect many statistical analyses so you should always be alert to them
Outliers
bull Away from the main portion of data
Where is the Center of the Distribution
bull 1048708 If you had to pick a single number to describe allbull the data what would you pickbull 1048708 Itrsquos easy to find the center when a histogram isbull unimodal and symmetricmdashitrsquos right in the middlebull 1048708 On the other hand itrsquos not so easy to find thebull center of a skewed histogram or a histogram withbull more than one modebull 1048708 For now we will ldquoeyeballrdquo the center of thebull distribution In the next chapter we will find thebull center numerically
How Spread Out is the Distribution
bull 1048708 Variation matters and Statistics is about
bull variation
bull 1048708 Are the values of the distribution tightly clustered
bull around the center or more spread out
bull 1048708 In the next two chapters we will talk about
bull spreadhellip
Comparing Distributions
bull 1048708 Often we would like to compare two or morebull distributions instead of looking at one distributionbull by itselfbull 1048708 When looking at two or more distributions it isbull very important that the histograms have been putbull on the same scale Otherwise we cannot reallybull compare the two distributionsbull 1048708 When we compare distributions we talk about thebull shape center and spread of each distribution
Example
Compare thefollowingdistributions ofages for femaleand male heartattack patients
Compare thefollowingdistributions ofages for femaleand male heartattack patients
HOMEWORK
Web Pages Used
bull httpwwwfaoorgwairdocsilrix5469ex5469e38gif
bull httpwwwsciencebuddiesorgscience-fair-projectsdescriptive_statistics_filesBimodalDistjpg
bull httpimagesabsoluteastronomycomimagesencyclopediaimagesbbibimodalpng
bull httpuploadwikimediaorgwikipediacommonsbbcBimodal_geologicalPNG
Web Pages Used
bull httpmathworldwolframcomimageseps-gifOutlierHistogram_1000gif
Timeplots Order Please
bull 1048708 For some data sets we are interested in how the
bull data behave over time In these cases we
bull construct timeplots of the data
Re-expressing Skewed Data toImprove Symmetry
Re-expressing Skewed Data toImprove Symmetry (cont)
One way to make a skeweddistribution more symmetric isto re-express or transform thedata by applying a simplefunction(eg logarithmic function)1048708 Note the change in skewnessfrom the raw data (Figure411) to the transformed data(Figure 412)
What Can Go Wrong
bull 1048708 Donrsquot make a histogram of a categorical variablemdash
bull bar charts or pie charts should be used for
bull categorical data
bull 1048708 Donrsquot look for shape
bull center and spread
bull of a bar chart
What Can Go Wrong (cont)
bull 1048708 Donrsquot use bars in every displaymdashsave them for
bull histograms and bar charts
bull 1048708 Below is a badly drawn timeplot and the proper
bull histogram for the number of eagles sighted in a
bull collection of weeks
What Can Go Wrong (cont)
What Can Go Wrong (cont)
Choose a bin width appropriate to the data1048708 Changing the bin width changes theappearance of the histogram
What Can Go Wrong (cont)
1048708 Avoid inconsistent scaleseither within the display orwhen comparing twodisplays1048708 Label clearly so a readerknows what the plotdisplays1048708 Good intentions badplot
What have we learned
bull 1048708 Wersquove learned how to make a picture for quantitative databull to help us see the story the data have to Tellbull 1048708 We can display the distribution of quantitative data with abull histogram stem-and-leaf display or dotplotbull 1048708 Tell about a distribution by talking about shape centerbull spread and any unusual featuresbull 1048708 We can compare two quantitative distributions by lookingbull at side-by-side displays (plotted on the same scale)bull 1048708 Trends in a quantitative variable can be displayed in abull timeplot
An example
bull The histogram shown below gives the number of children visited a particular zoo bull
Histogram
bull A histogram is more convenient than a dot-plot or a stem and leaf plot because you dont have to represent each data point However you dont get to see the value of each data point So a table of data and summary statistics would help people interpret the data
Be Careful
bull A histogram gives the number of data points that fall into equal intervals Care must be taken in choosing the intervals because it can affect the shape of the graph and misrepresent the true data
1st graph
bull The first graph is uses intervals of size 10 yielding the intervals 40-50 50-60 etc In this case Yemen had a life expectancy of 50 and was placed in the 50-60 column Usually borderline values are placed in the higher column
2nd Graph
bull In the second graph the intervals are 40-45 45-50 50-55 etc This affects the shape of the graph
Stem and Leaf Displays
bull Shows quantitative data values in a way that sketches the distribution of the data
bullThe stem-and-leaf plot below shows the number of students enrolledbull in a dance class in the past 12 yearsbull The number of students are 81 84 85 86 93 94 97 100 102 103 110 and 111
Dotplot
bull Graphs a dot for each case against a single axis
bull Graph the following number 5 5555551010101010 etc
Dotplot with two sets of data
Example
Shape
bull To describe the shape of a distribution look for
bull Symmetry versus skewness
bull Single versus multiple modes
Symmetrical
bull A distribution is symmetric if the two halves on either side of the center look approximately like the mirror images of each other
Symmetrical
bull Symmetrical Histogram
Dotplot
bull Dots are mirrored images
Stem and leaf
bull Example
Skewed
bull A distribution is skewed if it is not symmetric and one tail stretched out further than the other
bull Skewed left- when the longer tail stretches to the left
bull Skewed right-when the longer tail stretched to the right
Examples
bull Skewed right
Skewed left
bull Left
All three
bull Examples
Funny example
bull httpwwwherkimershideawayorgapstatisticsymmsum99ymm111htm
New seating chart
bull httpwwwrandomorgintegers
Stem-and-Leaf Revisited
1048708 Compare the histogram and stem-and-leafdisplay for the pulse rates of 24 women at ahealth clinic Which graphical display do youprefer
Think Before You Draw Again
bull 1048708 Remember the ldquoMake a picturerdquo rulebull 1048708 Now that we have options for data displays
youbull need to Think carefully about which type ofbull display to makebull 1048708 Before making a stem-and-leaf display abull histogram or a dotplot check thebull 1048708 Quantitative Data Condition The data arebull values of a quantitative variable whose unitsbull are known
Constructing a Stem-and-Leaf Display
bull 1048708 First cut each data value into leading digits
bull (ldquostemsrdquo) and trailing digits (ldquoleavesrdquo)bull 1048708 Use the stems to label the binsbull 1048708 Use only one digit for each leafmdasheither
round orbull truncate the data values to one decimal
placebull after the stem
Center
bull A value that attempts the impossible by summarizing the entire distribution with a single number a ldquotypicalrdquo value
bull Measures include the mean and median
Spread
bull A numerical summary of how tightly the values are clustered around the center
bull Measures of spread include the IQR and standard deviation
Mode
bull a hump or local high pint in the shape of the distribution of a variable is called the mode The apparent location of modes can change as the scale of a histogram is changed
Unimodal
bull Having one mode
Bimodal
bull Distribution with two modes
Example
Uniform
1048708 A histogram that doesnrsquot appear to have any mode andin which all the bars are approximately the same heightis called uniform
Anything Unusual
bull Do any unusual features stick outbull 1048708 Sometimes itrsquos the unusual features that tellbull us something interesting or exciting about thebull databull 1048708 You should always mention any stragglers orbull outliers that stand off away from the body ofbull the distributionbull 1048708 Are there any gaps in the distribution If sobull we might have data from more than onebull group
Outliers
The following histogram has outliersmdashthere arethree cities in the leftmost bar
Outliers
bull Are extreme values that do not appear to belong to the rest of the data They may be unusual values that deserve further investigation or they may be just mistakes therersquos no obvious way to tell Do not delete them Outliers can affect many statistical analyses so you should always be alert to them
Outliers
bull Away from the main portion of data
Where is the Center of the Distribution
bull 1048708 If you had to pick a single number to describe allbull the data what would you pickbull 1048708 Itrsquos easy to find the center when a histogram isbull unimodal and symmetricmdashitrsquos right in the middlebull 1048708 On the other hand itrsquos not so easy to find thebull center of a skewed histogram or a histogram withbull more than one modebull 1048708 For now we will ldquoeyeballrdquo the center of thebull distribution In the next chapter we will find thebull center numerically
How Spread Out is the Distribution
bull 1048708 Variation matters and Statistics is about
bull variation
bull 1048708 Are the values of the distribution tightly clustered
bull around the center or more spread out
bull 1048708 In the next two chapters we will talk about
bull spreadhellip
Comparing Distributions
bull 1048708 Often we would like to compare two or morebull distributions instead of looking at one distributionbull by itselfbull 1048708 When looking at two or more distributions it isbull very important that the histograms have been putbull on the same scale Otherwise we cannot reallybull compare the two distributionsbull 1048708 When we compare distributions we talk about thebull shape center and spread of each distribution
Example
Compare thefollowingdistributions ofages for femaleand male heartattack patients
Compare thefollowingdistributions ofages for femaleand male heartattack patients
HOMEWORK
Web Pages Used
bull httpwwwfaoorgwairdocsilrix5469ex5469e38gif
bull httpwwwsciencebuddiesorgscience-fair-projectsdescriptive_statistics_filesBimodalDistjpg
bull httpimagesabsoluteastronomycomimagesencyclopediaimagesbbibimodalpng
bull httpuploadwikimediaorgwikipediacommonsbbcBimodal_geologicalPNG
Web Pages Used
bull httpmathworldwolframcomimageseps-gifOutlierHistogram_1000gif
Timeplots Order Please
bull 1048708 For some data sets we are interested in how the
bull data behave over time In these cases we
bull construct timeplots of the data
Re-expressing Skewed Data toImprove Symmetry
Re-expressing Skewed Data toImprove Symmetry (cont)
One way to make a skeweddistribution more symmetric isto re-express or transform thedata by applying a simplefunction(eg logarithmic function)1048708 Note the change in skewnessfrom the raw data (Figure411) to the transformed data(Figure 412)
What Can Go Wrong
bull 1048708 Donrsquot make a histogram of a categorical variablemdash
bull bar charts or pie charts should be used for
bull categorical data
bull 1048708 Donrsquot look for shape
bull center and spread
bull of a bar chart
What Can Go Wrong (cont)
bull 1048708 Donrsquot use bars in every displaymdashsave them for
bull histograms and bar charts
bull 1048708 Below is a badly drawn timeplot and the proper
bull histogram for the number of eagles sighted in a
bull collection of weeks
What Can Go Wrong (cont)
What Can Go Wrong (cont)
Choose a bin width appropriate to the data1048708 Changing the bin width changes theappearance of the histogram
What Can Go Wrong (cont)
1048708 Avoid inconsistent scaleseither within the display orwhen comparing twodisplays1048708 Label clearly so a readerknows what the plotdisplays1048708 Good intentions badplot
What have we learned
bull 1048708 Wersquove learned how to make a picture for quantitative databull to help us see the story the data have to Tellbull 1048708 We can display the distribution of quantitative data with abull histogram stem-and-leaf display or dotplotbull 1048708 Tell about a distribution by talking about shape centerbull spread and any unusual featuresbull 1048708 We can compare two quantitative distributions by lookingbull at side-by-side displays (plotted on the same scale)bull 1048708 Trends in a quantitative variable can be displayed in abull timeplot
Histogram
bull A histogram is more convenient than a dot-plot or a stem and leaf plot because you dont have to represent each data point However you dont get to see the value of each data point So a table of data and summary statistics would help people interpret the data
Be Careful
bull A histogram gives the number of data points that fall into equal intervals Care must be taken in choosing the intervals because it can affect the shape of the graph and misrepresent the true data
1st graph
bull The first graph is uses intervals of size 10 yielding the intervals 40-50 50-60 etc In this case Yemen had a life expectancy of 50 and was placed in the 50-60 column Usually borderline values are placed in the higher column
2nd Graph
bull In the second graph the intervals are 40-45 45-50 50-55 etc This affects the shape of the graph
Stem and Leaf Displays
bull Shows quantitative data values in a way that sketches the distribution of the data
bullThe stem-and-leaf plot below shows the number of students enrolledbull in a dance class in the past 12 yearsbull The number of students are 81 84 85 86 93 94 97 100 102 103 110 and 111
Dotplot
bull Graphs a dot for each case against a single axis
bull Graph the following number 5 5555551010101010 etc
Dotplot with two sets of data
Example
Shape
bull To describe the shape of a distribution look for
bull Symmetry versus skewness
bull Single versus multiple modes
Symmetrical
bull A distribution is symmetric if the two halves on either side of the center look approximately like the mirror images of each other
Symmetrical
bull Symmetrical Histogram
Dotplot
bull Dots are mirrored images
Stem and leaf
bull Example
Skewed
bull A distribution is skewed if it is not symmetric and one tail stretched out further than the other
bull Skewed left- when the longer tail stretches to the left
bull Skewed right-when the longer tail stretched to the right
Examples
bull Skewed right
Skewed left
bull Left
All three
bull Examples
Funny example
bull httpwwwherkimershideawayorgapstatisticsymmsum99ymm111htm
New seating chart
bull httpwwwrandomorgintegers
Stem-and-Leaf Revisited
1048708 Compare the histogram and stem-and-leafdisplay for the pulse rates of 24 women at ahealth clinic Which graphical display do youprefer
Think Before You Draw Again
bull 1048708 Remember the ldquoMake a picturerdquo rulebull 1048708 Now that we have options for data displays
youbull need to Think carefully about which type ofbull display to makebull 1048708 Before making a stem-and-leaf display abull histogram or a dotplot check thebull 1048708 Quantitative Data Condition The data arebull values of a quantitative variable whose unitsbull are known
Constructing a Stem-and-Leaf Display
bull 1048708 First cut each data value into leading digits
bull (ldquostemsrdquo) and trailing digits (ldquoleavesrdquo)bull 1048708 Use the stems to label the binsbull 1048708 Use only one digit for each leafmdasheither
round orbull truncate the data values to one decimal
placebull after the stem
Center
bull A value that attempts the impossible by summarizing the entire distribution with a single number a ldquotypicalrdquo value
bull Measures include the mean and median
Spread
bull A numerical summary of how tightly the values are clustered around the center
bull Measures of spread include the IQR and standard deviation
Mode
bull a hump or local high pint in the shape of the distribution of a variable is called the mode The apparent location of modes can change as the scale of a histogram is changed
Unimodal
bull Having one mode
Bimodal
bull Distribution with two modes
Example
Uniform
1048708 A histogram that doesnrsquot appear to have any mode andin which all the bars are approximately the same heightis called uniform
Anything Unusual
bull Do any unusual features stick outbull 1048708 Sometimes itrsquos the unusual features that tellbull us something interesting or exciting about thebull databull 1048708 You should always mention any stragglers orbull outliers that stand off away from the body ofbull the distributionbull 1048708 Are there any gaps in the distribution If sobull we might have data from more than onebull group
Outliers
The following histogram has outliersmdashthere arethree cities in the leftmost bar
Outliers
bull Are extreme values that do not appear to belong to the rest of the data They may be unusual values that deserve further investigation or they may be just mistakes therersquos no obvious way to tell Do not delete them Outliers can affect many statistical analyses so you should always be alert to them
Outliers
bull Away from the main portion of data
Where is the Center of the Distribution
bull 1048708 If you had to pick a single number to describe allbull the data what would you pickbull 1048708 Itrsquos easy to find the center when a histogram isbull unimodal and symmetricmdashitrsquos right in the middlebull 1048708 On the other hand itrsquos not so easy to find thebull center of a skewed histogram or a histogram withbull more than one modebull 1048708 For now we will ldquoeyeballrdquo the center of thebull distribution In the next chapter we will find thebull center numerically
How Spread Out is the Distribution
bull 1048708 Variation matters and Statistics is about
bull variation
bull 1048708 Are the values of the distribution tightly clustered
bull around the center or more spread out
bull 1048708 In the next two chapters we will talk about
bull spreadhellip
Comparing Distributions
bull 1048708 Often we would like to compare two or morebull distributions instead of looking at one distributionbull by itselfbull 1048708 When looking at two or more distributions it isbull very important that the histograms have been putbull on the same scale Otherwise we cannot reallybull compare the two distributionsbull 1048708 When we compare distributions we talk about thebull shape center and spread of each distribution
Example
Compare thefollowingdistributions ofages for femaleand male heartattack patients
Compare thefollowingdistributions ofages for femaleand male heartattack patients
HOMEWORK
Web Pages Used
bull httpwwwfaoorgwairdocsilrix5469ex5469e38gif
bull httpwwwsciencebuddiesorgscience-fair-projectsdescriptive_statistics_filesBimodalDistjpg
bull httpimagesabsoluteastronomycomimagesencyclopediaimagesbbibimodalpng
bull httpuploadwikimediaorgwikipediacommonsbbcBimodal_geologicalPNG
Web Pages Used
bull httpmathworldwolframcomimageseps-gifOutlierHistogram_1000gif
Timeplots Order Please
bull 1048708 For some data sets we are interested in how the
bull data behave over time In these cases we
bull construct timeplots of the data
Re-expressing Skewed Data toImprove Symmetry
Re-expressing Skewed Data toImprove Symmetry (cont)
One way to make a skeweddistribution more symmetric isto re-express or transform thedata by applying a simplefunction(eg logarithmic function)1048708 Note the change in skewnessfrom the raw data (Figure411) to the transformed data(Figure 412)
What Can Go Wrong
bull 1048708 Donrsquot make a histogram of a categorical variablemdash
bull bar charts or pie charts should be used for
bull categorical data
bull 1048708 Donrsquot look for shape
bull center and spread
bull of a bar chart
What Can Go Wrong (cont)
bull 1048708 Donrsquot use bars in every displaymdashsave them for
bull histograms and bar charts
bull 1048708 Below is a badly drawn timeplot and the proper
bull histogram for the number of eagles sighted in a
bull collection of weeks
What Can Go Wrong (cont)
What Can Go Wrong (cont)
Choose a bin width appropriate to the data1048708 Changing the bin width changes theappearance of the histogram
What Can Go Wrong (cont)
1048708 Avoid inconsistent scaleseither within the display orwhen comparing twodisplays1048708 Label clearly so a readerknows what the plotdisplays1048708 Good intentions badplot
What have we learned
bull 1048708 Wersquove learned how to make a picture for quantitative databull to help us see the story the data have to Tellbull 1048708 We can display the distribution of quantitative data with abull histogram stem-and-leaf display or dotplotbull 1048708 Tell about a distribution by talking about shape centerbull spread and any unusual featuresbull 1048708 We can compare two quantitative distributions by lookingbull at side-by-side displays (plotted on the same scale)bull 1048708 Trends in a quantitative variable can be displayed in abull timeplot
Be Careful
bull A histogram gives the number of data points that fall into equal intervals Care must be taken in choosing the intervals because it can affect the shape of the graph and misrepresent the true data
1st graph
bull The first graph is uses intervals of size 10 yielding the intervals 40-50 50-60 etc In this case Yemen had a life expectancy of 50 and was placed in the 50-60 column Usually borderline values are placed in the higher column
2nd Graph
bull In the second graph the intervals are 40-45 45-50 50-55 etc This affects the shape of the graph
Stem and Leaf Displays
bull Shows quantitative data values in a way that sketches the distribution of the data
bullThe stem-and-leaf plot below shows the number of students enrolledbull in a dance class in the past 12 yearsbull The number of students are 81 84 85 86 93 94 97 100 102 103 110 and 111
Dotplot
bull Graphs a dot for each case against a single axis
bull Graph the following number 5 5555551010101010 etc
Dotplot with two sets of data
Example
Shape
bull To describe the shape of a distribution look for
bull Symmetry versus skewness
bull Single versus multiple modes
Symmetrical
bull A distribution is symmetric if the two halves on either side of the center look approximately like the mirror images of each other
Symmetrical
bull Symmetrical Histogram
Dotplot
bull Dots are mirrored images
Stem and leaf
bull Example
Skewed
bull A distribution is skewed if it is not symmetric and one tail stretched out further than the other
bull Skewed left- when the longer tail stretches to the left
bull Skewed right-when the longer tail stretched to the right
Examples
bull Skewed right
Skewed left
bull Left
All three
bull Examples
Funny example
bull httpwwwherkimershideawayorgapstatisticsymmsum99ymm111htm
New seating chart
bull httpwwwrandomorgintegers
Stem-and-Leaf Revisited
1048708 Compare the histogram and stem-and-leafdisplay for the pulse rates of 24 women at ahealth clinic Which graphical display do youprefer
Think Before You Draw Again
bull 1048708 Remember the ldquoMake a picturerdquo rulebull 1048708 Now that we have options for data displays
youbull need to Think carefully about which type ofbull display to makebull 1048708 Before making a stem-and-leaf display abull histogram or a dotplot check thebull 1048708 Quantitative Data Condition The data arebull values of a quantitative variable whose unitsbull are known
Constructing a Stem-and-Leaf Display
bull 1048708 First cut each data value into leading digits
bull (ldquostemsrdquo) and trailing digits (ldquoleavesrdquo)bull 1048708 Use the stems to label the binsbull 1048708 Use only one digit for each leafmdasheither
round orbull truncate the data values to one decimal
placebull after the stem
Center
bull A value that attempts the impossible by summarizing the entire distribution with a single number a ldquotypicalrdquo value
bull Measures include the mean and median
Spread
bull A numerical summary of how tightly the values are clustered around the center
bull Measures of spread include the IQR and standard deviation
Mode
bull a hump or local high pint in the shape of the distribution of a variable is called the mode The apparent location of modes can change as the scale of a histogram is changed
Unimodal
bull Having one mode
Bimodal
bull Distribution with two modes
Example
Uniform
1048708 A histogram that doesnrsquot appear to have any mode andin which all the bars are approximately the same heightis called uniform
Anything Unusual
bull Do any unusual features stick outbull 1048708 Sometimes itrsquos the unusual features that tellbull us something interesting or exciting about thebull databull 1048708 You should always mention any stragglers orbull outliers that stand off away from the body ofbull the distributionbull 1048708 Are there any gaps in the distribution If sobull we might have data from more than onebull group
Outliers
The following histogram has outliersmdashthere arethree cities in the leftmost bar
Outliers
bull Are extreme values that do not appear to belong to the rest of the data They may be unusual values that deserve further investigation or they may be just mistakes therersquos no obvious way to tell Do not delete them Outliers can affect many statistical analyses so you should always be alert to them
Outliers
bull Away from the main portion of data
Where is the Center of the Distribution
bull 1048708 If you had to pick a single number to describe allbull the data what would you pickbull 1048708 Itrsquos easy to find the center when a histogram isbull unimodal and symmetricmdashitrsquos right in the middlebull 1048708 On the other hand itrsquos not so easy to find thebull center of a skewed histogram or a histogram withbull more than one modebull 1048708 For now we will ldquoeyeballrdquo the center of thebull distribution In the next chapter we will find thebull center numerically
How Spread Out is the Distribution
bull 1048708 Variation matters and Statistics is about
bull variation
bull 1048708 Are the values of the distribution tightly clustered
bull around the center or more spread out
bull 1048708 In the next two chapters we will talk about
bull spreadhellip
Comparing Distributions
bull 1048708 Often we would like to compare two or morebull distributions instead of looking at one distributionbull by itselfbull 1048708 When looking at two or more distributions it isbull very important that the histograms have been putbull on the same scale Otherwise we cannot reallybull compare the two distributionsbull 1048708 When we compare distributions we talk about thebull shape center and spread of each distribution
Example
Compare thefollowingdistributions ofages for femaleand male heartattack patients
Compare thefollowingdistributions ofages for femaleand male heartattack patients
HOMEWORK
Web Pages Used
bull httpwwwfaoorgwairdocsilrix5469ex5469e38gif
bull httpwwwsciencebuddiesorgscience-fair-projectsdescriptive_statistics_filesBimodalDistjpg
bull httpimagesabsoluteastronomycomimagesencyclopediaimagesbbibimodalpng
bull httpuploadwikimediaorgwikipediacommonsbbcBimodal_geologicalPNG
Web Pages Used
bull httpmathworldwolframcomimageseps-gifOutlierHistogram_1000gif
Timeplots Order Please
bull 1048708 For some data sets we are interested in how the
bull data behave over time In these cases we
bull construct timeplots of the data
Re-expressing Skewed Data toImprove Symmetry
Re-expressing Skewed Data toImprove Symmetry (cont)
One way to make a skeweddistribution more symmetric isto re-express or transform thedata by applying a simplefunction(eg logarithmic function)1048708 Note the change in skewnessfrom the raw data (Figure411) to the transformed data(Figure 412)
What Can Go Wrong
bull 1048708 Donrsquot make a histogram of a categorical variablemdash
bull bar charts or pie charts should be used for
bull categorical data
bull 1048708 Donrsquot look for shape
bull center and spread
bull of a bar chart
What Can Go Wrong (cont)
bull 1048708 Donrsquot use bars in every displaymdashsave them for
bull histograms and bar charts
bull 1048708 Below is a badly drawn timeplot and the proper
bull histogram for the number of eagles sighted in a
bull collection of weeks
What Can Go Wrong (cont)
What Can Go Wrong (cont)
Choose a bin width appropriate to the data1048708 Changing the bin width changes theappearance of the histogram
What Can Go Wrong (cont)
1048708 Avoid inconsistent scaleseither within the display orwhen comparing twodisplays1048708 Label clearly so a readerknows what the plotdisplays1048708 Good intentions badplot
What have we learned
bull 1048708 Wersquove learned how to make a picture for quantitative databull to help us see the story the data have to Tellbull 1048708 We can display the distribution of quantitative data with abull histogram stem-and-leaf display or dotplotbull 1048708 Tell about a distribution by talking about shape centerbull spread and any unusual featuresbull 1048708 We can compare two quantitative distributions by lookingbull at side-by-side displays (plotted on the same scale)bull 1048708 Trends in a quantitative variable can be displayed in abull timeplot
1st graph
bull The first graph is uses intervals of size 10 yielding the intervals 40-50 50-60 etc In this case Yemen had a life expectancy of 50 and was placed in the 50-60 column Usually borderline values are placed in the higher column
2nd Graph
bull In the second graph the intervals are 40-45 45-50 50-55 etc This affects the shape of the graph
Stem and Leaf Displays
bull Shows quantitative data values in a way that sketches the distribution of the data
bullThe stem-and-leaf plot below shows the number of students enrolledbull in a dance class in the past 12 yearsbull The number of students are 81 84 85 86 93 94 97 100 102 103 110 and 111
Dotplot
bull Graphs a dot for each case against a single axis
bull Graph the following number 5 5555551010101010 etc
Dotplot with two sets of data
Example
Shape
bull To describe the shape of a distribution look for
bull Symmetry versus skewness
bull Single versus multiple modes
Symmetrical
bull A distribution is symmetric if the two halves on either side of the center look approximately like the mirror images of each other
Symmetrical
bull Symmetrical Histogram
Dotplot
bull Dots are mirrored images
Stem and leaf
bull Example
Skewed
bull A distribution is skewed if it is not symmetric and one tail stretched out further than the other
bull Skewed left- when the longer tail stretches to the left
bull Skewed right-when the longer tail stretched to the right
Examples
bull Skewed right
Skewed left
bull Left
All three
bull Examples
Funny example
bull httpwwwherkimershideawayorgapstatisticsymmsum99ymm111htm
New seating chart
bull httpwwwrandomorgintegers
Stem-and-Leaf Revisited
1048708 Compare the histogram and stem-and-leafdisplay for the pulse rates of 24 women at ahealth clinic Which graphical display do youprefer
Think Before You Draw Again
bull 1048708 Remember the ldquoMake a picturerdquo rulebull 1048708 Now that we have options for data displays
youbull need to Think carefully about which type ofbull display to makebull 1048708 Before making a stem-and-leaf display abull histogram or a dotplot check thebull 1048708 Quantitative Data Condition The data arebull values of a quantitative variable whose unitsbull are known
Constructing a Stem-and-Leaf Display
bull 1048708 First cut each data value into leading digits
bull (ldquostemsrdquo) and trailing digits (ldquoleavesrdquo)bull 1048708 Use the stems to label the binsbull 1048708 Use only one digit for each leafmdasheither
round orbull truncate the data values to one decimal
placebull after the stem
Center
bull A value that attempts the impossible by summarizing the entire distribution with a single number a ldquotypicalrdquo value
bull Measures include the mean and median
Spread
bull A numerical summary of how tightly the values are clustered around the center
bull Measures of spread include the IQR and standard deviation
Mode
bull a hump or local high pint in the shape of the distribution of a variable is called the mode The apparent location of modes can change as the scale of a histogram is changed
Unimodal
bull Having one mode
Bimodal
bull Distribution with two modes
Example
Uniform
1048708 A histogram that doesnrsquot appear to have any mode andin which all the bars are approximately the same heightis called uniform
Anything Unusual
bull Do any unusual features stick outbull 1048708 Sometimes itrsquos the unusual features that tellbull us something interesting or exciting about thebull databull 1048708 You should always mention any stragglers orbull outliers that stand off away from the body ofbull the distributionbull 1048708 Are there any gaps in the distribution If sobull we might have data from more than onebull group
Outliers
The following histogram has outliersmdashthere arethree cities in the leftmost bar
Outliers
bull Are extreme values that do not appear to belong to the rest of the data They may be unusual values that deserve further investigation or they may be just mistakes therersquos no obvious way to tell Do not delete them Outliers can affect many statistical analyses so you should always be alert to them
Outliers
bull Away from the main portion of data
Where is the Center of the Distribution
bull 1048708 If you had to pick a single number to describe allbull the data what would you pickbull 1048708 Itrsquos easy to find the center when a histogram isbull unimodal and symmetricmdashitrsquos right in the middlebull 1048708 On the other hand itrsquos not so easy to find thebull center of a skewed histogram or a histogram withbull more than one modebull 1048708 For now we will ldquoeyeballrdquo the center of thebull distribution In the next chapter we will find thebull center numerically
How Spread Out is the Distribution
bull 1048708 Variation matters and Statistics is about
bull variation
bull 1048708 Are the values of the distribution tightly clustered
bull around the center or more spread out
bull 1048708 In the next two chapters we will talk about
bull spreadhellip
Comparing Distributions
bull 1048708 Often we would like to compare two or morebull distributions instead of looking at one distributionbull by itselfbull 1048708 When looking at two or more distributions it isbull very important that the histograms have been putbull on the same scale Otherwise we cannot reallybull compare the two distributionsbull 1048708 When we compare distributions we talk about thebull shape center and spread of each distribution
Example
Compare thefollowingdistributions ofages for femaleand male heartattack patients
Compare thefollowingdistributions ofages for femaleand male heartattack patients
HOMEWORK
Web Pages Used
bull httpwwwfaoorgwairdocsilrix5469ex5469e38gif
bull httpwwwsciencebuddiesorgscience-fair-projectsdescriptive_statistics_filesBimodalDistjpg
bull httpimagesabsoluteastronomycomimagesencyclopediaimagesbbibimodalpng
bull httpuploadwikimediaorgwikipediacommonsbbcBimodal_geologicalPNG
Web Pages Used
bull httpmathworldwolframcomimageseps-gifOutlierHistogram_1000gif
Timeplots Order Please
bull 1048708 For some data sets we are interested in how the
bull data behave over time In these cases we
bull construct timeplots of the data
Re-expressing Skewed Data toImprove Symmetry
Re-expressing Skewed Data toImprove Symmetry (cont)
One way to make a skeweddistribution more symmetric isto re-express or transform thedata by applying a simplefunction(eg logarithmic function)1048708 Note the change in skewnessfrom the raw data (Figure411) to the transformed data(Figure 412)
What Can Go Wrong
bull 1048708 Donrsquot make a histogram of a categorical variablemdash
bull bar charts or pie charts should be used for
bull categorical data
bull 1048708 Donrsquot look for shape
bull center and spread
bull of a bar chart
What Can Go Wrong (cont)
bull 1048708 Donrsquot use bars in every displaymdashsave them for
bull histograms and bar charts
bull 1048708 Below is a badly drawn timeplot and the proper
bull histogram for the number of eagles sighted in a
bull collection of weeks
What Can Go Wrong (cont)
What Can Go Wrong (cont)
Choose a bin width appropriate to the data1048708 Changing the bin width changes theappearance of the histogram
What Can Go Wrong (cont)
1048708 Avoid inconsistent scaleseither within the display orwhen comparing twodisplays1048708 Label clearly so a readerknows what the plotdisplays1048708 Good intentions badplot
What have we learned
bull 1048708 Wersquove learned how to make a picture for quantitative databull to help us see the story the data have to Tellbull 1048708 We can display the distribution of quantitative data with abull histogram stem-and-leaf display or dotplotbull 1048708 Tell about a distribution by talking about shape centerbull spread and any unusual featuresbull 1048708 We can compare two quantitative distributions by lookingbull at side-by-side displays (plotted on the same scale)bull 1048708 Trends in a quantitative variable can be displayed in abull timeplot
2nd Graph
bull In the second graph the intervals are 40-45 45-50 50-55 etc This affects the shape of the graph
Stem and Leaf Displays
bull Shows quantitative data values in a way that sketches the distribution of the data
bullThe stem-and-leaf plot below shows the number of students enrolledbull in a dance class in the past 12 yearsbull The number of students are 81 84 85 86 93 94 97 100 102 103 110 and 111
Dotplot
bull Graphs a dot for each case against a single axis
bull Graph the following number 5 5555551010101010 etc
Dotplot with two sets of data
Example
Shape
bull To describe the shape of a distribution look for
bull Symmetry versus skewness
bull Single versus multiple modes
Symmetrical
bull A distribution is symmetric if the two halves on either side of the center look approximately like the mirror images of each other
Symmetrical
bull Symmetrical Histogram
Dotplot
bull Dots are mirrored images
Stem and leaf
bull Example
Skewed
bull A distribution is skewed if it is not symmetric and one tail stretched out further than the other
bull Skewed left- when the longer tail stretches to the left
bull Skewed right-when the longer tail stretched to the right
Examples
bull Skewed right
Skewed left
bull Left
All three
bull Examples
Funny example
bull httpwwwherkimershideawayorgapstatisticsymmsum99ymm111htm
New seating chart
bull httpwwwrandomorgintegers
Stem-and-Leaf Revisited
1048708 Compare the histogram and stem-and-leafdisplay for the pulse rates of 24 women at ahealth clinic Which graphical display do youprefer
Think Before You Draw Again
bull 1048708 Remember the ldquoMake a picturerdquo rulebull 1048708 Now that we have options for data displays
youbull need to Think carefully about which type ofbull display to makebull 1048708 Before making a stem-and-leaf display abull histogram or a dotplot check thebull 1048708 Quantitative Data Condition The data arebull values of a quantitative variable whose unitsbull are known
Constructing a Stem-and-Leaf Display
bull 1048708 First cut each data value into leading digits
bull (ldquostemsrdquo) and trailing digits (ldquoleavesrdquo)bull 1048708 Use the stems to label the binsbull 1048708 Use only one digit for each leafmdasheither
round orbull truncate the data values to one decimal
placebull after the stem
Center
bull A value that attempts the impossible by summarizing the entire distribution with a single number a ldquotypicalrdquo value
bull Measures include the mean and median
Spread
bull A numerical summary of how tightly the values are clustered around the center
bull Measures of spread include the IQR and standard deviation
Mode
bull a hump or local high pint in the shape of the distribution of a variable is called the mode The apparent location of modes can change as the scale of a histogram is changed
Unimodal
bull Having one mode
Bimodal
bull Distribution with two modes
Example
Uniform
1048708 A histogram that doesnrsquot appear to have any mode andin which all the bars are approximately the same heightis called uniform
Anything Unusual
bull Do any unusual features stick outbull 1048708 Sometimes itrsquos the unusual features that tellbull us something interesting or exciting about thebull databull 1048708 You should always mention any stragglers orbull outliers that stand off away from the body ofbull the distributionbull 1048708 Are there any gaps in the distribution If sobull we might have data from more than onebull group
Outliers
The following histogram has outliersmdashthere arethree cities in the leftmost bar
Outliers
bull Are extreme values that do not appear to belong to the rest of the data They may be unusual values that deserve further investigation or they may be just mistakes therersquos no obvious way to tell Do not delete them Outliers can affect many statistical analyses so you should always be alert to them
Outliers
bull Away from the main portion of data
Where is the Center of the Distribution
bull 1048708 If you had to pick a single number to describe allbull the data what would you pickbull 1048708 Itrsquos easy to find the center when a histogram isbull unimodal and symmetricmdashitrsquos right in the middlebull 1048708 On the other hand itrsquos not so easy to find thebull center of a skewed histogram or a histogram withbull more than one modebull 1048708 For now we will ldquoeyeballrdquo the center of thebull distribution In the next chapter we will find thebull center numerically
How Spread Out is the Distribution
bull 1048708 Variation matters and Statistics is about
bull variation
bull 1048708 Are the values of the distribution tightly clustered
bull around the center or more spread out
bull 1048708 In the next two chapters we will talk about
bull spreadhellip
Comparing Distributions
bull 1048708 Often we would like to compare two or morebull distributions instead of looking at one distributionbull by itselfbull 1048708 When looking at two or more distributions it isbull very important that the histograms have been putbull on the same scale Otherwise we cannot reallybull compare the two distributionsbull 1048708 When we compare distributions we talk about thebull shape center and spread of each distribution
Example
Compare thefollowingdistributions ofages for femaleand male heartattack patients
Compare thefollowingdistributions ofages for femaleand male heartattack patients
HOMEWORK
Web Pages Used
bull httpwwwfaoorgwairdocsilrix5469ex5469e38gif
bull httpwwwsciencebuddiesorgscience-fair-projectsdescriptive_statistics_filesBimodalDistjpg
bull httpimagesabsoluteastronomycomimagesencyclopediaimagesbbibimodalpng
bull httpuploadwikimediaorgwikipediacommonsbbcBimodal_geologicalPNG
Web Pages Used
bull httpmathworldwolframcomimageseps-gifOutlierHistogram_1000gif
Timeplots Order Please
bull 1048708 For some data sets we are interested in how the
bull data behave over time In these cases we
bull construct timeplots of the data
Re-expressing Skewed Data toImprove Symmetry
Re-expressing Skewed Data toImprove Symmetry (cont)
One way to make a skeweddistribution more symmetric isto re-express or transform thedata by applying a simplefunction(eg logarithmic function)1048708 Note the change in skewnessfrom the raw data (Figure411) to the transformed data(Figure 412)
What Can Go Wrong
bull 1048708 Donrsquot make a histogram of a categorical variablemdash
bull bar charts or pie charts should be used for
bull categorical data
bull 1048708 Donrsquot look for shape
bull center and spread
bull of a bar chart
What Can Go Wrong (cont)
bull 1048708 Donrsquot use bars in every displaymdashsave them for
bull histograms and bar charts
bull 1048708 Below is a badly drawn timeplot and the proper
bull histogram for the number of eagles sighted in a
bull collection of weeks
What Can Go Wrong (cont)
What Can Go Wrong (cont)
Choose a bin width appropriate to the data1048708 Changing the bin width changes theappearance of the histogram
What Can Go Wrong (cont)
1048708 Avoid inconsistent scaleseither within the display orwhen comparing twodisplays1048708 Label clearly so a readerknows what the plotdisplays1048708 Good intentions badplot
What have we learned
bull 1048708 Wersquove learned how to make a picture for quantitative databull to help us see the story the data have to Tellbull 1048708 We can display the distribution of quantitative data with abull histogram stem-and-leaf display or dotplotbull 1048708 Tell about a distribution by talking about shape centerbull spread and any unusual featuresbull 1048708 We can compare two quantitative distributions by lookingbull at side-by-side displays (plotted on the same scale)bull 1048708 Trends in a quantitative variable can be displayed in abull timeplot
Stem and Leaf Displays
bull Shows quantitative data values in a way that sketches the distribution of the data
bullThe stem-and-leaf plot below shows the number of students enrolledbull in a dance class in the past 12 yearsbull The number of students are 81 84 85 86 93 94 97 100 102 103 110 and 111
Dotplot
bull Graphs a dot for each case against a single axis
bull Graph the following number 5 5555551010101010 etc
Dotplot with two sets of data
Example
Shape
bull To describe the shape of a distribution look for
bull Symmetry versus skewness
bull Single versus multiple modes
Symmetrical
bull A distribution is symmetric if the two halves on either side of the center look approximately like the mirror images of each other
Symmetrical
bull Symmetrical Histogram
Dotplot
bull Dots are mirrored images
Stem and leaf
bull Example
Skewed
bull A distribution is skewed if it is not symmetric and one tail stretched out further than the other
bull Skewed left- when the longer tail stretches to the left
bull Skewed right-when the longer tail stretched to the right
Examples
bull Skewed right
Skewed left
bull Left
All three
bull Examples
Funny example
bull httpwwwherkimershideawayorgapstatisticsymmsum99ymm111htm
New seating chart
bull httpwwwrandomorgintegers
Stem-and-Leaf Revisited
1048708 Compare the histogram and stem-and-leafdisplay for the pulse rates of 24 women at ahealth clinic Which graphical display do youprefer
Think Before You Draw Again
bull 1048708 Remember the ldquoMake a picturerdquo rulebull 1048708 Now that we have options for data displays
youbull need to Think carefully about which type ofbull display to makebull 1048708 Before making a stem-and-leaf display abull histogram or a dotplot check thebull 1048708 Quantitative Data Condition The data arebull values of a quantitative variable whose unitsbull are known
Constructing a Stem-and-Leaf Display
bull 1048708 First cut each data value into leading digits
bull (ldquostemsrdquo) and trailing digits (ldquoleavesrdquo)bull 1048708 Use the stems to label the binsbull 1048708 Use only one digit for each leafmdasheither
round orbull truncate the data values to one decimal
placebull after the stem
Center
bull A value that attempts the impossible by summarizing the entire distribution with a single number a ldquotypicalrdquo value
bull Measures include the mean and median
Spread
bull A numerical summary of how tightly the values are clustered around the center
bull Measures of spread include the IQR and standard deviation
Mode
bull a hump or local high pint in the shape of the distribution of a variable is called the mode The apparent location of modes can change as the scale of a histogram is changed
Unimodal
bull Having one mode
Bimodal
bull Distribution with two modes
Example
Uniform
1048708 A histogram that doesnrsquot appear to have any mode andin which all the bars are approximately the same heightis called uniform
Anything Unusual
bull Do any unusual features stick outbull 1048708 Sometimes itrsquos the unusual features that tellbull us something interesting or exciting about thebull databull 1048708 You should always mention any stragglers orbull outliers that stand off away from the body ofbull the distributionbull 1048708 Are there any gaps in the distribution If sobull we might have data from more than onebull group
Outliers
The following histogram has outliersmdashthere arethree cities in the leftmost bar
Outliers
bull Are extreme values that do not appear to belong to the rest of the data They may be unusual values that deserve further investigation or they may be just mistakes therersquos no obvious way to tell Do not delete them Outliers can affect many statistical analyses so you should always be alert to them
Outliers
bull Away from the main portion of data
Where is the Center of the Distribution
bull 1048708 If you had to pick a single number to describe allbull the data what would you pickbull 1048708 Itrsquos easy to find the center when a histogram isbull unimodal and symmetricmdashitrsquos right in the middlebull 1048708 On the other hand itrsquos not so easy to find thebull center of a skewed histogram or a histogram withbull more than one modebull 1048708 For now we will ldquoeyeballrdquo the center of thebull distribution In the next chapter we will find thebull center numerically
How Spread Out is the Distribution
bull 1048708 Variation matters and Statistics is about
bull variation
bull 1048708 Are the values of the distribution tightly clustered
bull around the center or more spread out
bull 1048708 In the next two chapters we will talk about
bull spreadhellip
Comparing Distributions
bull 1048708 Often we would like to compare two or morebull distributions instead of looking at one distributionbull by itselfbull 1048708 When looking at two or more distributions it isbull very important that the histograms have been putbull on the same scale Otherwise we cannot reallybull compare the two distributionsbull 1048708 When we compare distributions we talk about thebull shape center and spread of each distribution
Example
Compare thefollowingdistributions ofages for femaleand male heartattack patients
Compare thefollowingdistributions ofages for femaleand male heartattack patients
HOMEWORK
Web Pages Used
bull httpwwwfaoorgwairdocsilrix5469ex5469e38gif
bull httpwwwsciencebuddiesorgscience-fair-projectsdescriptive_statistics_filesBimodalDistjpg
bull httpimagesabsoluteastronomycomimagesencyclopediaimagesbbibimodalpng
bull httpuploadwikimediaorgwikipediacommonsbbcBimodal_geologicalPNG
Web Pages Used
bull httpmathworldwolframcomimageseps-gifOutlierHistogram_1000gif
Timeplots Order Please
bull 1048708 For some data sets we are interested in how the
bull data behave over time In these cases we
bull construct timeplots of the data
Re-expressing Skewed Data toImprove Symmetry
Re-expressing Skewed Data toImprove Symmetry (cont)
One way to make a skeweddistribution more symmetric isto re-express or transform thedata by applying a simplefunction(eg logarithmic function)1048708 Note the change in skewnessfrom the raw data (Figure411) to the transformed data(Figure 412)
What Can Go Wrong
bull 1048708 Donrsquot make a histogram of a categorical variablemdash
bull bar charts or pie charts should be used for
bull categorical data
bull 1048708 Donrsquot look for shape
bull center and spread
bull of a bar chart
What Can Go Wrong (cont)
bull 1048708 Donrsquot use bars in every displaymdashsave them for
bull histograms and bar charts
bull 1048708 Below is a badly drawn timeplot and the proper
bull histogram for the number of eagles sighted in a
bull collection of weeks
What Can Go Wrong (cont)
What Can Go Wrong (cont)
Choose a bin width appropriate to the data1048708 Changing the bin width changes theappearance of the histogram
What Can Go Wrong (cont)
1048708 Avoid inconsistent scaleseither within the display orwhen comparing twodisplays1048708 Label clearly so a readerknows what the plotdisplays1048708 Good intentions badplot
What have we learned
bull 1048708 Wersquove learned how to make a picture for quantitative databull to help us see the story the data have to Tellbull 1048708 We can display the distribution of quantitative data with abull histogram stem-and-leaf display or dotplotbull 1048708 Tell about a distribution by talking about shape centerbull spread and any unusual featuresbull 1048708 We can compare two quantitative distributions by lookingbull at side-by-side displays (plotted on the same scale)bull 1048708 Trends in a quantitative variable can be displayed in abull timeplot
Dotplot
bull Graphs a dot for each case against a single axis
bull Graph the following number 5 5555551010101010 etc
Dotplot with two sets of data
Example
Shape
bull To describe the shape of a distribution look for
bull Symmetry versus skewness
bull Single versus multiple modes
Symmetrical
bull A distribution is symmetric if the two halves on either side of the center look approximately like the mirror images of each other
Symmetrical
bull Symmetrical Histogram
Dotplot
bull Dots are mirrored images
Stem and leaf
bull Example
Skewed
bull A distribution is skewed if it is not symmetric and one tail stretched out further than the other
bull Skewed left- when the longer tail stretches to the left
bull Skewed right-when the longer tail stretched to the right
Examples
bull Skewed right
Skewed left
bull Left
All three
bull Examples
Funny example
bull httpwwwherkimershideawayorgapstatisticsymmsum99ymm111htm
New seating chart
bull httpwwwrandomorgintegers
Stem-and-Leaf Revisited
1048708 Compare the histogram and stem-and-leafdisplay for the pulse rates of 24 women at ahealth clinic Which graphical display do youprefer
Think Before You Draw Again
bull 1048708 Remember the ldquoMake a picturerdquo rulebull 1048708 Now that we have options for data displays
youbull need to Think carefully about which type ofbull display to makebull 1048708 Before making a stem-and-leaf display abull histogram or a dotplot check thebull 1048708 Quantitative Data Condition The data arebull values of a quantitative variable whose unitsbull are known
Constructing a Stem-and-Leaf Display
bull 1048708 First cut each data value into leading digits
bull (ldquostemsrdquo) and trailing digits (ldquoleavesrdquo)bull 1048708 Use the stems to label the binsbull 1048708 Use only one digit for each leafmdasheither
round orbull truncate the data values to one decimal
placebull after the stem
Center
bull A value that attempts the impossible by summarizing the entire distribution with a single number a ldquotypicalrdquo value
bull Measures include the mean and median
Spread
bull A numerical summary of how tightly the values are clustered around the center
bull Measures of spread include the IQR and standard deviation
Mode
bull a hump or local high pint in the shape of the distribution of a variable is called the mode The apparent location of modes can change as the scale of a histogram is changed
Unimodal
bull Having one mode
Bimodal
bull Distribution with two modes
Example
Uniform
1048708 A histogram that doesnrsquot appear to have any mode andin which all the bars are approximately the same heightis called uniform
Anything Unusual
bull Do any unusual features stick outbull 1048708 Sometimes itrsquos the unusual features that tellbull us something interesting or exciting about thebull databull 1048708 You should always mention any stragglers orbull outliers that stand off away from the body ofbull the distributionbull 1048708 Are there any gaps in the distribution If sobull we might have data from more than onebull group
Outliers
The following histogram has outliersmdashthere arethree cities in the leftmost bar
Outliers
bull Are extreme values that do not appear to belong to the rest of the data They may be unusual values that deserve further investigation or they may be just mistakes therersquos no obvious way to tell Do not delete them Outliers can affect many statistical analyses so you should always be alert to them
Outliers
bull Away from the main portion of data
Where is the Center of the Distribution
bull 1048708 If you had to pick a single number to describe allbull the data what would you pickbull 1048708 Itrsquos easy to find the center when a histogram isbull unimodal and symmetricmdashitrsquos right in the middlebull 1048708 On the other hand itrsquos not so easy to find thebull center of a skewed histogram or a histogram withbull more than one modebull 1048708 For now we will ldquoeyeballrdquo the center of thebull distribution In the next chapter we will find thebull center numerically
How Spread Out is the Distribution
bull 1048708 Variation matters and Statistics is about
bull variation
bull 1048708 Are the values of the distribution tightly clustered
bull around the center or more spread out
bull 1048708 In the next two chapters we will talk about
bull spreadhellip
Comparing Distributions
bull 1048708 Often we would like to compare two or morebull distributions instead of looking at one distributionbull by itselfbull 1048708 When looking at two or more distributions it isbull very important that the histograms have been putbull on the same scale Otherwise we cannot reallybull compare the two distributionsbull 1048708 When we compare distributions we talk about thebull shape center and spread of each distribution
Example
Compare thefollowingdistributions ofages for femaleand male heartattack patients
Compare thefollowingdistributions ofages for femaleand male heartattack patients
HOMEWORK
Web Pages Used
bull httpwwwfaoorgwairdocsilrix5469ex5469e38gif
bull httpwwwsciencebuddiesorgscience-fair-projectsdescriptive_statistics_filesBimodalDistjpg
bull httpimagesabsoluteastronomycomimagesencyclopediaimagesbbibimodalpng
bull httpuploadwikimediaorgwikipediacommonsbbcBimodal_geologicalPNG
Web Pages Used
bull httpmathworldwolframcomimageseps-gifOutlierHistogram_1000gif
Timeplots Order Please
bull 1048708 For some data sets we are interested in how the
bull data behave over time In these cases we
bull construct timeplots of the data
Re-expressing Skewed Data toImprove Symmetry
Re-expressing Skewed Data toImprove Symmetry (cont)
One way to make a skeweddistribution more symmetric isto re-express or transform thedata by applying a simplefunction(eg logarithmic function)1048708 Note the change in skewnessfrom the raw data (Figure411) to the transformed data(Figure 412)
What Can Go Wrong
bull 1048708 Donrsquot make a histogram of a categorical variablemdash
bull bar charts or pie charts should be used for
bull categorical data
bull 1048708 Donrsquot look for shape
bull center and spread
bull of a bar chart
What Can Go Wrong (cont)
bull 1048708 Donrsquot use bars in every displaymdashsave them for
bull histograms and bar charts
bull 1048708 Below is a badly drawn timeplot and the proper
bull histogram for the number of eagles sighted in a
bull collection of weeks
What Can Go Wrong (cont)
What Can Go Wrong (cont)
Choose a bin width appropriate to the data1048708 Changing the bin width changes theappearance of the histogram
What Can Go Wrong (cont)
1048708 Avoid inconsistent scaleseither within the display orwhen comparing twodisplays1048708 Label clearly so a readerknows what the plotdisplays1048708 Good intentions badplot
What have we learned
bull 1048708 Wersquove learned how to make a picture for quantitative databull to help us see the story the data have to Tellbull 1048708 We can display the distribution of quantitative data with abull histogram stem-and-leaf display or dotplotbull 1048708 Tell about a distribution by talking about shape centerbull spread and any unusual featuresbull 1048708 We can compare two quantitative distributions by lookingbull at side-by-side displays (plotted on the same scale)bull 1048708 Trends in a quantitative variable can be displayed in abull timeplot
Dotplot with two sets of data
Example
Shape
bull To describe the shape of a distribution look for
bull Symmetry versus skewness
bull Single versus multiple modes
Symmetrical
bull A distribution is symmetric if the two halves on either side of the center look approximately like the mirror images of each other
Symmetrical
bull Symmetrical Histogram
Dotplot
bull Dots are mirrored images
Stem and leaf
bull Example
Skewed
bull A distribution is skewed if it is not symmetric and one tail stretched out further than the other
bull Skewed left- when the longer tail stretches to the left
bull Skewed right-when the longer tail stretched to the right
Examples
bull Skewed right
Skewed left
bull Left
All three
bull Examples
Funny example
bull httpwwwherkimershideawayorgapstatisticsymmsum99ymm111htm
New seating chart
bull httpwwwrandomorgintegers
Stem-and-Leaf Revisited
1048708 Compare the histogram and stem-and-leafdisplay for the pulse rates of 24 women at ahealth clinic Which graphical display do youprefer
Think Before You Draw Again
bull 1048708 Remember the ldquoMake a picturerdquo rulebull 1048708 Now that we have options for data displays
youbull need to Think carefully about which type ofbull display to makebull 1048708 Before making a stem-and-leaf display abull histogram or a dotplot check thebull 1048708 Quantitative Data Condition The data arebull values of a quantitative variable whose unitsbull are known
Constructing a Stem-and-Leaf Display
bull 1048708 First cut each data value into leading digits
bull (ldquostemsrdquo) and trailing digits (ldquoleavesrdquo)bull 1048708 Use the stems to label the binsbull 1048708 Use only one digit for each leafmdasheither
round orbull truncate the data values to one decimal
placebull after the stem
Center
bull A value that attempts the impossible by summarizing the entire distribution with a single number a ldquotypicalrdquo value
bull Measures include the mean and median
Spread
bull A numerical summary of how tightly the values are clustered around the center
bull Measures of spread include the IQR and standard deviation
Mode
bull a hump or local high pint in the shape of the distribution of a variable is called the mode The apparent location of modes can change as the scale of a histogram is changed
Unimodal
bull Having one mode
Bimodal
bull Distribution with two modes
Example
Uniform
1048708 A histogram that doesnrsquot appear to have any mode andin which all the bars are approximately the same heightis called uniform
Anything Unusual
bull Do any unusual features stick outbull 1048708 Sometimes itrsquos the unusual features that tellbull us something interesting or exciting about thebull databull 1048708 You should always mention any stragglers orbull outliers that stand off away from the body ofbull the distributionbull 1048708 Are there any gaps in the distribution If sobull we might have data from more than onebull group
Outliers
The following histogram has outliersmdashthere arethree cities in the leftmost bar
Outliers
bull Are extreme values that do not appear to belong to the rest of the data They may be unusual values that deserve further investigation or they may be just mistakes therersquos no obvious way to tell Do not delete them Outliers can affect many statistical analyses so you should always be alert to them
Outliers
bull Away from the main portion of data
Where is the Center of the Distribution
bull 1048708 If you had to pick a single number to describe allbull the data what would you pickbull 1048708 Itrsquos easy to find the center when a histogram isbull unimodal and symmetricmdashitrsquos right in the middlebull 1048708 On the other hand itrsquos not so easy to find thebull center of a skewed histogram or a histogram withbull more than one modebull 1048708 For now we will ldquoeyeballrdquo the center of thebull distribution In the next chapter we will find thebull center numerically
How Spread Out is the Distribution
bull 1048708 Variation matters and Statistics is about
bull variation
bull 1048708 Are the values of the distribution tightly clustered
bull around the center or more spread out
bull 1048708 In the next two chapters we will talk about
bull spreadhellip
Comparing Distributions
bull 1048708 Often we would like to compare two or morebull distributions instead of looking at one distributionbull by itselfbull 1048708 When looking at two or more distributions it isbull very important that the histograms have been putbull on the same scale Otherwise we cannot reallybull compare the two distributionsbull 1048708 When we compare distributions we talk about thebull shape center and spread of each distribution
Example
Compare thefollowingdistributions ofages for femaleand male heartattack patients
Compare thefollowingdistributions ofages for femaleand male heartattack patients
HOMEWORK
Web Pages Used
bull httpwwwfaoorgwairdocsilrix5469ex5469e38gif
bull httpwwwsciencebuddiesorgscience-fair-projectsdescriptive_statistics_filesBimodalDistjpg
bull httpimagesabsoluteastronomycomimagesencyclopediaimagesbbibimodalpng
bull httpuploadwikimediaorgwikipediacommonsbbcBimodal_geologicalPNG
Web Pages Used
bull httpmathworldwolframcomimageseps-gifOutlierHistogram_1000gif
Timeplots Order Please
bull 1048708 For some data sets we are interested in how the
bull data behave over time In these cases we
bull construct timeplots of the data
Re-expressing Skewed Data toImprove Symmetry
Re-expressing Skewed Data toImprove Symmetry (cont)
One way to make a skeweddistribution more symmetric isto re-express or transform thedata by applying a simplefunction(eg logarithmic function)1048708 Note the change in skewnessfrom the raw data (Figure411) to the transformed data(Figure 412)
What Can Go Wrong
bull 1048708 Donrsquot make a histogram of a categorical variablemdash
bull bar charts or pie charts should be used for
bull categorical data
bull 1048708 Donrsquot look for shape
bull center and spread
bull of a bar chart
What Can Go Wrong (cont)
bull 1048708 Donrsquot use bars in every displaymdashsave them for
bull histograms and bar charts
bull 1048708 Below is a badly drawn timeplot and the proper
bull histogram for the number of eagles sighted in a
bull collection of weeks
What Can Go Wrong (cont)
What Can Go Wrong (cont)
Choose a bin width appropriate to the data1048708 Changing the bin width changes theappearance of the histogram
What Can Go Wrong (cont)
1048708 Avoid inconsistent scaleseither within the display orwhen comparing twodisplays1048708 Label clearly so a readerknows what the plotdisplays1048708 Good intentions badplot
What have we learned
bull 1048708 Wersquove learned how to make a picture for quantitative databull to help us see the story the data have to Tellbull 1048708 We can display the distribution of quantitative data with abull histogram stem-and-leaf display or dotplotbull 1048708 Tell about a distribution by talking about shape centerbull spread and any unusual featuresbull 1048708 We can compare two quantitative distributions by lookingbull at side-by-side displays (plotted on the same scale)bull 1048708 Trends in a quantitative variable can be displayed in abull timeplot
Shape
bull To describe the shape of a distribution look for
bull Symmetry versus skewness
bull Single versus multiple modes
Symmetrical
bull A distribution is symmetric if the two halves on either side of the center look approximately like the mirror images of each other
Symmetrical
bull Symmetrical Histogram
Dotplot
bull Dots are mirrored images
Stem and leaf
bull Example
Skewed
bull A distribution is skewed if it is not symmetric and one tail stretched out further than the other
bull Skewed left- when the longer tail stretches to the left
bull Skewed right-when the longer tail stretched to the right
Examples
bull Skewed right
Skewed left
bull Left
All three
bull Examples
Funny example
bull httpwwwherkimershideawayorgapstatisticsymmsum99ymm111htm
New seating chart
bull httpwwwrandomorgintegers
Stem-and-Leaf Revisited
1048708 Compare the histogram and stem-and-leafdisplay for the pulse rates of 24 women at ahealth clinic Which graphical display do youprefer
Think Before You Draw Again
bull 1048708 Remember the ldquoMake a picturerdquo rulebull 1048708 Now that we have options for data displays
youbull need to Think carefully about which type ofbull display to makebull 1048708 Before making a stem-and-leaf display abull histogram or a dotplot check thebull 1048708 Quantitative Data Condition The data arebull values of a quantitative variable whose unitsbull are known
Constructing a Stem-and-Leaf Display
bull 1048708 First cut each data value into leading digits
bull (ldquostemsrdquo) and trailing digits (ldquoleavesrdquo)bull 1048708 Use the stems to label the binsbull 1048708 Use only one digit for each leafmdasheither
round orbull truncate the data values to one decimal
placebull after the stem
Center
bull A value that attempts the impossible by summarizing the entire distribution with a single number a ldquotypicalrdquo value
bull Measures include the mean and median
Spread
bull A numerical summary of how tightly the values are clustered around the center
bull Measures of spread include the IQR and standard deviation
Mode
bull a hump or local high pint in the shape of the distribution of a variable is called the mode The apparent location of modes can change as the scale of a histogram is changed
Unimodal
bull Having one mode
Bimodal
bull Distribution with two modes
Example
Uniform
1048708 A histogram that doesnrsquot appear to have any mode andin which all the bars are approximately the same heightis called uniform
Anything Unusual
bull Do any unusual features stick outbull 1048708 Sometimes itrsquos the unusual features that tellbull us something interesting or exciting about thebull databull 1048708 You should always mention any stragglers orbull outliers that stand off away from the body ofbull the distributionbull 1048708 Are there any gaps in the distribution If sobull we might have data from more than onebull group
Outliers
The following histogram has outliersmdashthere arethree cities in the leftmost bar
Outliers
bull Are extreme values that do not appear to belong to the rest of the data They may be unusual values that deserve further investigation or they may be just mistakes therersquos no obvious way to tell Do not delete them Outliers can affect many statistical analyses so you should always be alert to them
Outliers
bull Away from the main portion of data
Where is the Center of the Distribution
bull 1048708 If you had to pick a single number to describe allbull the data what would you pickbull 1048708 Itrsquos easy to find the center when a histogram isbull unimodal and symmetricmdashitrsquos right in the middlebull 1048708 On the other hand itrsquos not so easy to find thebull center of a skewed histogram or a histogram withbull more than one modebull 1048708 For now we will ldquoeyeballrdquo the center of thebull distribution In the next chapter we will find thebull center numerically
How Spread Out is the Distribution
bull 1048708 Variation matters and Statistics is about
bull variation
bull 1048708 Are the values of the distribution tightly clustered
bull around the center or more spread out
bull 1048708 In the next two chapters we will talk about
bull spreadhellip
Comparing Distributions
bull 1048708 Often we would like to compare two or morebull distributions instead of looking at one distributionbull by itselfbull 1048708 When looking at two or more distributions it isbull very important that the histograms have been putbull on the same scale Otherwise we cannot reallybull compare the two distributionsbull 1048708 When we compare distributions we talk about thebull shape center and spread of each distribution
Example
Compare thefollowingdistributions ofages for femaleand male heartattack patients
Compare thefollowingdistributions ofages for femaleand male heartattack patients
HOMEWORK
Web Pages Used
bull httpwwwfaoorgwairdocsilrix5469ex5469e38gif
bull httpwwwsciencebuddiesorgscience-fair-projectsdescriptive_statistics_filesBimodalDistjpg
bull httpimagesabsoluteastronomycomimagesencyclopediaimagesbbibimodalpng
bull httpuploadwikimediaorgwikipediacommonsbbcBimodal_geologicalPNG
Web Pages Used
bull httpmathworldwolframcomimageseps-gifOutlierHistogram_1000gif
Timeplots Order Please
bull 1048708 For some data sets we are interested in how the
bull data behave over time In these cases we
bull construct timeplots of the data
Re-expressing Skewed Data toImprove Symmetry
Re-expressing Skewed Data toImprove Symmetry (cont)
One way to make a skeweddistribution more symmetric isto re-express or transform thedata by applying a simplefunction(eg logarithmic function)1048708 Note the change in skewnessfrom the raw data (Figure411) to the transformed data(Figure 412)
What Can Go Wrong
bull 1048708 Donrsquot make a histogram of a categorical variablemdash
bull bar charts or pie charts should be used for
bull categorical data
bull 1048708 Donrsquot look for shape
bull center and spread
bull of a bar chart
What Can Go Wrong (cont)
bull 1048708 Donrsquot use bars in every displaymdashsave them for
bull histograms and bar charts
bull 1048708 Below is a badly drawn timeplot and the proper
bull histogram for the number of eagles sighted in a
bull collection of weeks
What Can Go Wrong (cont)
What Can Go Wrong (cont)
Choose a bin width appropriate to the data1048708 Changing the bin width changes theappearance of the histogram
What Can Go Wrong (cont)
1048708 Avoid inconsistent scaleseither within the display orwhen comparing twodisplays1048708 Label clearly so a readerknows what the plotdisplays1048708 Good intentions badplot
What have we learned
bull 1048708 Wersquove learned how to make a picture for quantitative databull to help us see the story the data have to Tellbull 1048708 We can display the distribution of quantitative data with abull histogram stem-and-leaf display or dotplotbull 1048708 Tell about a distribution by talking about shape centerbull spread and any unusual featuresbull 1048708 We can compare two quantitative distributions by lookingbull at side-by-side displays (plotted on the same scale)bull 1048708 Trends in a quantitative variable can be displayed in abull timeplot
Symmetrical
bull A distribution is symmetric if the two halves on either side of the center look approximately like the mirror images of each other
Symmetrical
bull Symmetrical Histogram
Dotplot
bull Dots are mirrored images
Stem and leaf
bull Example
Skewed
bull A distribution is skewed if it is not symmetric and one tail stretched out further than the other
bull Skewed left- when the longer tail stretches to the left
bull Skewed right-when the longer tail stretched to the right
Examples
bull Skewed right
Skewed left
bull Left
All three
bull Examples
Funny example
bull httpwwwherkimershideawayorgapstatisticsymmsum99ymm111htm
New seating chart
bull httpwwwrandomorgintegers
Stem-and-Leaf Revisited
1048708 Compare the histogram and stem-and-leafdisplay for the pulse rates of 24 women at ahealth clinic Which graphical display do youprefer
Think Before You Draw Again
bull 1048708 Remember the ldquoMake a picturerdquo rulebull 1048708 Now that we have options for data displays
youbull need to Think carefully about which type ofbull display to makebull 1048708 Before making a stem-and-leaf display abull histogram or a dotplot check thebull 1048708 Quantitative Data Condition The data arebull values of a quantitative variable whose unitsbull are known
Constructing a Stem-and-Leaf Display
bull 1048708 First cut each data value into leading digits
bull (ldquostemsrdquo) and trailing digits (ldquoleavesrdquo)bull 1048708 Use the stems to label the binsbull 1048708 Use only one digit for each leafmdasheither
round orbull truncate the data values to one decimal
placebull after the stem
Center
bull A value that attempts the impossible by summarizing the entire distribution with a single number a ldquotypicalrdquo value
bull Measures include the mean and median
Spread
bull A numerical summary of how tightly the values are clustered around the center
bull Measures of spread include the IQR and standard deviation
Mode
bull a hump or local high pint in the shape of the distribution of a variable is called the mode The apparent location of modes can change as the scale of a histogram is changed
Unimodal
bull Having one mode
Bimodal
bull Distribution with two modes
Example
Uniform
1048708 A histogram that doesnrsquot appear to have any mode andin which all the bars are approximately the same heightis called uniform
Anything Unusual
bull Do any unusual features stick outbull 1048708 Sometimes itrsquos the unusual features that tellbull us something interesting or exciting about thebull databull 1048708 You should always mention any stragglers orbull outliers that stand off away from the body ofbull the distributionbull 1048708 Are there any gaps in the distribution If sobull we might have data from more than onebull group
Outliers
The following histogram has outliersmdashthere arethree cities in the leftmost bar
Outliers
bull Are extreme values that do not appear to belong to the rest of the data They may be unusual values that deserve further investigation or they may be just mistakes therersquos no obvious way to tell Do not delete them Outliers can affect many statistical analyses so you should always be alert to them
Outliers
bull Away from the main portion of data
Where is the Center of the Distribution
bull 1048708 If you had to pick a single number to describe allbull the data what would you pickbull 1048708 Itrsquos easy to find the center when a histogram isbull unimodal and symmetricmdashitrsquos right in the middlebull 1048708 On the other hand itrsquos not so easy to find thebull center of a skewed histogram or a histogram withbull more than one modebull 1048708 For now we will ldquoeyeballrdquo the center of thebull distribution In the next chapter we will find thebull center numerically
How Spread Out is the Distribution
bull 1048708 Variation matters and Statistics is about
bull variation
bull 1048708 Are the values of the distribution tightly clustered
bull around the center or more spread out
bull 1048708 In the next two chapters we will talk about
bull spreadhellip
Comparing Distributions
bull 1048708 Often we would like to compare two or morebull distributions instead of looking at one distributionbull by itselfbull 1048708 When looking at two or more distributions it isbull very important that the histograms have been putbull on the same scale Otherwise we cannot reallybull compare the two distributionsbull 1048708 When we compare distributions we talk about thebull shape center and spread of each distribution
Example
Compare thefollowingdistributions ofages for femaleand male heartattack patients
Compare thefollowingdistributions ofages for femaleand male heartattack patients
HOMEWORK
Web Pages Used
bull httpwwwfaoorgwairdocsilrix5469ex5469e38gif
bull httpwwwsciencebuddiesorgscience-fair-projectsdescriptive_statistics_filesBimodalDistjpg
bull httpimagesabsoluteastronomycomimagesencyclopediaimagesbbibimodalpng
bull httpuploadwikimediaorgwikipediacommonsbbcBimodal_geologicalPNG
Web Pages Used
bull httpmathworldwolframcomimageseps-gifOutlierHistogram_1000gif
Timeplots Order Please
bull 1048708 For some data sets we are interested in how the
bull data behave over time In these cases we
bull construct timeplots of the data
Re-expressing Skewed Data toImprove Symmetry
Re-expressing Skewed Data toImprove Symmetry (cont)
One way to make a skeweddistribution more symmetric isto re-express or transform thedata by applying a simplefunction(eg logarithmic function)1048708 Note the change in skewnessfrom the raw data (Figure411) to the transformed data(Figure 412)
What Can Go Wrong
bull 1048708 Donrsquot make a histogram of a categorical variablemdash
bull bar charts or pie charts should be used for
bull categorical data
bull 1048708 Donrsquot look for shape
bull center and spread
bull of a bar chart
What Can Go Wrong (cont)
bull 1048708 Donrsquot use bars in every displaymdashsave them for
bull histograms and bar charts
bull 1048708 Below is a badly drawn timeplot and the proper
bull histogram for the number of eagles sighted in a
bull collection of weeks
What Can Go Wrong (cont)
What Can Go Wrong (cont)
Choose a bin width appropriate to the data1048708 Changing the bin width changes theappearance of the histogram
What Can Go Wrong (cont)
1048708 Avoid inconsistent scaleseither within the display orwhen comparing twodisplays1048708 Label clearly so a readerknows what the plotdisplays1048708 Good intentions badplot
What have we learned
bull 1048708 Wersquove learned how to make a picture for quantitative databull to help us see the story the data have to Tellbull 1048708 We can display the distribution of quantitative data with abull histogram stem-and-leaf display or dotplotbull 1048708 Tell about a distribution by talking about shape centerbull spread and any unusual featuresbull 1048708 We can compare two quantitative distributions by lookingbull at side-by-side displays (plotted on the same scale)bull 1048708 Trends in a quantitative variable can be displayed in abull timeplot
Symmetrical
bull Symmetrical Histogram
Dotplot
bull Dots are mirrored images
Stem and leaf
bull Example
Skewed
bull A distribution is skewed if it is not symmetric and one tail stretched out further than the other
bull Skewed left- when the longer tail stretches to the left
bull Skewed right-when the longer tail stretched to the right
Examples
bull Skewed right
Skewed left
bull Left
All three
bull Examples
Funny example
bull httpwwwherkimershideawayorgapstatisticsymmsum99ymm111htm
New seating chart
bull httpwwwrandomorgintegers
Stem-and-Leaf Revisited
1048708 Compare the histogram and stem-and-leafdisplay for the pulse rates of 24 women at ahealth clinic Which graphical display do youprefer
Think Before You Draw Again
bull 1048708 Remember the ldquoMake a picturerdquo rulebull 1048708 Now that we have options for data displays
youbull need to Think carefully about which type ofbull display to makebull 1048708 Before making a stem-and-leaf display abull histogram or a dotplot check thebull 1048708 Quantitative Data Condition The data arebull values of a quantitative variable whose unitsbull are known
Constructing a Stem-and-Leaf Display
bull 1048708 First cut each data value into leading digits
bull (ldquostemsrdquo) and trailing digits (ldquoleavesrdquo)bull 1048708 Use the stems to label the binsbull 1048708 Use only one digit for each leafmdasheither
round orbull truncate the data values to one decimal
placebull after the stem
Center
bull A value that attempts the impossible by summarizing the entire distribution with a single number a ldquotypicalrdquo value
bull Measures include the mean and median
Spread
bull A numerical summary of how tightly the values are clustered around the center
bull Measures of spread include the IQR and standard deviation
Mode
bull a hump or local high pint in the shape of the distribution of a variable is called the mode The apparent location of modes can change as the scale of a histogram is changed
Unimodal
bull Having one mode
Bimodal
bull Distribution with two modes
Example
Uniform
1048708 A histogram that doesnrsquot appear to have any mode andin which all the bars are approximately the same heightis called uniform
Anything Unusual
bull Do any unusual features stick outbull 1048708 Sometimes itrsquos the unusual features that tellbull us something interesting or exciting about thebull databull 1048708 You should always mention any stragglers orbull outliers that stand off away from the body ofbull the distributionbull 1048708 Are there any gaps in the distribution If sobull we might have data from more than onebull group
Outliers
The following histogram has outliersmdashthere arethree cities in the leftmost bar
Outliers
bull Are extreme values that do not appear to belong to the rest of the data They may be unusual values that deserve further investigation or they may be just mistakes therersquos no obvious way to tell Do not delete them Outliers can affect many statistical analyses so you should always be alert to them
Outliers
bull Away from the main portion of data
Where is the Center of the Distribution
bull 1048708 If you had to pick a single number to describe allbull the data what would you pickbull 1048708 Itrsquos easy to find the center when a histogram isbull unimodal and symmetricmdashitrsquos right in the middlebull 1048708 On the other hand itrsquos not so easy to find thebull center of a skewed histogram or a histogram withbull more than one modebull 1048708 For now we will ldquoeyeballrdquo the center of thebull distribution In the next chapter we will find thebull center numerically
How Spread Out is the Distribution
bull 1048708 Variation matters and Statistics is about
bull variation
bull 1048708 Are the values of the distribution tightly clustered
bull around the center or more spread out
bull 1048708 In the next two chapters we will talk about
bull spreadhellip
Comparing Distributions
bull 1048708 Often we would like to compare two or morebull distributions instead of looking at one distributionbull by itselfbull 1048708 When looking at two or more distributions it isbull very important that the histograms have been putbull on the same scale Otherwise we cannot reallybull compare the two distributionsbull 1048708 When we compare distributions we talk about thebull shape center and spread of each distribution
Example
Compare thefollowingdistributions ofages for femaleand male heartattack patients
Compare thefollowingdistributions ofages for femaleand male heartattack patients
HOMEWORK
Web Pages Used
bull httpwwwfaoorgwairdocsilrix5469ex5469e38gif
bull httpwwwsciencebuddiesorgscience-fair-projectsdescriptive_statistics_filesBimodalDistjpg
bull httpimagesabsoluteastronomycomimagesencyclopediaimagesbbibimodalpng
bull httpuploadwikimediaorgwikipediacommonsbbcBimodal_geologicalPNG
Web Pages Used
bull httpmathworldwolframcomimageseps-gifOutlierHistogram_1000gif
Timeplots Order Please
bull 1048708 For some data sets we are interested in how the
bull data behave over time In these cases we
bull construct timeplots of the data
Re-expressing Skewed Data toImprove Symmetry
Re-expressing Skewed Data toImprove Symmetry (cont)
One way to make a skeweddistribution more symmetric isto re-express or transform thedata by applying a simplefunction(eg logarithmic function)1048708 Note the change in skewnessfrom the raw data (Figure411) to the transformed data(Figure 412)
What Can Go Wrong
bull 1048708 Donrsquot make a histogram of a categorical variablemdash
bull bar charts or pie charts should be used for
bull categorical data
bull 1048708 Donrsquot look for shape
bull center and spread
bull of a bar chart
What Can Go Wrong (cont)
bull 1048708 Donrsquot use bars in every displaymdashsave them for
bull histograms and bar charts
bull 1048708 Below is a badly drawn timeplot and the proper
bull histogram for the number of eagles sighted in a
bull collection of weeks
What Can Go Wrong (cont)
What Can Go Wrong (cont)
Choose a bin width appropriate to the data1048708 Changing the bin width changes theappearance of the histogram
What Can Go Wrong (cont)
1048708 Avoid inconsistent scaleseither within the display orwhen comparing twodisplays1048708 Label clearly so a readerknows what the plotdisplays1048708 Good intentions badplot
What have we learned
bull 1048708 Wersquove learned how to make a picture for quantitative databull to help us see the story the data have to Tellbull 1048708 We can display the distribution of quantitative data with abull histogram stem-and-leaf display or dotplotbull 1048708 Tell about a distribution by talking about shape centerbull spread and any unusual featuresbull 1048708 We can compare two quantitative distributions by lookingbull at side-by-side displays (plotted on the same scale)bull 1048708 Trends in a quantitative variable can be displayed in abull timeplot
Dotplot
bull Dots are mirrored images
Stem and leaf
bull Example
Skewed
bull A distribution is skewed if it is not symmetric and one tail stretched out further than the other
bull Skewed left- when the longer tail stretches to the left
bull Skewed right-when the longer tail stretched to the right
Examples
bull Skewed right
Skewed left
bull Left
All three
bull Examples
Funny example
bull httpwwwherkimershideawayorgapstatisticsymmsum99ymm111htm
New seating chart
bull httpwwwrandomorgintegers
Stem-and-Leaf Revisited
1048708 Compare the histogram and stem-and-leafdisplay for the pulse rates of 24 women at ahealth clinic Which graphical display do youprefer
Think Before You Draw Again
bull 1048708 Remember the ldquoMake a picturerdquo rulebull 1048708 Now that we have options for data displays
youbull need to Think carefully about which type ofbull display to makebull 1048708 Before making a stem-and-leaf display abull histogram or a dotplot check thebull 1048708 Quantitative Data Condition The data arebull values of a quantitative variable whose unitsbull are known
Constructing a Stem-and-Leaf Display
bull 1048708 First cut each data value into leading digits
bull (ldquostemsrdquo) and trailing digits (ldquoleavesrdquo)bull 1048708 Use the stems to label the binsbull 1048708 Use only one digit for each leafmdasheither
round orbull truncate the data values to one decimal
placebull after the stem
Center
bull A value that attempts the impossible by summarizing the entire distribution with a single number a ldquotypicalrdquo value
bull Measures include the mean and median
Spread
bull A numerical summary of how tightly the values are clustered around the center
bull Measures of spread include the IQR and standard deviation
Mode
bull a hump or local high pint in the shape of the distribution of a variable is called the mode The apparent location of modes can change as the scale of a histogram is changed
Unimodal
bull Having one mode
Bimodal
bull Distribution with two modes
Example
Uniform
1048708 A histogram that doesnrsquot appear to have any mode andin which all the bars are approximately the same heightis called uniform
Anything Unusual
bull Do any unusual features stick outbull 1048708 Sometimes itrsquos the unusual features that tellbull us something interesting or exciting about thebull databull 1048708 You should always mention any stragglers orbull outliers that stand off away from the body ofbull the distributionbull 1048708 Are there any gaps in the distribution If sobull we might have data from more than onebull group
Outliers
The following histogram has outliersmdashthere arethree cities in the leftmost bar
Outliers
bull Are extreme values that do not appear to belong to the rest of the data They may be unusual values that deserve further investigation or they may be just mistakes therersquos no obvious way to tell Do not delete them Outliers can affect many statistical analyses so you should always be alert to them
Outliers
bull Away from the main portion of data
Where is the Center of the Distribution
bull 1048708 If you had to pick a single number to describe allbull the data what would you pickbull 1048708 Itrsquos easy to find the center when a histogram isbull unimodal and symmetricmdashitrsquos right in the middlebull 1048708 On the other hand itrsquos not so easy to find thebull center of a skewed histogram or a histogram withbull more than one modebull 1048708 For now we will ldquoeyeballrdquo the center of thebull distribution In the next chapter we will find thebull center numerically
How Spread Out is the Distribution
bull 1048708 Variation matters and Statistics is about
bull variation
bull 1048708 Are the values of the distribution tightly clustered
bull around the center or more spread out
bull 1048708 In the next two chapters we will talk about
bull spreadhellip
Comparing Distributions
bull 1048708 Often we would like to compare two or morebull distributions instead of looking at one distributionbull by itselfbull 1048708 When looking at two or more distributions it isbull very important that the histograms have been putbull on the same scale Otherwise we cannot reallybull compare the two distributionsbull 1048708 When we compare distributions we talk about thebull shape center and spread of each distribution
Example
Compare thefollowingdistributions ofages for femaleand male heartattack patients
Compare thefollowingdistributions ofages for femaleand male heartattack patients
HOMEWORK
Web Pages Used
bull httpwwwfaoorgwairdocsilrix5469ex5469e38gif
bull httpwwwsciencebuddiesorgscience-fair-projectsdescriptive_statistics_filesBimodalDistjpg
bull httpimagesabsoluteastronomycomimagesencyclopediaimagesbbibimodalpng
bull httpuploadwikimediaorgwikipediacommonsbbcBimodal_geologicalPNG
Web Pages Used
bull httpmathworldwolframcomimageseps-gifOutlierHistogram_1000gif
Timeplots Order Please
bull 1048708 For some data sets we are interested in how the
bull data behave over time In these cases we
bull construct timeplots of the data
Re-expressing Skewed Data toImprove Symmetry
Re-expressing Skewed Data toImprove Symmetry (cont)
One way to make a skeweddistribution more symmetric isto re-express or transform thedata by applying a simplefunction(eg logarithmic function)1048708 Note the change in skewnessfrom the raw data (Figure411) to the transformed data(Figure 412)
What Can Go Wrong
bull 1048708 Donrsquot make a histogram of a categorical variablemdash
bull bar charts or pie charts should be used for
bull categorical data
bull 1048708 Donrsquot look for shape
bull center and spread
bull of a bar chart
What Can Go Wrong (cont)
bull 1048708 Donrsquot use bars in every displaymdashsave them for
bull histograms and bar charts
bull 1048708 Below is a badly drawn timeplot and the proper
bull histogram for the number of eagles sighted in a
bull collection of weeks
What Can Go Wrong (cont)
What Can Go Wrong (cont)
Choose a bin width appropriate to the data1048708 Changing the bin width changes theappearance of the histogram
What Can Go Wrong (cont)
1048708 Avoid inconsistent scaleseither within the display orwhen comparing twodisplays1048708 Label clearly so a readerknows what the plotdisplays1048708 Good intentions badplot
What have we learned
bull 1048708 Wersquove learned how to make a picture for quantitative databull to help us see the story the data have to Tellbull 1048708 We can display the distribution of quantitative data with abull histogram stem-and-leaf display or dotplotbull 1048708 Tell about a distribution by talking about shape centerbull spread and any unusual featuresbull 1048708 We can compare two quantitative distributions by lookingbull at side-by-side displays (plotted on the same scale)bull 1048708 Trends in a quantitative variable can be displayed in abull timeplot
Stem and leaf
bull Example
Skewed
bull A distribution is skewed if it is not symmetric and one tail stretched out further than the other
bull Skewed left- when the longer tail stretches to the left
bull Skewed right-when the longer tail stretched to the right
Examples
bull Skewed right
Skewed left
bull Left
All three
bull Examples
Funny example
bull httpwwwherkimershideawayorgapstatisticsymmsum99ymm111htm
New seating chart
bull httpwwwrandomorgintegers
Stem-and-Leaf Revisited
1048708 Compare the histogram and stem-and-leafdisplay for the pulse rates of 24 women at ahealth clinic Which graphical display do youprefer
Think Before You Draw Again
bull 1048708 Remember the ldquoMake a picturerdquo rulebull 1048708 Now that we have options for data displays
youbull need to Think carefully about which type ofbull display to makebull 1048708 Before making a stem-and-leaf display abull histogram or a dotplot check thebull 1048708 Quantitative Data Condition The data arebull values of a quantitative variable whose unitsbull are known
Constructing a Stem-and-Leaf Display
bull 1048708 First cut each data value into leading digits
bull (ldquostemsrdquo) and trailing digits (ldquoleavesrdquo)bull 1048708 Use the stems to label the binsbull 1048708 Use only one digit for each leafmdasheither
round orbull truncate the data values to one decimal
placebull after the stem
Center
bull A value that attempts the impossible by summarizing the entire distribution with a single number a ldquotypicalrdquo value
bull Measures include the mean and median
Spread
bull A numerical summary of how tightly the values are clustered around the center
bull Measures of spread include the IQR and standard deviation
Mode
bull a hump or local high pint in the shape of the distribution of a variable is called the mode The apparent location of modes can change as the scale of a histogram is changed
Unimodal
bull Having one mode
Bimodal
bull Distribution with two modes
Example
Uniform
1048708 A histogram that doesnrsquot appear to have any mode andin which all the bars are approximately the same heightis called uniform
Anything Unusual
bull Do any unusual features stick outbull 1048708 Sometimes itrsquos the unusual features that tellbull us something interesting or exciting about thebull databull 1048708 You should always mention any stragglers orbull outliers that stand off away from the body ofbull the distributionbull 1048708 Are there any gaps in the distribution If sobull we might have data from more than onebull group
Outliers
The following histogram has outliersmdashthere arethree cities in the leftmost bar
Outliers
bull Are extreme values that do not appear to belong to the rest of the data They may be unusual values that deserve further investigation or they may be just mistakes therersquos no obvious way to tell Do not delete them Outliers can affect many statistical analyses so you should always be alert to them
Outliers
bull Away from the main portion of data
Where is the Center of the Distribution
bull 1048708 If you had to pick a single number to describe allbull the data what would you pickbull 1048708 Itrsquos easy to find the center when a histogram isbull unimodal and symmetricmdashitrsquos right in the middlebull 1048708 On the other hand itrsquos not so easy to find thebull center of a skewed histogram or a histogram withbull more than one modebull 1048708 For now we will ldquoeyeballrdquo the center of thebull distribution In the next chapter we will find thebull center numerically
How Spread Out is the Distribution
bull 1048708 Variation matters and Statistics is about
bull variation
bull 1048708 Are the values of the distribution tightly clustered
bull around the center or more spread out
bull 1048708 In the next two chapters we will talk about
bull spreadhellip
Comparing Distributions
bull 1048708 Often we would like to compare two or morebull distributions instead of looking at one distributionbull by itselfbull 1048708 When looking at two or more distributions it isbull very important that the histograms have been putbull on the same scale Otherwise we cannot reallybull compare the two distributionsbull 1048708 When we compare distributions we talk about thebull shape center and spread of each distribution
Example
Compare thefollowingdistributions ofages for femaleand male heartattack patients
Compare thefollowingdistributions ofages for femaleand male heartattack patients
HOMEWORK
Web Pages Used
bull httpwwwfaoorgwairdocsilrix5469ex5469e38gif
bull httpwwwsciencebuddiesorgscience-fair-projectsdescriptive_statistics_filesBimodalDistjpg
bull httpimagesabsoluteastronomycomimagesencyclopediaimagesbbibimodalpng
bull httpuploadwikimediaorgwikipediacommonsbbcBimodal_geologicalPNG
Web Pages Used
bull httpmathworldwolframcomimageseps-gifOutlierHistogram_1000gif
Timeplots Order Please
bull 1048708 For some data sets we are interested in how the
bull data behave over time In these cases we
bull construct timeplots of the data
Re-expressing Skewed Data toImprove Symmetry
Re-expressing Skewed Data toImprove Symmetry (cont)
One way to make a skeweddistribution more symmetric isto re-express or transform thedata by applying a simplefunction(eg logarithmic function)1048708 Note the change in skewnessfrom the raw data (Figure411) to the transformed data(Figure 412)
What Can Go Wrong
bull 1048708 Donrsquot make a histogram of a categorical variablemdash
bull bar charts or pie charts should be used for
bull categorical data
bull 1048708 Donrsquot look for shape
bull center and spread
bull of a bar chart
What Can Go Wrong (cont)
bull 1048708 Donrsquot use bars in every displaymdashsave them for
bull histograms and bar charts
bull 1048708 Below is a badly drawn timeplot and the proper
bull histogram for the number of eagles sighted in a
bull collection of weeks
What Can Go Wrong (cont)
What Can Go Wrong (cont)
Choose a bin width appropriate to the data1048708 Changing the bin width changes theappearance of the histogram
What Can Go Wrong (cont)
1048708 Avoid inconsistent scaleseither within the display orwhen comparing twodisplays1048708 Label clearly so a readerknows what the plotdisplays1048708 Good intentions badplot
What have we learned
bull 1048708 Wersquove learned how to make a picture for quantitative databull to help us see the story the data have to Tellbull 1048708 We can display the distribution of quantitative data with abull histogram stem-and-leaf display or dotplotbull 1048708 Tell about a distribution by talking about shape centerbull spread and any unusual featuresbull 1048708 We can compare two quantitative distributions by lookingbull at side-by-side displays (plotted on the same scale)bull 1048708 Trends in a quantitative variable can be displayed in abull timeplot
Skewed
bull A distribution is skewed if it is not symmetric and one tail stretched out further than the other
bull Skewed left- when the longer tail stretches to the left
bull Skewed right-when the longer tail stretched to the right
Examples
bull Skewed right
Skewed left
bull Left
All three
bull Examples
Funny example
bull httpwwwherkimershideawayorgapstatisticsymmsum99ymm111htm
New seating chart
bull httpwwwrandomorgintegers
Stem-and-Leaf Revisited
1048708 Compare the histogram and stem-and-leafdisplay for the pulse rates of 24 women at ahealth clinic Which graphical display do youprefer
Think Before You Draw Again
bull 1048708 Remember the ldquoMake a picturerdquo rulebull 1048708 Now that we have options for data displays
youbull need to Think carefully about which type ofbull display to makebull 1048708 Before making a stem-and-leaf display abull histogram or a dotplot check thebull 1048708 Quantitative Data Condition The data arebull values of a quantitative variable whose unitsbull are known
Constructing a Stem-and-Leaf Display
bull 1048708 First cut each data value into leading digits
bull (ldquostemsrdquo) and trailing digits (ldquoleavesrdquo)bull 1048708 Use the stems to label the binsbull 1048708 Use only one digit for each leafmdasheither
round orbull truncate the data values to one decimal
placebull after the stem
Center
bull A value that attempts the impossible by summarizing the entire distribution with a single number a ldquotypicalrdquo value
bull Measures include the mean and median
Spread
bull A numerical summary of how tightly the values are clustered around the center
bull Measures of spread include the IQR and standard deviation
Mode
bull a hump or local high pint in the shape of the distribution of a variable is called the mode The apparent location of modes can change as the scale of a histogram is changed
Unimodal
bull Having one mode
Bimodal
bull Distribution with two modes
Example
Uniform
1048708 A histogram that doesnrsquot appear to have any mode andin which all the bars are approximately the same heightis called uniform
Anything Unusual
bull Do any unusual features stick outbull 1048708 Sometimes itrsquos the unusual features that tellbull us something interesting or exciting about thebull databull 1048708 You should always mention any stragglers orbull outliers that stand off away from the body ofbull the distributionbull 1048708 Are there any gaps in the distribution If sobull we might have data from more than onebull group
Outliers
The following histogram has outliersmdashthere arethree cities in the leftmost bar
Outliers
bull Are extreme values that do not appear to belong to the rest of the data They may be unusual values that deserve further investigation or they may be just mistakes therersquos no obvious way to tell Do not delete them Outliers can affect many statistical analyses so you should always be alert to them
Outliers
bull Away from the main portion of data
Where is the Center of the Distribution
bull 1048708 If you had to pick a single number to describe allbull the data what would you pickbull 1048708 Itrsquos easy to find the center when a histogram isbull unimodal and symmetricmdashitrsquos right in the middlebull 1048708 On the other hand itrsquos not so easy to find thebull center of a skewed histogram or a histogram withbull more than one modebull 1048708 For now we will ldquoeyeballrdquo the center of thebull distribution In the next chapter we will find thebull center numerically
How Spread Out is the Distribution
bull 1048708 Variation matters and Statistics is about
bull variation
bull 1048708 Are the values of the distribution tightly clustered
bull around the center or more spread out
bull 1048708 In the next two chapters we will talk about
bull spreadhellip
Comparing Distributions
bull 1048708 Often we would like to compare two or morebull distributions instead of looking at one distributionbull by itselfbull 1048708 When looking at two or more distributions it isbull very important that the histograms have been putbull on the same scale Otherwise we cannot reallybull compare the two distributionsbull 1048708 When we compare distributions we talk about thebull shape center and spread of each distribution
Example
Compare thefollowingdistributions ofages for femaleand male heartattack patients
Compare thefollowingdistributions ofages for femaleand male heartattack patients
HOMEWORK
Web Pages Used
bull httpwwwfaoorgwairdocsilrix5469ex5469e38gif
bull httpwwwsciencebuddiesorgscience-fair-projectsdescriptive_statistics_filesBimodalDistjpg
bull httpimagesabsoluteastronomycomimagesencyclopediaimagesbbibimodalpng
bull httpuploadwikimediaorgwikipediacommonsbbcBimodal_geologicalPNG
Web Pages Used
bull httpmathworldwolframcomimageseps-gifOutlierHistogram_1000gif
Timeplots Order Please
bull 1048708 For some data sets we are interested in how the
bull data behave over time In these cases we
bull construct timeplots of the data
Re-expressing Skewed Data toImprove Symmetry
Re-expressing Skewed Data toImprove Symmetry (cont)
One way to make a skeweddistribution more symmetric isto re-express or transform thedata by applying a simplefunction(eg logarithmic function)1048708 Note the change in skewnessfrom the raw data (Figure411) to the transformed data(Figure 412)
What Can Go Wrong
bull 1048708 Donrsquot make a histogram of a categorical variablemdash
bull bar charts or pie charts should be used for
bull categorical data
bull 1048708 Donrsquot look for shape
bull center and spread
bull of a bar chart
What Can Go Wrong (cont)
bull 1048708 Donrsquot use bars in every displaymdashsave them for
bull histograms and bar charts
bull 1048708 Below is a badly drawn timeplot and the proper
bull histogram for the number of eagles sighted in a
bull collection of weeks
What Can Go Wrong (cont)
What Can Go Wrong (cont)
Choose a bin width appropriate to the data1048708 Changing the bin width changes theappearance of the histogram
What Can Go Wrong (cont)
1048708 Avoid inconsistent scaleseither within the display orwhen comparing twodisplays1048708 Label clearly so a readerknows what the plotdisplays1048708 Good intentions badplot
What have we learned
bull 1048708 Wersquove learned how to make a picture for quantitative databull to help us see the story the data have to Tellbull 1048708 We can display the distribution of quantitative data with abull histogram stem-and-leaf display or dotplotbull 1048708 Tell about a distribution by talking about shape centerbull spread and any unusual featuresbull 1048708 We can compare two quantitative distributions by lookingbull at side-by-side displays (plotted on the same scale)bull 1048708 Trends in a quantitative variable can be displayed in abull timeplot
Examples
bull Skewed right
Skewed left
bull Left
All three
bull Examples
Funny example
bull httpwwwherkimershideawayorgapstatisticsymmsum99ymm111htm
New seating chart
bull httpwwwrandomorgintegers
Stem-and-Leaf Revisited
1048708 Compare the histogram and stem-and-leafdisplay for the pulse rates of 24 women at ahealth clinic Which graphical display do youprefer
Think Before You Draw Again
bull 1048708 Remember the ldquoMake a picturerdquo rulebull 1048708 Now that we have options for data displays
youbull need to Think carefully about which type ofbull display to makebull 1048708 Before making a stem-and-leaf display abull histogram or a dotplot check thebull 1048708 Quantitative Data Condition The data arebull values of a quantitative variable whose unitsbull are known
Constructing a Stem-and-Leaf Display
bull 1048708 First cut each data value into leading digits
bull (ldquostemsrdquo) and trailing digits (ldquoleavesrdquo)bull 1048708 Use the stems to label the binsbull 1048708 Use only one digit for each leafmdasheither
round orbull truncate the data values to one decimal
placebull after the stem
Center
bull A value that attempts the impossible by summarizing the entire distribution with a single number a ldquotypicalrdquo value
bull Measures include the mean and median
Spread
bull A numerical summary of how tightly the values are clustered around the center
bull Measures of spread include the IQR and standard deviation
Mode
bull a hump or local high pint in the shape of the distribution of a variable is called the mode The apparent location of modes can change as the scale of a histogram is changed
Unimodal
bull Having one mode
Bimodal
bull Distribution with two modes
Example
Uniform
1048708 A histogram that doesnrsquot appear to have any mode andin which all the bars are approximately the same heightis called uniform
Anything Unusual
bull Do any unusual features stick outbull 1048708 Sometimes itrsquos the unusual features that tellbull us something interesting or exciting about thebull databull 1048708 You should always mention any stragglers orbull outliers that stand off away from the body ofbull the distributionbull 1048708 Are there any gaps in the distribution If sobull we might have data from more than onebull group
Outliers
The following histogram has outliersmdashthere arethree cities in the leftmost bar
Outliers
bull Are extreme values that do not appear to belong to the rest of the data They may be unusual values that deserve further investigation or they may be just mistakes therersquos no obvious way to tell Do not delete them Outliers can affect many statistical analyses so you should always be alert to them
Outliers
bull Away from the main portion of data
Where is the Center of the Distribution
bull 1048708 If you had to pick a single number to describe allbull the data what would you pickbull 1048708 Itrsquos easy to find the center when a histogram isbull unimodal and symmetricmdashitrsquos right in the middlebull 1048708 On the other hand itrsquos not so easy to find thebull center of a skewed histogram or a histogram withbull more than one modebull 1048708 For now we will ldquoeyeballrdquo the center of thebull distribution In the next chapter we will find thebull center numerically
How Spread Out is the Distribution
bull 1048708 Variation matters and Statistics is about
bull variation
bull 1048708 Are the values of the distribution tightly clustered
bull around the center or more spread out
bull 1048708 In the next two chapters we will talk about
bull spreadhellip
Comparing Distributions
bull 1048708 Often we would like to compare two or morebull distributions instead of looking at one distributionbull by itselfbull 1048708 When looking at two or more distributions it isbull very important that the histograms have been putbull on the same scale Otherwise we cannot reallybull compare the two distributionsbull 1048708 When we compare distributions we talk about thebull shape center and spread of each distribution
Example
Compare thefollowingdistributions ofages for femaleand male heartattack patients
Compare thefollowingdistributions ofages for femaleand male heartattack patients
HOMEWORK
Web Pages Used
bull httpwwwfaoorgwairdocsilrix5469ex5469e38gif
bull httpwwwsciencebuddiesorgscience-fair-projectsdescriptive_statistics_filesBimodalDistjpg
bull httpimagesabsoluteastronomycomimagesencyclopediaimagesbbibimodalpng
bull httpuploadwikimediaorgwikipediacommonsbbcBimodal_geologicalPNG
Web Pages Used
bull httpmathworldwolframcomimageseps-gifOutlierHistogram_1000gif
Timeplots Order Please
bull 1048708 For some data sets we are interested in how the
bull data behave over time In these cases we
bull construct timeplots of the data
Re-expressing Skewed Data toImprove Symmetry
Re-expressing Skewed Data toImprove Symmetry (cont)
One way to make a skeweddistribution more symmetric isto re-express or transform thedata by applying a simplefunction(eg logarithmic function)1048708 Note the change in skewnessfrom the raw data (Figure411) to the transformed data(Figure 412)
What Can Go Wrong
bull 1048708 Donrsquot make a histogram of a categorical variablemdash
bull bar charts or pie charts should be used for
bull categorical data
bull 1048708 Donrsquot look for shape
bull center and spread
bull of a bar chart
What Can Go Wrong (cont)
bull 1048708 Donrsquot use bars in every displaymdashsave them for
bull histograms and bar charts
bull 1048708 Below is a badly drawn timeplot and the proper
bull histogram for the number of eagles sighted in a
bull collection of weeks
What Can Go Wrong (cont)
What Can Go Wrong (cont)
Choose a bin width appropriate to the data1048708 Changing the bin width changes theappearance of the histogram
What Can Go Wrong (cont)
1048708 Avoid inconsistent scaleseither within the display orwhen comparing twodisplays1048708 Label clearly so a readerknows what the plotdisplays1048708 Good intentions badplot
What have we learned
bull 1048708 Wersquove learned how to make a picture for quantitative databull to help us see the story the data have to Tellbull 1048708 We can display the distribution of quantitative data with abull histogram stem-and-leaf display or dotplotbull 1048708 Tell about a distribution by talking about shape centerbull spread and any unusual featuresbull 1048708 We can compare two quantitative distributions by lookingbull at side-by-side displays (plotted on the same scale)bull 1048708 Trends in a quantitative variable can be displayed in abull timeplot
Skewed left
bull Left
All three
bull Examples
Funny example
bull httpwwwherkimershideawayorgapstatisticsymmsum99ymm111htm
New seating chart
bull httpwwwrandomorgintegers
Stem-and-Leaf Revisited
1048708 Compare the histogram and stem-and-leafdisplay for the pulse rates of 24 women at ahealth clinic Which graphical display do youprefer
Think Before You Draw Again
bull 1048708 Remember the ldquoMake a picturerdquo rulebull 1048708 Now that we have options for data displays
youbull need to Think carefully about which type ofbull display to makebull 1048708 Before making a stem-and-leaf display abull histogram or a dotplot check thebull 1048708 Quantitative Data Condition The data arebull values of a quantitative variable whose unitsbull are known
Constructing a Stem-and-Leaf Display
bull 1048708 First cut each data value into leading digits
bull (ldquostemsrdquo) and trailing digits (ldquoleavesrdquo)bull 1048708 Use the stems to label the binsbull 1048708 Use only one digit for each leafmdasheither
round orbull truncate the data values to one decimal
placebull after the stem
Center
bull A value that attempts the impossible by summarizing the entire distribution with a single number a ldquotypicalrdquo value
bull Measures include the mean and median
Spread
bull A numerical summary of how tightly the values are clustered around the center
bull Measures of spread include the IQR and standard deviation
Mode
bull a hump or local high pint in the shape of the distribution of a variable is called the mode The apparent location of modes can change as the scale of a histogram is changed
Unimodal
bull Having one mode
Bimodal
bull Distribution with two modes
Example
Uniform
1048708 A histogram that doesnrsquot appear to have any mode andin which all the bars are approximately the same heightis called uniform
Anything Unusual
bull Do any unusual features stick outbull 1048708 Sometimes itrsquos the unusual features that tellbull us something interesting or exciting about thebull databull 1048708 You should always mention any stragglers orbull outliers that stand off away from the body ofbull the distributionbull 1048708 Are there any gaps in the distribution If sobull we might have data from more than onebull group
Outliers
The following histogram has outliersmdashthere arethree cities in the leftmost bar
Outliers
bull Are extreme values that do not appear to belong to the rest of the data They may be unusual values that deserve further investigation or they may be just mistakes therersquos no obvious way to tell Do not delete them Outliers can affect many statistical analyses so you should always be alert to them
Outliers
bull Away from the main portion of data
Where is the Center of the Distribution
bull 1048708 If you had to pick a single number to describe allbull the data what would you pickbull 1048708 Itrsquos easy to find the center when a histogram isbull unimodal and symmetricmdashitrsquos right in the middlebull 1048708 On the other hand itrsquos not so easy to find thebull center of a skewed histogram or a histogram withbull more than one modebull 1048708 For now we will ldquoeyeballrdquo the center of thebull distribution In the next chapter we will find thebull center numerically
How Spread Out is the Distribution
bull 1048708 Variation matters and Statistics is about
bull variation
bull 1048708 Are the values of the distribution tightly clustered
bull around the center or more spread out
bull 1048708 In the next two chapters we will talk about
bull spreadhellip
Comparing Distributions
bull 1048708 Often we would like to compare two or morebull distributions instead of looking at one distributionbull by itselfbull 1048708 When looking at two or more distributions it isbull very important that the histograms have been putbull on the same scale Otherwise we cannot reallybull compare the two distributionsbull 1048708 When we compare distributions we talk about thebull shape center and spread of each distribution
Example
Compare thefollowingdistributions ofages for femaleand male heartattack patients
Compare thefollowingdistributions ofages for femaleand male heartattack patients
HOMEWORK
Web Pages Used
bull httpwwwfaoorgwairdocsilrix5469ex5469e38gif
bull httpwwwsciencebuddiesorgscience-fair-projectsdescriptive_statistics_filesBimodalDistjpg
bull httpimagesabsoluteastronomycomimagesencyclopediaimagesbbibimodalpng
bull httpuploadwikimediaorgwikipediacommonsbbcBimodal_geologicalPNG
Web Pages Used
bull httpmathworldwolframcomimageseps-gifOutlierHistogram_1000gif
Timeplots Order Please
bull 1048708 For some data sets we are interested in how the
bull data behave over time In these cases we
bull construct timeplots of the data
Re-expressing Skewed Data toImprove Symmetry
Re-expressing Skewed Data toImprove Symmetry (cont)
One way to make a skeweddistribution more symmetric isto re-express or transform thedata by applying a simplefunction(eg logarithmic function)1048708 Note the change in skewnessfrom the raw data (Figure411) to the transformed data(Figure 412)
What Can Go Wrong
bull 1048708 Donrsquot make a histogram of a categorical variablemdash
bull bar charts or pie charts should be used for
bull categorical data
bull 1048708 Donrsquot look for shape
bull center and spread
bull of a bar chart
What Can Go Wrong (cont)
bull 1048708 Donrsquot use bars in every displaymdashsave them for
bull histograms and bar charts
bull 1048708 Below is a badly drawn timeplot and the proper
bull histogram for the number of eagles sighted in a
bull collection of weeks
What Can Go Wrong (cont)
What Can Go Wrong (cont)
Choose a bin width appropriate to the data1048708 Changing the bin width changes theappearance of the histogram
What Can Go Wrong (cont)
1048708 Avoid inconsistent scaleseither within the display orwhen comparing twodisplays1048708 Label clearly so a readerknows what the plotdisplays1048708 Good intentions badplot
What have we learned
bull 1048708 Wersquove learned how to make a picture for quantitative databull to help us see the story the data have to Tellbull 1048708 We can display the distribution of quantitative data with abull histogram stem-and-leaf display or dotplotbull 1048708 Tell about a distribution by talking about shape centerbull spread and any unusual featuresbull 1048708 We can compare two quantitative distributions by lookingbull at side-by-side displays (plotted on the same scale)bull 1048708 Trends in a quantitative variable can be displayed in abull timeplot
All three
bull Examples
Funny example
bull httpwwwherkimershideawayorgapstatisticsymmsum99ymm111htm
New seating chart
bull httpwwwrandomorgintegers
Stem-and-Leaf Revisited
1048708 Compare the histogram and stem-and-leafdisplay for the pulse rates of 24 women at ahealth clinic Which graphical display do youprefer
Think Before You Draw Again
bull 1048708 Remember the ldquoMake a picturerdquo rulebull 1048708 Now that we have options for data displays
youbull need to Think carefully about which type ofbull display to makebull 1048708 Before making a stem-and-leaf display abull histogram or a dotplot check thebull 1048708 Quantitative Data Condition The data arebull values of a quantitative variable whose unitsbull are known
Constructing a Stem-and-Leaf Display
bull 1048708 First cut each data value into leading digits
bull (ldquostemsrdquo) and trailing digits (ldquoleavesrdquo)bull 1048708 Use the stems to label the binsbull 1048708 Use only one digit for each leafmdasheither
round orbull truncate the data values to one decimal
placebull after the stem
Center
bull A value that attempts the impossible by summarizing the entire distribution with a single number a ldquotypicalrdquo value
bull Measures include the mean and median
Spread
bull A numerical summary of how tightly the values are clustered around the center
bull Measures of spread include the IQR and standard deviation
Mode
bull a hump or local high pint in the shape of the distribution of a variable is called the mode The apparent location of modes can change as the scale of a histogram is changed
Unimodal
bull Having one mode
Bimodal
bull Distribution with two modes
Example
Uniform
1048708 A histogram that doesnrsquot appear to have any mode andin which all the bars are approximately the same heightis called uniform
Anything Unusual
bull Do any unusual features stick outbull 1048708 Sometimes itrsquos the unusual features that tellbull us something interesting or exciting about thebull databull 1048708 You should always mention any stragglers orbull outliers that stand off away from the body ofbull the distributionbull 1048708 Are there any gaps in the distribution If sobull we might have data from more than onebull group
Outliers
The following histogram has outliersmdashthere arethree cities in the leftmost bar
Outliers
bull Are extreme values that do not appear to belong to the rest of the data They may be unusual values that deserve further investigation or they may be just mistakes therersquos no obvious way to tell Do not delete them Outliers can affect many statistical analyses so you should always be alert to them
Outliers
bull Away from the main portion of data
Where is the Center of the Distribution
bull 1048708 If you had to pick a single number to describe allbull the data what would you pickbull 1048708 Itrsquos easy to find the center when a histogram isbull unimodal and symmetricmdashitrsquos right in the middlebull 1048708 On the other hand itrsquos not so easy to find thebull center of a skewed histogram or a histogram withbull more than one modebull 1048708 For now we will ldquoeyeballrdquo the center of thebull distribution In the next chapter we will find thebull center numerically
How Spread Out is the Distribution
bull 1048708 Variation matters and Statistics is about
bull variation
bull 1048708 Are the values of the distribution tightly clustered
bull around the center or more spread out
bull 1048708 In the next two chapters we will talk about
bull spreadhellip
Comparing Distributions
bull 1048708 Often we would like to compare two or morebull distributions instead of looking at one distributionbull by itselfbull 1048708 When looking at two or more distributions it isbull very important that the histograms have been putbull on the same scale Otherwise we cannot reallybull compare the two distributionsbull 1048708 When we compare distributions we talk about thebull shape center and spread of each distribution
Example
Compare thefollowingdistributions ofages for femaleand male heartattack patients
Compare thefollowingdistributions ofages for femaleand male heartattack patients
HOMEWORK
Web Pages Used
bull httpwwwfaoorgwairdocsilrix5469ex5469e38gif
bull httpwwwsciencebuddiesorgscience-fair-projectsdescriptive_statistics_filesBimodalDistjpg
bull httpimagesabsoluteastronomycomimagesencyclopediaimagesbbibimodalpng
bull httpuploadwikimediaorgwikipediacommonsbbcBimodal_geologicalPNG
Web Pages Used
bull httpmathworldwolframcomimageseps-gifOutlierHistogram_1000gif
Timeplots Order Please
bull 1048708 For some data sets we are interested in how the
bull data behave over time In these cases we
bull construct timeplots of the data
Re-expressing Skewed Data toImprove Symmetry
Re-expressing Skewed Data toImprove Symmetry (cont)
One way to make a skeweddistribution more symmetric isto re-express or transform thedata by applying a simplefunction(eg logarithmic function)1048708 Note the change in skewnessfrom the raw data (Figure411) to the transformed data(Figure 412)
What Can Go Wrong
bull 1048708 Donrsquot make a histogram of a categorical variablemdash
bull bar charts or pie charts should be used for
bull categorical data
bull 1048708 Donrsquot look for shape
bull center and spread
bull of a bar chart
What Can Go Wrong (cont)
bull 1048708 Donrsquot use bars in every displaymdashsave them for
bull histograms and bar charts
bull 1048708 Below is a badly drawn timeplot and the proper
bull histogram for the number of eagles sighted in a
bull collection of weeks
What Can Go Wrong (cont)
What Can Go Wrong (cont)
Choose a bin width appropriate to the data1048708 Changing the bin width changes theappearance of the histogram
What Can Go Wrong (cont)
1048708 Avoid inconsistent scaleseither within the display orwhen comparing twodisplays1048708 Label clearly so a readerknows what the plotdisplays1048708 Good intentions badplot
What have we learned
bull 1048708 Wersquove learned how to make a picture for quantitative databull to help us see the story the data have to Tellbull 1048708 We can display the distribution of quantitative data with abull histogram stem-and-leaf display or dotplotbull 1048708 Tell about a distribution by talking about shape centerbull spread and any unusual featuresbull 1048708 We can compare two quantitative distributions by lookingbull at side-by-side displays (plotted on the same scale)bull 1048708 Trends in a quantitative variable can be displayed in abull timeplot
Funny example
bull httpwwwherkimershideawayorgapstatisticsymmsum99ymm111htm
New seating chart
bull httpwwwrandomorgintegers
Stem-and-Leaf Revisited
1048708 Compare the histogram and stem-and-leafdisplay for the pulse rates of 24 women at ahealth clinic Which graphical display do youprefer
Think Before You Draw Again
bull 1048708 Remember the ldquoMake a picturerdquo rulebull 1048708 Now that we have options for data displays
youbull need to Think carefully about which type ofbull display to makebull 1048708 Before making a stem-and-leaf display abull histogram or a dotplot check thebull 1048708 Quantitative Data Condition The data arebull values of a quantitative variable whose unitsbull are known
Constructing a Stem-and-Leaf Display
bull 1048708 First cut each data value into leading digits
bull (ldquostemsrdquo) and trailing digits (ldquoleavesrdquo)bull 1048708 Use the stems to label the binsbull 1048708 Use only one digit for each leafmdasheither
round orbull truncate the data values to one decimal
placebull after the stem
Center
bull A value that attempts the impossible by summarizing the entire distribution with a single number a ldquotypicalrdquo value
bull Measures include the mean and median
Spread
bull A numerical summary of how tightly the values are clustered around the center
bull Measures of spread include the IQR and standard deviation
Mode
bull a hump or local high pint in the shape of the distribution of a variable is called the mode The apparent location of modes can change as the scale of a histogram is changed
Unimodal
bull Having one mode
Bimodal
bull Distribution with two modes
Example
Uniform
1048708 A histogram that doesnrsquot appear to have any mode andin which all the bars are approximately the same heightis called uniform
Anything Unusual
bull Do any unusual features stick outbull 1048708 Sometimes itrsquos the unusual features that tellbull us something interesting or exciting about thebull databull 1048708 You should always mention any stragglers orbull outliers that stand off away from the body ofbull the distributionbull 1048708 Are there any gaps in the distribution If sobull we might have data from more than onebull group
Outliers
The following histogram has outliersmdashthere arethree cities in the leftmost bar
Outliers
bull Are extreme values that do not appear to belong to the rest of the data They may be unusual values that deserve further investigation or they may be just mistakes therersquos no obvious way to tell Do not delete them Outliers can affect many statistical analyses so you should always be alert to them
Outliers
bull Away from the main portion of data
Where is the Center of the Distribution
bull 1048708 If you had to pick a single number to describe allbull the data what would you pickbull 1048708 Itrsquos easy to find the center when a histogram isbull unimodal and symmetricmdashitrsquos right in the middlebull 1048708 On the other hand itrsquos not so easy to find thebull center of a skewed histogram or a histogram withbull more than one modebull 1048708 For now we will ldquoeyeballrdquo the center of thebull distribution In the next chapter we will find thebull center numerically
How Spread Out is the Distribution
bull 1048708 Variation matters and Statistics is about
bull variation
bull 1048708 Are the values of the distribution tightly clustered
bull around the center or more spread out
bull 1048708 In the next two chapters we will talk about
bull spreadhellip
Comparing Distributions
bull 1048708 Often we would like to compare two or morebull distributions instead of looking at one distributionbull by itselfbull 1048708 When looking at two or more distributions it isbull very important that the histograms have been putbull on the same scale Otherwise we cannot reallybull compare the two distributionsbull 1048708 When we compare distributions we talk about thebull shape center and spread of each distribution
Example
Compare thefollowingdistributions ofages for femaleand male heartattack patients
Compare thefollowingdistributions ofages for femaleand male heartattack patients
HOMEWORK
Web Pages Used
bull httpwwwfaoorgwairdocsilrix5469ex5469e38gif
bull httpwwwsciencebuddiesorgscience-fair-projectsdescriptive_statistics_filesBimodalDistjpg
bull httpimagesabsoluteastronomycomimagesencyclopediaimagesbbibimodalpng
bull httpuploadwikimediaorgwikipediacommonsbbcBimodal_geologicalPNG
Web Pages Used
bull httpmathworldwolframcomimageseps-gifOutlierHistogram_1000gif
Timeplots Order Please
bull 1048708 For some data sets we are interested in how the
bull data behave over time In these cases we
bull construct timeplots of the data
Re-expressing Skewed Data toImprove Symmetry
Re-expressing Skewed Data toImprove Symmetry (cont)
One way to make a skeweddistribution more symmetric isto re-express or transform thedata by applying a simplefunction(eg logarithmic function)1048708 Note the change in skewnessfrom the raw data (Figure411) to the transformed data(Figure 412)
What Can Go Wrong
bull 1048708 Donrsquot make a histogram of a categorical variablemdash
bull bar charts or pie charts should be used for
bull categorical data
bull 1048708 Donrsquot look for shape
bull center and spread
bull of a bar chart
What Can Go Wrong (cont)
bull 1048708 Donrsquot use bars in every displaymdashsave them for
bull histograms and bar charts
bull 1048708 Below is a badly drawn timeplot and the proper
bull histogram for the number of eagles sighted in a
bull collection of weeks
What Can Go Wrong (cont)
What Can Go Wrong (cont)
Choose a bin width appropriate to the data1048708 Changing the bin width changes theappearance of the histogram
What Can Go Wrong (cont)
1048708 Avoid inconsistent scaleseither within the display orwhen comparing twodisplays1048708 Label clearly so a readerknows what the plotdisplays1048708 Good intentions badplot
What have we learned
bull 1048708 Wersquove learned how to make a picture for quantitative databull to help us see the story the data have to Tellbull 1048708 We can display the distribution of quantitative data with abull histogram stem-and-leaf display or dotplotbull 1048708 Tell about a distribution by talking about shape centerbull spread and any unusual featuresbull 1048708 We can compare two quantitative distributions by lookingbull at side-by-side displays (plotted on the same scale)bull 1048708 Trends in a quantitative variable can be displayed in abull timeplot
New seating chart
bull httpwwwrandomorgintegers
Stem-and-Leaf Revisited
1048708 Compare the histogram and stem-and-leafdisplay for the pulse rates of 24 women at ahealth clinic Which graphical display do youprefer
Think Before You Draw Again
bull 1048708 Remember the ldquoMake a picturerdquo rulebull 1048708 Now that we have options for data displays
youbull need to Think carefully about which type ofbull display to makebull 1048708 Before making a stem-and-leaf display abull histogram or a dotplot check thebull 1048708 Quantitative Data Condition The data arebull values of a quantitative variable whose unitsbull are known
Constructing a Stem-and-Leaf Display
bull 1048708 First cut each data value into leading digits
bull (ldquostemsrdquo) and trailing digits (ldquoleavesrdquo)bull 1048708 Use the stems to label the binsbull 1048708 Use only one digit for each leafmdasheither
round orbull truncate the data values to one decimal
placebull after the stem
Center
bull A value that attempts the impossible by summarizing the entire distribution with a single number a ldquotypicalrdquo value
bull Measures include the mean and median
Spread
bull A numerical summary of how tightly the values are clustered around the center
bull Measures of spread include the IQR and standard deviation
Mode
bull a hump or local high pint in the shape of the distribution of a variable is called the mode The apparent location of modes can change as the scale of a histogram is changed
Unimodal
bull Having one mode
Bimodal
bull Distribution with two modes
Example
Uniform
1048708 A histogram that doesnrsquot appear to have any mode andin which all the bars are approximately the same heightis called uniform
Anything Unusual
bull Do any unusual features stick outbull 1048708 Sometimes itrsquos the unusual features that tellbull us something interesting or exciting about thebull databull 1048708 You should always mention any stragglers orbull outliers that stand off away from the body ofbull the distributionbull 1048708 Are there any gaps in the distribution If sobull we might have data from more than onebull group
Outliers
The following histogram has outliersmdashthere arethree cities in the leftmost bar
Outliers
bull Are extreme values that do not appear to belong to the rest of the data They may be unusual values that deserve further investigation or they may be just mistakes therersquos no obvious way to tell Do not delete them Outliers can affect many statistical analyses so you should always be alert to them
Outliers
bull Away from the main portion of data
Where is the Center of the Distribution
bull 1048708 If you had to pick a single number to describe allbull the data what would you pickbull 1048708 Itrsquos easy to find the center when a histogram isbull unimodal and symmetricmdashitrsquos right in the middlebull 1048708 On the other hand itrsquos not so easy to find thebull center of a skewed histogram or a histogram withbull more than one modebull 1048708 For now we will ldquoeyeballrdquo the center of thebull distribution In the next chapter we will find thebull center numerically
How Spread Out is the Distribution
bull 1048708 Variation matters and Statistics is about
bull variation
bull 1048708 Are the values of the distribution tightly clustered
bull around the center or more spread out
bull 1048708 In the next two chapters we will talk about
bull spreadhellip
Comparing Distributions
bull 1048708 Often we would like to compare two or morebull distributions instead of looking at one distributionbull by itselfbull 1048708 When looking at two or more distributions it isbull very important that the histograms have been putbull on the same scale Otherwise we cannot reallybull compare the two distributionsbull 1048708 When we compare distributions we talk about thebull shape center and spread of each distribution
Example
Compare thefollowingdistributions ofages for femaleand male heartattack patients
Compare thefollowingdistributions ofages for femaleand male heartattack patients
HOMEWORK
Web Pages Used
bull httpwwwfaoorgwairdocsilrix5469ex5469e38gif
bull httpwwwsciencebuddiesorgscience-fair-projectsdescriptive_statistics_filesBimodalDistjpg
bull httpimagesabsoluteastronomycomimagesencyclopediaimagesbbibimodalpng
bull httpuploadwikimediaorgwikipediacommonsbbcBimodal_geologicalPNG
Web Pages Used
bull httpmathworldwolframcomimageseps-gifOutlierHistogram_1000gif
Timeplots Order Please
bull 1048708 For some data sets we are interested in how the
bull data behave over time In these cases we
bull construct timeplots of the data
Re-expressing Skewed Data toImprove Symmetry
Re-expressing Skewed Data toImprove Symmetry (cont)
One way to make a skeweddistribution more symmetric isto re-express or transform thedata by applying a simplefunction(eg logarithmic function)1048708 Note the change in skewnessfrom the raw data (Figure411) to the transformed data(Figure 412)
What Can Go Wrong
bull 1048708 Donrsquot make a histogram of a categorical variablemdash
bull bar charts or pie charts should be used for
bull categorical data
bull 1048708 Donrsquot look for shape
bull center and spread
bull of a bar chart
What Can Go Wrong (cont)
bull 1048708 Donrsquot use bars in every displaymdashsave them for
bull histograms and bar charts
bull 1048708 Below is a badly drawn timeplot and the proper
bull histogram for the number of eagles sighted in a
bull collection of weeks
What Can Go Wrong (cont)
What Can Go Wrong (cont)
Choose a bin width appropriate to the data1048708 Changing the bin width changes theappearance of the histogram
What Can Go Wrong (cont)
1048708 Avoid inconsistent scaleseither within the display orwhen comparing twodisplays1048708 Label clearly so a readerknows what the plotdisplays1048708 Good intentions badplot
What have we learned
bull 1048708 Wersquove learned how to make a picture for quantitative databull to help us see the story the data have to Tellbull 1048708 We can display the distribution of quantitative data with abull histogram stem-and-leaf display or dotplotbull 1048708 Tell about a distribution by talking about shape centerbull spread and any unusual featuresbull 1048708 We can compare two quantitative distributions by lookingbull at side-by-side displays (plotted on the same scale)bull 1048708 Trends in a quantitative variable can be displayed in abull timeplot
Stem-and-Leaf Revisited
1048708 Compare the histogram and stem-and-leafdisplay for the pulse rates of 24 women at ahealth clinic Which graphical display do youprefer
Think Before You Draw Again
bull 1048708 Remember the ldquoMake a picturerdquo rulebull 1048708 Now that we have options for data displays
youbull need to Think carefully about which type ofbull display to makebull 1048708 Before making a stem-and-leaf display abull histogram or a dotplot check thebull 1048708 Quantitative Data Condition The data arebull values of a quantitative variable whose unitsbull are known
Constructing a Stem-and-Leaf Display
bull 1048708 First cut each data value into leading digits
bull (ldquostemsrdquo) and trailing digits (ldquoleavesrdquo)bull 1048708 Use the stems to label the binsbull 1048708 Use only one digit for each leafmdasheither
round orbull truncate the data values to one decimal
placebull after the stem
Center
bull A value that attempts the impossible by summarizing the entire distribution with a single number a ldquotypicalrdquo value
bull Measures include the mean and median
Spread
bull A numerical summary of how tightly the values are clustered around the center
bull Measures of spread include the IQR and standard deviation
Mode
bull a hump or local high pint in the shape of the distribution of a variable is called the mode The apparent location of modes can change as the scale of a histogram is changed
Unimodal
bull Having one mode
Bimodal
bull Distribution with two modes
Example
Uniform
1048708 A histogram that doesnrsquot appear to have any mode andin which all the bars are approximately the same heightis called uniform
Anything Unusual
bull Do any unusual features stick outbull 1048708 Sometimes itrsquos the unusual features that tellbull us something interesting or exciting about thebull databull 1048708 You should always mention any stragglers orbull outliers that stand off away from the body ofbull the distributionbull 1048708 Are there any gaps in the distribution If sobull we might have data from more than onebull group
Outliers
The following histogram has outliersmdashthere arethree cities in the leftmost bar
Outliers
bull Are extreme values that do not appear to belong to the rest of the data They may be unusual values that deserve further investigation or they may be just mistakes therersquos no obvious way to tell Do not delete them Outliers can affect many statistical analyses so you should always be alert to them
Outliers
bull Away from the main portion of data
Where is the Center of the Distribution
bull 1048708 If you had to pick a single number to describe allbull the data what would you pickbull 1048708 Itrsquos easy to find the center when a histogram isbull unimodal and symmetricmdashitrsquos right in the middlebull 1048708 On the other hand itrsquos not so easy to find thebull center of a skewed histogram or a histogram withbull more than one modebull 1048708 For now we will ldquoeyeballrdquo the center of thebull distribution In the next chapter we will find thebull center numerically
How Spread Out is the Distribution
bull 1048708 Variation matters and Statistics is about
bull variation
bull 1048708 Are the values of the distribution tightly clustered
bull around the center or more spread out
bull 1048708 In the next two chapters we will talk about
bull spreadhellip
Comparing Distributions
bull 1048708 Often we would like to compare two or morebull distributions instead of looking at one distributionbull by itselfbull 1048708 When looking at two or more distributions it isbull very important that the histograms have been putbull on the same scale Otherwise we cannot reallybull compare the two distributionsbull 1048708 When we compare distributions we talk about thebull shape center and spread of each distribution
Example
Compare thefollowingdistributions ofages for femaleand male heartattack patients
Compare thefollowingdistributions ofages for femaleand male heartattack patients
HOMEWORK
Web Pages Used
bull httpwwwfaoorgwairdocsilrix5469ex5469e38gif
bull httpwwwsciencebuddiesorgscience-fair-projectsdescriptive_statistics_filesBimodalDistjpg
bull httpimagesabsoluteastronomycomimagesencyclopediaimagesbbibimodalpng
bull httpuploadwikimediaorgwikipediacommonsbbcBimodal_geologicalPNG
Web Pages Used
bull httpmathworldwolframcomimageseps-gifOutlierHistogram_1000gif
Timeplots Order Please
bull 1048708 For some data sets we are interested in how the
bull data behave over time In these cases we
bull construct timeplots of the data
Re-expressing Skewed Data toImprove Symmetry
Re-expressing Skewed Data toImprove Symmetry (cont)
One way to make a skeweddistribution more symmetric isto re-express or transform thedata by applying a simplefunction(eg logarithmic function)1048708 Note the change in skewnessfrom the raw data (Figure411) to the transformed data(Figure 412)
What Can Go Wrong
bull 1048708 Donrsquot make a histogram of a categorical variablemdash
bull bar charts or pie charts should be used for
bull categorical data
bull 1048708 Donrsquot look for shape
bull center and spread
bull of a bar chart
What Can Go Wrong (cont)
bull 1048708 Donrsquot use bars in every displaymdashsave them for
bull histograms and bar charts
bull 1048708 Below is a badly drawn timeplot and the proper
bull histogram for the number of eagles sighted in a
bull collection of weeks
What Can Go Wrong (cont)
What Can Go Wrong (cont)
Choose a bin width appropriate to the data1048708 Changing the bin width changes theappearance of the histogram
What Can Go Wrong (cont)
1048708 Avoid inconsistent scaleseither within the display orwhen comparing twodisplays1048708 Label clearly so a readerknows what the plotdisplays1048708 Good intentions badplot
What have we learned
bull 1048708 Wersquove learned how to make a picture for quantitative databull to help us see the story the data have to Tellbull 1048708 We can display the distribution of quantitative data with abull histogram stem-and-leaf display or dotplotbull 1048708 Tell about a distribution by talking about shape centerbull spread and any unusual featuresbull 1048708 We can compare two quantitative distributions by lookingbull at side-by-side displays (plotted on the same scale)bull 1048708 Trends in a quantitative variable can be displayed in abull timeplot
Think Before You Draw Again
bull 1048708 Remember the ldquoMake a picturerdquo rulebull 1048708 Now that we have options for data displays
youbull need to Think carefully about which type ofbull display to makebull 1048708 Before making a stem-and-leaf display abull histogram or a dotplot check thebull 1048708 Quantitative Data Condition The data arebull values of a quantitative variable whose unitsbull are known
Constructing a Stem-and-Leaf Display
bull 1048708 First cut each data value into leading digits
bull (ldquostemsrdquo) and trailing digits (ldquoleavesrdquo)bull 1048708 Use the stems to label the binsbull 1048708 Use only one digit for each leafmdasheither
round orbull truncate the data values to one decimal
placebull after the stem
Center
bull A value that attempts the impossible by summarizing the entire distribution with a single number a ldquotypicalrdquo value
bull Measures include the mean and median
Spread
bull A numerical summary of how tightly the values are clustered around the center
bull Measures of spread include the IQR and standard deviation
Mode
bull a hump or local high pint in the shape of the distribution of a variable is called the mode The apparent location of modes can change as the scale of a histogram is changed
Unimodal
bull Having one mode
Bimodal
bull Distribution with two modes
Example
Uniform
1048708 A histogram that doesnrsquot appear to have any mode andin which all the bars are approximately the same heightis called uniform
Anything Unusual
bull Do any unusual features stick outbull 1048708 Sometimes itrsquos the unusual features that tellbull us something interesting or exciting about thebull databull 1048708 You should always mention any stragglers orbull outliers that stand off away from the body ofbull the distributionbull 1048708 Are there any gaps in the distribution If sobull we might have data from more than onebull group
Outliers
The following histogram has outliersmdashthere arethree cities in the leftmost bar
Outliers
bull Are extreme values that do not appear to belong to the rest of the data They may be unusual values that deserve further investigation or they may be just mistakes therersquos no obvious way to tell Do not delete them Outliers can affect many statistical analyses so you should always be alert to them
Outliers
bull Away from the main portion of data
Where is the Center of the Distribution
bull 1048708 If you had to pick a single number to describe allbull the data what would you pickbull 1048708 Itrsquos easy to find the center when a histogram isbull unimodal and symmetricmdashitrsquos right in the middlebull 1048708 On the other hand itrsquos not so easy to find thebull center of a skewed histogram or a histogram withbull more than one modebull 1048708 For now we will ldquoeyeballrdquo the center of thebull distribution In the next chapter we will find thebull center numerically
How Spread Out is the Distribution
bull 1048708 Variation matters and Statistics is about
bull variation
bull 1048708 Are the values of the distribution tightly clustered
bull around the center or more spread out
bull 1048708 In the next two chapters we will talk about
bull spreadhellip
Comparing Distributions
bull 1048708 Often we would like to compare two or morebull distributions instead of looking at one distributionbull by itselfbull 1048708 When looking at two or more distributions it isbull very important that the histograms have been putbull on the same scale Otherwise we cannot reallybull compare the two distributionsbull 1048708 When we compare distributions we talk about thebull shape center and spread of each distribution
Example
Compare thefollowingdistributions ofages for femaleand male heartattack patients
Compare thefollowingdistributions ofages for femaleand male heartattack patients
HOMEWORK
Web Pages Used
bull httpwwwfaoorgwairdocsilrix5469ex5469e38gif
bull httpwwwsciencebuddiesorgscience-fair-projectsdescriptive_statistics_filesBimodalDistjpg
bull httpimagesabsoluteastronomycomimagesencyclopediaimagesbbibimodalpng
bull httpuploadwikimediaorgwikipediacommonsbbcBimodal_geologicalPNG
Web Pages Used
bull httpmathworldwolframcomimageseps-gifOutlierHistogram_1000gif
Timeplots Order Please
bull 1048708 For some data sets we are interested in how the
bull data behave over time In these cases we
bull construct timeplots of the data
Re-expressing Skewed Data toImprove Symmetry
Re-expressing Skewed Data toImprove Symmetry (cont)
One way to make a skeweddistribution more symmetric isto re-express or transform thedata by applying a simplefunction(eg logarithmic function)1048708 Note the change in skewnessfrom the raw data (Figure411) to the transformed data(Figure 412)
What Can Go Wrong
bull 1048708 Donrsquot make a histogram of a categorical variablemdash
bull bar charts or pie charts should be used for
bull categorical data
bull 1048708 Donrsquot look for shape
bull center and spread
bull of a bar chart
What Can Go Wrong (cont)
bull 1048708 Donrsquot use bars in every displaymdashsave them for
bull histograms and bar charts
bull 1048708 Below is a badly drawn timeplot and the proper
bull histogram for the number of eagles sighted in a
bull collection of weeks
What Can Go Wrong (cont)
What Can Go Wrong (cont)
Choose a bin width appropriate to the data1048708 Changing the bin width changes theappearance of the histogram
What Can Go Wrong (cont)
1048708 Avoid inconsistent scaleseither within the display orwhen comparing twodisplays1048708 Label clearly so a readerknows what the plotdisplays1048708 Good intentions badplot
What have we learned
bull 1048708 Wersquove learned how to make a picture for quantitative databull to help us see the story the data have to Tellbull 1048708 We can display the distribution of quantitative data with abull histogram stem-and-leaf display or dotplotbull 1048708 Tell about a distribution by talking about shape centerbull spread and any unusual featuresbull 1048708 We can compare two quantitative distributions by lookingbull at side-by-side displays (plotted on the same scale)bull 1048708 Trends in a quantitative variable can be displayed in abull timeplot
Constructing a Stem-and-Leaf Display
bull 1048708 First cut each data value into leading digits
bull (ldquostemsrdquo) and trailing digits (ldquoleavesrdquo)bull 1048708 Use the stems to label the binsbull 1048708 Use only one digit for each leafmdasheither
round orbull truncate the data values to one decimal
placebull after the stem
Center
bull A value that attempts the impossible by summarizing the entire distribution with a single number a ldquotypicalrdquo value
bull Measures include the mean and median
Spread
bull A numerical summary of how tightly the values are clustered around the center
bull Measures of spread include the IQR and standard deviation
Mode
bull a hump or local high pint in the shape of the distribution of a variable is called the mode The apparent location of modes can change as the scale of a histogram is changed
Unimodal
bull Having one mode
Bimodal
bull Distribution with two modes
Example
Uniform
1048708 A histogram that doesnrsquot appear to have any mode andin which all the bars are approximately the same heightis called uniform
Anything Unusual
bull Do any unusual features stick outbull 1048708 Sometimes itrsquos the unusual features that tellbull us something interesting or exciting about thebull databull 1048708 You should always mention any stragglers orbull outliers that stand off away from the body ofbull the distributionbull 1048708 Are there any gaps in the distribution If sobull we might have data from more than onebull group
Outliers
The following histogram has outliersmdashthere arethree cities in the leftmost bar
Outliers
bull Are extreme values that do not appear to belong to the rest of the data They may be unusual values that deserve further investigation or they may be just mistakes therersquos no obvious way to tell Do not delete them Outliers can affect many statistical analyses so you should always be alert to them
Outliers
bull Away from the main portion of data
Where is the Center of the Distribution
bull 1048708 If you had to pick a single number to describe allbull the data what would you pickbull 1048708 Itrsquos easy to find the center when a histogram isbull unimodal and symmetricmdashitrsquos right in the middlebull 1048708 On the other hand itrsquos not so easy to find thebull center of a skewed histogram or a histogram withbull more than one modebull 1048708 For now we will ldquoeyeballrdquo the center of thebull distribution In the next chapter we will find thebull center numerically
How Spread Out is the Distribution
bull 1048708 Variation matters and Statistics is about
bull variation
bull 1048708 Are the values of the distribution tightly clustered
bull around the center or more spread out
bull 1048708 In the next two chapters we will talk about
bull spreadhellip
Comparing Distributions
bull 1048708 Often we would like to compare two or morebull distributions instead of looking at one distributionbull by itselfbull 1048708 When looking at two or more distributions it isbull very important that the histograms have been putbull on the same scale Otherwise we cannot reallybull compare the two distributionsbull 1048708 When we compare distributions we talk about thebull shape center and spread of each distribution
Example
Compare thefollowingdistributions ofages for femaleand male heartattack patients
Compare thefollowingdistributions ofages for femaleand male heartattack patients
HOMEWORK
Web Pages Used
bull httpwwwfaoorgwairdocsilrix5469ex5469e38gif
bull httpwwwsciencebuddiesorgscience-fair-projectsdescriptive_statistics_filesBimodalDistjpg
bull httpimagesabsoluteastronomycomimagesencyclopediaimagesbbibimodalpng
bull httpuploadwikimediaorgwikipediacommonsbbcBimodal_geologicalPNG
Web Pages Used
bull httpmathworldwolframcomimageseps-gifOutlierHistogram_1000gif
Timeplots Order Please
bull 1048708 For some data sets we are interested in how the
bull data behave over time In these cases we
bull construct timeplots of the data
Re-expressing Skewed Data toImprove Symmetry
Re-expressing Skewed Data toImprove Symmetry (cont)
One way to make a skeweddistribution more symmetric isto re-express or transform thedata by applying a simplefunction(eg logarithmic function)1048708 Note the change in skewnessfrom the raw data (Figure411) to the transformed data(Figure 412)
What Can Go Wrong
bull 1048708 Donrsquot make a histogram of a categorical variablemdash
bull bar charts or pie charts should be used for
bull categorical data
bull 1048708 Donrsquot look for shape
bull center and spread
bull of a bar chart
What Can Go Wrong (cont)
bull 1048708 Donrsquot use bars in every displaymdashsave them for
bull histograms and bar charts
bull 1048708 Below is a badly drawn timeplot and the proper
bull histogram for the number of eagles sighted in a
bull collection of weeks
What Can Go Wrong (cont)
What Can Go Wrong (cont)
Choose a bin width appropriate to the data1048708 Changing the bin width changes theappearance of the histogram
What Can Go Wrong (cont)
1048708 Avoid inconsistent scaleseither within the display orwhen comparing twodisplays1048708 Label clearly so a readerknows what the plotdisplays1048708 Good intentions badplot
What have we learned
bull 1048708 Wersquove learned how to make a picture for quantitative databull to help us see the story the data have to Tellbull 1048708 We can display the distribution of quantitative data with abull histogram stem-and-leaf display or dotplotbull 1048708 Tell about a distribution by talking about shape centerbull spread and any unusual featuresbull 1048708 We can compare two quantitative distributions by lookingbull at side-by-side displays (plotted on the same scale)bull 1048708 Trends in a quantitative variable can be displayed in abull timeplot
Center
bull A value that attempts the impossible by summarizing the entire distribution with a single number a ldquotypicalrdquo value
bull Measures include the mean and median
Spread
bull A numerical summary of how tightly the values are clustered around the center
bull Measures of spread include the IQR and standard deviation
Mode
bull a hump or local high pint in the shape of the distribution of a variable is called the mode The apparent location of modes can change as the scale of a histogram is changed
Unimodal
bull Having one mode
Bimodal
bull Distribution with two modes
Example
Uniform
1048708 A histogram that doesnrsquot appear to have any mode andin which all the bars are approximately the same heightis called uniform
Anything Unusual
bull Do any unusual features stick outbull 1048708 Sometimes itrsquos the unusual features that tellbull us something interesting or exciting about thebull databull 1048708 You should always mention any stragglers orbull outliers that stand off away from the body ofbull the distributionbull 1048708 Are there any gaps in the distribution If sobull we might have data from more than onebull group
Outliers
The following histogram has outliersmdashthere arethree cities in the leftmost bar
Outliers
bull Are extreme values that do not appear to belong to the rest of the data They may be unusual values that deserve further investigation or they may be just mistakes therersquos no obvious way to tell Do not delete them Outliers can affect many statistical analyses so you should always be alert to them
Outliers
bull Away from the main portion of data
Where is the Center of the Distribution
bull 1048708 If you had to pick a single number to describe allbull the data what would you pickbull 1048708 Itrsquos easy to find the center when a histogram isbull unimodal and symmetricmdashitrsquos right in the middlebull 1048708 On the other hand itrsquos not so easy to find thebull center of a skewed histogram or a histogram withbull more than one modebull 1048708 For now we will ldquoeyeballrdquo the center of thebull distribution In the next chapter we will find thebull center numerically
How Spread Out is the Distribution
bull 1048708 Variation matters and Statistics is about
bull variation
bull 1048708 Are the values of the distribution tightly clustered
bull around the center or more spread out
bull 1048708 In the next two chapters we will talk about
bull spreadhellip
Comparing Distributions
bull 1048708 Often we would like to compare two or morebull distributions instead of looking at one distributionbull by itselfbull 1048708 When looking at two or more distributions it isbull very important that the histograms have been putbull on the same scale Otherwise we cannot reallybull compare the two distributionsbull 1048708 When we compare distributions we talk about thebull shape center and spread of each distribution
Example
Compare thefollowingdistributions ofages for femaleand male heartattack patients
Compare thefollowingdistributions ofages for femaleand male heartattack patients
HOMEWORK
Web Pages Used
bull httpwwwfaoorgwairdocsilrix5469ex5469e38gif
bull httpwwwsciencebuddiesorgscience-fair-projectsdescriptive_statistics_filesBimodalDistjpg
bull httpimagesabsoluteastronomycomimagesencyclopediaimagesbbibimodalpng
bull httpuploadwikimediaorgwikipediacommonsbbcBimodal_geologicalPNG
Web Pages Used
bull httpmathworldwolframcomimageseps-gifOutlierHistogram_1000gif
Timeplots Order Please
bull 1048708 For some data sets we are interested in how the
bull data behave over time In these cases we
bull construct timeplots of the data
Re-expressing Skewed Data toImprove Symmetry
Re-expressing Skewed Data toImprove Symmetry (cont)
One way to make a skeweddistribution more symmetric isto re-express or transform thedata by applying a simplefunction(eg logarithmic function)1048708 Note the change in skewnessfrom the raw data (Figure411) to the transformed data(Figure 412)
What Can Go Wrong
bull 1048708 Donrsquot make a histogram of a categorical variablemdash
bull bar charts or pie charts should be used for
bull categorical data
bull 1048708 Donrsquot look for shape
bull center and spread
bull of a bar chart
What Can Go Wrong (cont)
bull 1048708 Donrsquot use bars in every displaymdashsave them for
bull histograms and bar charts
bull 1048708 Below is a badly drawn timeplot and the proper
bull histogram for the number of eagles sighted in a
bull collection of weeks
What Can Go Wrong (cont)
What Can Go Wrong (cont)
Choose a bin width appropriate to the data1048708 Changing the bin width changes theappearance of the histogram
What Can Go Wrong (cont)
1048708 Avoid inconsistent scaleseither within the display orwhen comparing twodisplays1048708 Label clearly so a readerknows what the plotdisplays1048708 Good intentions badplot
What have we learned
bull 1048708 Wersquove learned how to make a picture for quantitative databull to help us see the story the data have to Tellbull 1048708 We can display the distribution of quantitative data with abull histogram stem-and-leaf display or dotplotbull 1048708 Tell about a distribution by talking about shape centerbull spread and any unusual featuresbull 1048708 We can compare two quantitative distributions by lookingbull at side-by-side displays (plotted on the same scale)bull 1048708 Trends in a quantitative variable can be displayed in abull timeplot
Spread
bull A numerical summary of how tightly the values are clustered around the center
bull Measures of spread include the IQR and standard deviation
Mode
bull a hump or local high pint in the shape of the distribution of a variable is called the mode The apparent location of modes can change as the scale of a histogram is changed
Unimodal
bull Having one mode
Bimodal
bull Distribution with two modes
Example
Uniform
1048708 A histogram that doesnrsquot appear to have any mode andin which all the bars are approximately the same heightis called uniform
Anything Unusual
bull Do any unusual features stick outbull 1048708 Sometimes itrsquos the unusual features that tellbull us something interesting or exciting about thebull databull 1048708 You should always mention any stragglers orbull outliers that stand off away from the body ofbull the distributionbull 1048708 Are there any gaps in the distribution If sobull we might have data from more than onebull group
Outliers
The following histogram has outliersmdashthere arethree cities in the leftmost bar
Outliers
bull Are extreme values that do not appear to belong to the rest of the data They may be unusual values that deserve further investigation or they may be just mistakes therersquos no obvious way to tell Do not delete them Outliers can affect many statistical analyses so you should always be alert to them
Outliers
bull Away from the main portion of data
Where is the Center of the Distribution
bull 1048708 If you had to pick a single number to describe allbull the data what would you pickbull 1048708 Itrsquos easy to find the center when a histogram isbull unimodal and symmetricmdashitrsquos right in the middlebull 1048708 On the other hand itrsquos not so easy to find thebull center of a skewed histogram or a histogram withbull more than one modebull 1048708 For now we will ldquoeyeballrdquo the center of thebull distribution In the next chapter we will find thebull center numerically
How Spread Out is the Distribution
bull 1048708 Variation matters and Statistics is about
bull variation
bull 1048708 Are the values of the distribution tightly clustered
bull around the center or more spread out
bull 1048708 In the next two chapters we will talk about
bull spreadhellip
Comparing Distributions
bull 1048708 Often we would like to compare two or morebull distributions instead of looking at one distributionbull by itselfbull 1048708 When looking at two or more distributions it isbull very important that the histograms have been putbull on the same scale Otherwise we cannot reallybull compare the two distributionsbull 1048708 When we compare distributions we talk about thebull shape center and spread of each distribution
Example
Compare thefollowingdistributions ofages for femaleand male heartattack patients
Compare thefollowingdistributions ofages for femaleand male heartattack patients
HOMEWORK
Web Pages Used
bull httpwwwfaoorgwairdocsilrix5469ex5469e38gif
bull httpwwwsciencebuddiesorgscience-fair-projectsdescriptive_statistics_filesBimodalDistjpg
bull httpimagesabsoluteastronomycomimagesencyclopediaimagesbbibimodalpng
bull httpuploadwikimediaorgwikipediacommonsbbcBimodal_geologicalPNG
Web Pages Used
bull httpmathworldwolframcomimageseps-gifOutlierHistogram_1000gif
Timeplots Order Please
bull 1048708 For some data sets we are interested in how the
bull data behave over time In these cases we
bull construct timeplots of the data
Re-expressing Skewed Data toImprove Symmetry
Re-expressing Skewed Data toImprove Symmetry (cont)
One way to make a skeweddistribution more symmetric isto re-express or transform thedata by applying a simplefunction(eg logarithmic function)1048708 Note the change in skewnessfrom the raw data (Figure411) to the transformed data(Figure 412)
What Can Go Wrong
bull 1048708 Donrsquot make a histogram of a categorical variablemdash
bull bar charts or pie charts should be used for
bull categorical data
bull 1048708 Donrsquot look for shape
bull center and spread
bull of a bar chart
What Can Go Wrong (cont)
bull 1048708 Donrsquot use bars in every displaymdashsave them for
bull histograms and bar charts
bull 1048708 Below is a badly drawn timeplot and the proper
bull histogram for the number of eagles sighted in a
bull collection of weeks
What Can Go Wrong (cont)
What Can Go Wrong (cont)
Choose a bin width appropriate to the data1048708 Changing the bin width changes theappearance of the histogram
What Can Go Wrong (cont)
1048708 Avoid inconsistent scaleseither within the display orwhen comparing twodisplays1048708 Label clearly so a readerknows what the plotdisplays1048708 Good intentions badplot
What have we learned
bull 1048708 Wersquove learned how to make a picture for quantitative databull to help us see the story the data have to Tellbull 1048708 We can display the distribution of quantitative data with abull histogram stem-and-leaf display or dotplotbull 1048708 Tell about a distribution by talking about shape centerbull spread and any unusual featuresbull 1048708 We can compare two quantitative distributions by lookingbull at side-by-side displays (plotted on the same scale)bull 1048708 Trends in a quantitative variable can be displayed in abull timeplot
Mode
bull a hump or local high pint in the shape of the distribution of a variable is called the mode The apparent location of modes can change as the scale of a histogram is changed
Unimodal
bull Having one mode
Bimodal
bull Distribution with two modes
Example
Uniform
1048708 A histogram that doesnrsquot appear to have any mode andin which all the bars are approximately the same heightis called uniform
Anything Unusual
bull Do any unusual features stick outbull 1048708 Sometimes itrsquos the unusual features that tellbull us something interesting or exciting about thebull databull 1048708 You should always mention any stragglers orbull outliers that stand off away from the body ofbull the distributionbull 1048708 Are there any gaps in the distribution If sobull we might have data from more than onebull group
Outliers
The following histogram has outliersmdashthere arethree cities in the leftmost bar
Outliers
bull Are extreme values that do not appear to belong to the rest of the data They may be unusual values that deserve further investigation or they may be just mistakes therersquos no obvious way to tell Do not delete them Outliers can affect many statistical analyses so you should always be alert to them
Outliers
bull Away from the main portion of data
Where is the Center of the Distribution
bull 1048708 If you had to pick a single number to describe allbull the data what would you pickbull 1048708 Itrsquos easy to find the center when a histogram isbull unimodal and symmetricmdashitrsquos right in the middlebull 1048708 On the other hand itrsquos not so easy to find thebull center of a skewed histogram or a histogram withbull more than one modebull 1048708 For now we will ldquoeyeballrdquo the center of thebull distribution In the next chapter we will find thebull center numerically
How Spread Out is the Distribution
bull 1048708 Variation matters and Statistics is about
bull variation
bull 1048708 Are the values of the distribution tightly clustered
bull around the center or more spread out
bull 1048708 In the next two chapters we will talk about
bull spreadhellip
Comparing Distributions
bull 1048708 Often we would like to compare two or morebull distributions instead of looking at one distributionbull by itselfbull 1048708 When looking at two or more distributions it isbull very important that the histograms have been putbull on the same scale Otherwise we cannot reallybull compare the two distributionsbull 1048708 When we compare distributions we talk about thebull shape center and spread of each distribution
Example
Compare thefollowingdistributions ofages for femaleand male heartattack patients
Compare thefollowingdistributions ofages for femaleand male heartattack patients
HOMEWORK
Web Pages Used
bull httpwwwfaoorgwairdocsilrix5469ex5469e38gif
bull httpwwwsciencebuddiesorgscience-fair-projectsdescriptive_statistics_filesBimodalDistjpg
bull httpimagesabsoluteastronomycomimagesencyclopediaimagesbbibimodalpng
bull httpuploadwikimediaorgwikipediacommonsbbcBimodal_geologicalPNG
Web Pages Used
bull httpmathworldwolframcomimageseps-gifOutlierHistogram_1000gif
Timeplots Order Please
bull 1048708 For some data sets we are interested in how the
bull data behave over time In these cases we
bull construct timeplots of the data
Re-expressing Skewed Data toImprove Symmetry
Re-expressing Skewed Data toImprove Symmetry (cont)
One way to make a skeweddistribution more symmetric isto re-express or transform thedata by applying a simplefunction(eg logarithmic function)1048708 Note the change in skewnessfrom the raw data (Figure411) to the transformed data(Figure 412)
What Can Go Wrong
bull 1048708 Donrsquot make a histogram of a categorical variablemdash
bull bar charts or pie charts should be used for
bull categorical data
bull 1048708 Donrsquot look for shape
bull center and spread
bull of a bar chart
What Can Go Wrong (cont)
bull 1048708 Donrsquot use bars in every displaymdashsave them for
bull histograms and bar charts
bull 1048708 Below is a badly drawn timeplot and the proper
bull histogram for the number of eagles sighted in a
bull collection of weeks
What Can Go Wrong (cont)
What Can Go Wrong (cont)
Choose a bin width appropriate to the data1048708 Changing the bin width changes theappearance of the histogram
What Can Go Wrong (cont)
1048708 Avoid inconsistent scaleseither within the display orwhen comparing twodisplays1048708 Label clearly so a readerknows what the plotdisplays1048708 Good intentions badplot
What have we learned
bull 1048708 Wersquove learned how to make a picture for quantitative databull to help us see the story the data have to Tellbull 1048708 We can display the distribution of quantitative data with abull histogram stem-and-leaf display or dotplotbull 1048708 Tell about a distribution by talking about shape centerbull spread and any unusual featuresbull 1048708 We can compare two quantitative distributions by lookingbull at side-by-side displays (plotted on the same scale)bull 1048708 Trends in a quantitative variable can be displayed in abull timeplot
Unimodal
bull Having one mode
Bimodal
bull Distribution with two modes
Example
Uniform
1048708 A histogram that doesnrsquot appear to have any mode andin which all the bars are approximately the same heightis called uniform
Anything Unusual
bull Do any unusual features stick outbull 1048708 Sometimes itrsquos the unusual features that tellbull us something interesting or exciting about thebull databull 1048708 You should always mention any stragglers orbull outliers that stand off away from the body ofbull the distributionbull 1048708 Are there any gaps in the distribution If sobull we might have data from more than onebull group
Outliers
The following histogram has outliersmdashthere arethree cities in the leftmost bar
Outliers
bull Are extreme values that do not appear to belong to the rest of the data They may be unusual values that deserve further investigation or they may be just mistakes therersquos no obvious way to tell Do not delete them Outliers can affect many statistical analyses so you should always be alert to them
Outliers
bull Away from the main portion of data
Where is the Center of the Distribution
bull 1048708 If you had to pick a single number to describe allbull the data what would you pickbull 1048708 Itrsquos easy to find the center when a histogram isbull unimodal and symmetricmdashitrsquos right in the middlebull 1048708 On the other hand itrsquos not so easy to find thebull center of a skewed histogram or a histogram withbull more than one modebull 1048708 For now we will ldquoeyeballrdquo the center of thebull distribution In the next chapter we will find thebull center numerically
How Spread Out is the Distribution
bull 1048708 Variation matters and Statistics is about
bull variation
bull 1048708 Are the values of the distribution tightly clustered
bull around the center or more spread out
bull 1048708 In the next two chapters we will talk about
bull spreadhellip
Comparing Distributions
bull 1048708 Often we would like to compare two or morebull distributions instead of looking at one distributionbull by itselfbull 1048708 When looking at two or more distributions it isbull very important that the histograms have been putbull on the same scale Otherwise we cannot reallybull compare the two distributionsbull 1048708 When we compare distributions we talk about thebull shape center and spread of each distribution
Example
Compare thefollowingdistributions ofages for femaleand male heartattack patients
Compare thefollowingdistributions ofages for femaleand male heartattack patients
HOMEWORK
Web Pages Used
bull httpwwwfaoorgwairdocsilrix5469ex5469e38gif
bull httpwwwsciencebuddiesorgscience-fair-projectsdescriptive_statistics_filesBimodalDistjpg
bull httpimagesabsoluteastronomycomimagesencyclopediaimagesbbibimodalpng
bull httpuploadwikimediaorgwikipediacommonsbbcBimodal_geologicalPNG
Web Pages Used
bull httpmathworldwolframcomimageseps-gifOutlierHistogram_1000gif
Timeplots Order Please
bull 1048708 For some data sets we are interested in how the
bull data behave over time In these cases we
bull construct timeplots of the data
Re-expressing Skewed Data toImprove Symmetry
Re-expressing Skewed Data toImprove Symmetry (cont)
One way to make a skeweddistribution more symmetric isto re-express or transform thedata by applying a simplefunction(eg logarithmic function)1048708 Note the change in skewnessfrom the raw data (Figure411) to the transformed data(Figure 412)
What Can Go Wrong
bull 1048708 Donrsquot make a histogram of a categorical variablemdash
bull bar charts or pie charts should be used for
bull categorical data
bull 1048708 Donrsquot look for shape
bull center and spread
bull of a bar chart
What Can Go Wrong (cont)
bull 1048708 Donrsquot use bars in every displaymdashsave them for
bull histograms and bar charts
bull 1048708 Below is a badly drawn timeplot and the proper
bull histogram for the number of eagles sighted in a
bull collection of weeks
What Can Go Wrong (cont)
What Can Go Wrong (cont)
Choose a bin width appropriate to the data1048708 Changing the bin width changes theappearance of the histogram
What Can Go Wrong (cont)
1048708 Avoid inconsistent scaleseither within the display orwhen comparing twodisplays1048708 Label clearly so a readerknows what the plotdisplays1048708 Good intentions badplot
What have we learned
bull 1048708 Wersquove learned how to make a picture for quantitative databull to help us see the story the data have to Tellbull 1048708 We can display the distribution of quantitative data with abull histogram stem-and-leaf display or dotplotbull 1048708 Tell about a distribution by talking about shape centerbull spread and any unusual featuresbull 1048708 We can compare two quantitative distributions by lookingbull at side-by-side displays (plotted on the same scale)bull 1048708 Trends in a quantitative variable can be displayed in abull timeplot
Bimodal
bull Distribution with two modes
Example
Uniform
1048708 A histogram that doesnrsquot appear to have any mode andin which all the bars are approximately the same heightis called uniform
Anything Unusual
bull Do any unusual features stick outbull 1048708 Sometimes itrsquos the unusual features that tellbull us something interesting or exciting about thebull databull 1048708 You should always mention any stragglers orbull outliers that stand off away from the body ofbull the distributionbull 1048708 Are there any gaps in the distribution If sobull we might have data from more than onebull group
Outliers
The following histogram has outliersmdashthere arethree cities in the leftmost bar
Outliers
bull Are extreme values that do not appear to belong to the rest of the data They may be unusual values that deserve further investigation or they may be just mistakes therersquos no obvious way to tell Do not delete them Outliers can affect many statistical analyses so you should always be alert to them
Outliers
bull Away from the main portion of data
Where is the Center of the Distribution
bull 1048708 If you had to pick a single number to describe allbull the data what would you pickbull 1048708 Itrsquos easy to find the center when a histogram isbull unimodal and symmetricmdashitrsquos right in the middlebull 1048708 On the other hand itrsquos not so easy to find thebull center of a skewed histogram or a histogram withbull more than one modebull 1048708 For now we will ldquoeyeballrdquo the center of thebull distribution In the next chapter we will find thebull center numerically
How Spread Out is the Distribution
bull 1048708 Variation matters and Statistics is about
bull variation
bull 1048708 Are the values of the distribution tightly clustered
bull around the center or more spread out
bull 1048708 In the next two chapters we will talk about
bull spreadhellip
Comparing Distributions
bull 1048708 Often we would like to compare two or morebull distributions instead of looking at one distributionbull by itselfbull 1048708 When looking at two or more distributions it isbull very important that the histograms have been putbull on the same scale Otherwise we cannot reallybull compare the two distributionsbull 1048708 When we compare distributions we talk about thebull shape center and spread of each distribution
Example
Compare thefollowingdistributions ofages for femaleand male heartattack patients
Compare thefollowingdistributions ofages for femaleand male heartattack patients
HOMEWORK
Web Pages Used
bull httpwwwfaoorgwairdocsilrix5469ex5469e38gif
bull httpwwwsciencebuddiesorgscience-fair-projectsdescriptive_statistics_filesBimodalDistjpg
bull httpimagesabsoluteastronomycomimagesencyclopediaimagesbbibimodalpng
bull httpuploadwikimediaorgwikipediacommonsbbcBimodal_geologicalPNG
Web Pages Used
bull httpmathworldwolframcomimageseps-gifOutlierHistogram_1000gif
Timeplots Order Please
bull 1048708 For some data sets we are interested in how the
bull data behave over time In these cases we
bull construct timeplots of the data
Re-expressing Skewed Data toImprove Symmetry
Re-expressing Skewed Data toImprove Symmetry (cont)
One way to make a skeweddistribution more symmetric isto re-express or transform thedata by applying a simplefunction(eg logarithmic function)1048708 Note the change in skewnessfrom the raw data (Figure411) to the transformed data(Figure 412)
What Can Go Wrong
bull 1048708 Donrsquot make a histogram of a categorical variablemdash
bull bar charts or pie charts should be used for
bull categorical data
bull 1048708 Donrsquot look for shape
bull center and spread
bull of a bar chart
What Can Go Wrong (cont)
bull 1048708 Donrsquot use bars in every displaymdashsave them for
bull histograms and bar charts
bull 1048708 Below is a badly drawn timeplot and the proper
bull histogram for the number of eagles sighted in a
bull collection of weeks
What Can Go Wrong (cont)
What Can Go Wrong (cont)
Choose a bin width appropriate to the data1048708 Changing the bin width changes theappearance of the histogram
What Can Go Wrong (cont)
1048708 Avoid inconsistent scaleseither within the display orwhen comparing twodisplays1048708 Label clearly so a readerknows what the plotdisplays1048708 Good intentions badplot
What have we learned
bull 1048708 Wersquove learned how to make a picture for quantitative databull to help us see the story the data have to Tellbull 1048708 We can display the distribution of quantitative data with abull histogram stem-and-leaf display or dotplotbull 1048708 Tell about a distribution by talking about shape centerbull spread and any unusual featuresbull 1048708 We can compare two quantitative distributions by lookingbull at side-by-side displays (plotted on the same scale)bull 1048708 Trends in a quantitative variable can be displayed in abull timeplot
Example
Uniform
1048708 A histogram that doesnrsquot appear to have any mode andin which all the bars are approximately the same heightis called uniform
Anything Unusual
bull Do any unusual features stick outbull 1048708 Sometimes itrsquos the unusual features that tellbull us something interesting or exciting about thebull databull 1048708 You should always mention any stragglers orbull outliers that stand off away from the body ofbull the distributionbull 1048708 Are there any gaps in the distribution If sobull we might have data from more than onebull group
Outliers
The following histogram has outliersmdashthere arethree cities in the leftmost bar
Outliers
bull Are extreme values that do not appear to belong to the rest of the data They may be unusual values that deserve further investigation or they may be just mistakes therersquos no obvious way to tell Do not delete them Outliers can affect many statistical analyses so you should always be alert to them
Outliers
bull Away from the main portion of data
Where is the Center of the Distribution
bull 1048708 If you had to pick a single number to describe allbull the data what would you pickbull 1048708 Itrsquos easy to find the center when a histogram isbull unimodal and symmetricmdashitrsquos right in the middlebull 1048708 On the other hand itrsquos not so easy to find thebull center of a skewed histogram or a histogram withbull more than one modebull 1048708 For now we will ldquoeyeballrdquo the center of thebull distribution In the next chapter we will find thebull center numerically
How Spread Out is the Distribution
bull 1048708 Variation matters and Statistics is about
bull variation
bull 1048708 Are the values of the distribution tightly clustered
bull around the center or more spread out
bull 1048708 In the next two chapters we will talk about
bull spreadhellip
Comparing Distributions
bull 1048708 Often we would like to compare two or morebull distributions instead of looking at one distributionbull by itselfbull 1048708 When looking at two or more distributions it isbull very important that the histograms have been putbull on the same scale Otherwise we cannot reallybull compare the two distributionsbull 1048708 When we compare distributions we talk about thebull shape center and spread of each distribution
Example
Compare thefollowingdistributions ofages for femaleand male heartattack patients
Compare thefollowingdistributions ofages for femaleand male heartattack patients
HOMEWORK
Web Pages Used
bull httpwwwfaoorgwairdocsilrix5469ex5469e38gif
bull httpwwwsciencebuddiesorgscience-fair-projectsdescriptive_statistics_filesBimodalDistjpg
bull httpimagesabsoluteastronomycomimagesencyclopediaimagesbbibimodalpng
bull httpuploadwikimediaorgwikipediacommonsbbcBimodal_geologicalPNG
Web Pages Used
bull httpmathworldwolframcomimageseps-gifOutlierHistogram_1000gif
Timeplots Order Please
bull 1048708 For some data sets we are interested in how the
bull data behave over time In these cases we
bull construct timeplots of the data
Re-expressing Skewed Data toImprove Symmetry
Re-expressing Skewed Data toImprove Symmetry (cont)
One way to make a skeweddistribution more symmetric isto re-express or transform thedata by applying a simplefunction(eg logarithmic function)1048708 Note the change in skewnessfrom the raw data (Figure411) to the transformed data(Figure 412)
What Can Go Wrong
bull 1048708 Donrsquot make a histogram of a categorical variablemdash
bull bar charts or pie charts should be used for
bull categorical data
bull 1048708 Donrsquot look for shape
bull center and spread
bull of a bar chart
What Can Go Wrong (cont)
bull 1048708 Donrsquot use bars in every displaymdashsave them for
bull histograms and bar charts
bull 1048708 Below is a badly drawn timeplot and the proper
bull histogram for the number of eagles sighted in a
bull collection of weeks
What Can Go Wrong (cont)
What Can Go Wrong (cont)
Choose a bin width appropriate to the data1048708 Changing the bin width changes theappearance of the histogram
What Can Go Wrong (cont)
1048708 Avoid inconsistent scaleseither within the display orwhen comparing twodisplays1048708 Label clearly so a readerknows what the plotdisplays1048708 Good intentions badplot
What have we learned
bull 1048708 Wersquove learned how to make a picture for quantitative databull to help us see the story the data have to Tellbull 1048708 We can display the distribution of quantitative data with abull histogram stem-and-leaf display or dotplotbull 1048708 Tell about a distribution by talking about shape centerbull spread and any unusual featuresbull 1048708 We can compare two quantitative distributions by lookingbull at side-by-side displays (plotted on the same scale)bull 1048708 Trends in a quantitative variable can be displayed in abull timeplot
Uniform
1048708 A histogram that doesnrsquot appear to have any mode andin which all the bars are approximately the same heightis called uniform
Anything Unusual
bull Do any unusual features stick outbull 1048708 Sometimes itrsquos the unusual features that tellbull us something interesting or exciting about thebull databull 1048708 You should always mention any stragglers orbull outliers that stand off away from the body ofbull the distributionbull 1048708 Are there any gaps in the distribution If sobull we might have data from more than onebull group
Outliers
The following histogram has outliersmdashthere arethree cities in the leftmost bar
Outliers
bull Are extreme values that do not appear to belong to the rest of the data They may be unusual values that deserve further investigation or they may be just mistakes therersquos no obvious way to tell Do not delete them Outliers can affect many statistical analyses so you should always be alert to them
Outliers
bull Away from the main portion of data
Where is the Center of the Distribution
bull 1048708 If you had to pick a single number to describe allbull the data what would you pickbull 1048708 Itrsquos easy to find the center when a histogram isbull unimodal and symmetricmdashitrsquos right in the middlebull 1048708 On the other hand itrsquos not so easy to find thebull center of a skewed histogram or a histogram withbull more than one modebull 1048708 For now we will ldquoeyeballrdquo the center of thebull distribution In the next chapter we will find thebull center numerically
How Spread Out is the Distribution
bull 1048708 Variation matters and Statistics is about
bull variation
bull 1048708 Are the values of the distribution tightly clustered
bull around the center or more spread out
bull 1048708 In the next two chapters we will talk about
bull spreadhellip
Comparing Distributions
bull 1048708 Often we would like to compare two or morebull distributions instead of looking at one distributionbull by itselfbull 1048708 When looking at two or more distributions it isbull very important that the histograms have been putbull on the same scale Otherwise we cannot reallybull compare the two distributionsbull 1048708 When we compare distributions we talk about thebull shape center and spread of each distribution
Example
Compare thefollowingdistributions ofages for femaleand male heartattack patients
Compare thefollowingdistributions ofages for femaleand male heartattack patients
HOMEWORK
Web Pages Used
bull httpwwwfaoorgwairdocsilrix5469ex5469e38gif
bull httpwwwsciencebuddiesorgscience-fair-projectsdescriptive_statistics_filesBimodalDistjpg
bull httpimagesabsoluteastronomycomimagesencyclopediaimagesbbibimodalpng
bull httpuploadwikimediaorgwikipediacommonsbbcBimodal_geologicalPNG
Web Pages Used
bull httpmathworldwolframcomimageseps-gifOutlierHistogram_1000gif
Timeplots Order Please
bull 1048708 For some data sets we are interested in how the
bull data behave over time In these cases we
bull construct timeplots of the data
Re-expressing Skewed Data toImprove Symmetry
Re-expressing Skewed Data toImprove Symmetry (cont)
One way to make a skeweddistribution more symmetric isto re-express or transform thedata by applying a simplefunction(eg logarithmic function)1048708 Note the change in skewnessfrom the raw data (Figure411) to the transformed data(Figure 412)
What Can Go Wrong
bull 1048708 Donrsquot make a histogram of a categorical variablemdash
bull bar charts or pie charts should be used for
bull categorical data
bull 1048708 Donrsquot look for shape
bull center and spread
bull of a bar chart
What Can Go Wrong (cont)
bull 1048708 Donrsquot use bars in every displaymdashsave them for
bull histograms and bar charts
bull 1048708 Below is a badly drawn timeplot and the proper
bull histogram for the number of eagles sighted in a
bull collection of weeks
What Can Go Wrong (cont)
What Can Go Wrong (cont)
Choose a bin width appropriate to the data1048708 Changing the bin width changes theappearance of the histogram
What Can Go Wrong (cont)
1048708 Avoid inconsistent scaleseither within the display orwhen comparing twodisplays1048708 Label clearly so a readerknows what the plotdisplays1048708 Good intentions badplot
What have we learned
bull 1048708 Wersquove learned how to make a picture for quantitative databull to help us see the story the data have to Tellbull 1048708 We can display the distribution of quantitative data with abull histogram stem-and-leaf display or dotplotbull 1048708 Tell about a distribution by talking about shape centerbull spread and any unusual featuresbull 1048708 We can compare two quantitative distributions by lookingbull at side-by-side displays (plotted on the same scale)bull 1048708 Trends in a quantitative variable can be displayed in abull timeplot
Anything Unusual
bull Do any unusual features stick outbull 1048708 Sometimes itrsquos the unusual features that tellbull us something interesting or exciting about thebull databull 1048708 You should always mention any stragglers orbull outliers that stand off away from the body ofbull the distributionbull 1048708 Are there any gaps in the distribution If sobull we might have data from more than onebull group
Outliers
The following histogram has outliersmdashthere arethree cities in the leftmost bar
Outliers
bull Are extreme values that do not appear to belong to the rest of the data They may be unusual values that deserve further investigation or they may be just mistakes therersquos no obvious way to tell Do not delete them Outliers can affect many statistical analyses so you should always be alert to them
Outliers
bull Away from the main portion of data
Where is the Center of the Distribution
bull 1048708 If you had to pick a single number to describe allbull the data what would you pickbull 1048708 Itrsquos easy to find the center when a histogram isbull unimodal and symmetricmdashitrsquos right in the middlebull 1048708 On the other hand itrsquos not so easy to find thebull center of a skewed histogram or a histogram withbull more than one modebull 1048708 For now we will ldquoeyeballrdquo the center of thebull distribution In the next chapter we will find thebull center numerically
How Spread Out is the Distribution
bull 1048708 Variation matters and Statistics is about
bull variation
bull 1048708 Are the values of the distribution tightly clustered
bull around the center or more spread out
bull 1048708 In the next two chapters we will talk about
bull spreadhellip
Comparing Distributions
bull 1048708 Often we would like to compare two or morebull distributions instead of looking at one distributionbull by itselfbull 1048708 When looking at two or more distributions it isbull very important that the histograms have been putbull on the same scale Otherwise we cannot reallybull compare the two distributionsbull 1048708 When we compare distributions we talk about thebull shape center and spread of each distribution
Example
Compare thefollowingdistributions ofages for femaleand male heartattack patients
Compare thefollowingdistributions ofages for femaleand male heartattack patients
HOMEWORK
Web Pages Used
bull httpwwwfaoorgwairdocsilrix5469ex5469e38gif
bull httpwwwsciencebuddiesorgscience-fair-projectsdescriptive_statistics_filesBimodalDistjpg
bull httpimagesabsoluteastronomycomimagesencyclopediaimagesbbibimodalpng
bull httpuploadwikimediaorgwikipediacommonsbbcBimodal_geologicalPNG
Web Pages Used
bull httpmathworldwolframcomimageseps-gifOutlierHistogram_1000gif
Timeplots Order Please
bull 1048708 For some data sets we are interested in how the
bull data behave over time In these cases we
bull construct timeplots of the data
Re-expressing Skewed Data toImprove Symmetry
Re-expressing Skewed Data toImprove Symmetry (cont)
One way to make a skeweddistribution more symmetric isto re-express or transform thedata by applying a simplefunction(eg logarithmic function)1048708 Note the change in skewnessfrom the raw data (Figure411) to the transformed data(Figure 412)
What Can Go Wrong
bull 1048708 Donrsquot make a histogram of a categorical variablemdash
bull bar charts or pie charts should be used for
bull categorical data
bull 1048708 Donrsquot look for shape
bull center and spread
bull of a bar chart
What Can Go Wrong (cont)
bull 1048708 Donrsquot use bars in every displaymdashsave them for
bull histograms and bar charts
bull 1048708 Below is a badly drawn timeplot and the proper
bull histogram for the number of eagles sighted in a
bull collection of weeks
What Can Go Wrong (cont)
What Can Go Wrong (cont)
Choose a bin width appropriate to the data1048708 Changing the bin width changes theappearance of the histogram
What Can Go Wrong (cont)
1048708 Avoid inconsistent scaleseither within the display orwhen comparing twodisplays1048708 Label clearly so a readerknows what the plotdisplays1048708 Good intentions badplot
What have we learned
bull 1048708 Wersquove learned how to make a picture for quantitative databull to help us see the story the data have to Tellbull 1048708 We can display the distribution of quantitative data with abull histogram stem-and-leaf display or dotplotbull 1048708 Tell about a distribution by talking about shape centerbull spread and any unusual featuresbull 1048708 We can compare two quantitative distributions by lookingbull at side-by-side displays (plotted on the same scale)bull 1048708 Trends in a quantitative variable can be displayed in abull timeplot
Outliers
The following histogram has outliersmdashthere arethree cities in the leftmost bar
Outliers
bull Are extreme values that do not appear to belong to the rest of the data They may be unusual values that deserve further investigation or they may be just mistakes therersquos no obvious way to tell Do not delete them Outliers can affect many statistical analyses so you should always be alert to them
Outliers
bull Away from the main portion of data
Where is the Center of the Distribution
bull 1048708 If you had to pick a single number to describe allbull the data what would you pickbull 1048708 Itrsquos easy to find the center when a histogram isbull unimodal and symmetricmdashitrsquos right in the middlebull 1048708 On the other hand itrsquos not so easy to find thebull center of a skewed histogram or a histogram withbull more than one modebull 1048708 For now we will ldquoeyeballrdquo the center of thebull distribution In the next chapter we will find thebull center numerically
How Spread Out is the Distribution
bull 1048708 Variation matters and Statistics is about
bull variation
bull 1048708 Are the values of the distribution tightly clustered
bull around the center or more spread out
bull 1048708 In the next two chapters we will talk about
bull spreadhellip
Comparing Distributions
bull 1048708 Often we would like to compare two or morebull distributions instead of looking at one distributionbull by itselfbull 1048708 When looking at two or more distributions it isbull very important that the histograms have been putbull on the same scale Otherwise we cannot reallybull compare the two distributionsbull 1048708 When we compare distributions we talk about thebull shape center and spread of each distribution
Example
Compare thefollowingdistributions ofages for femaleand male heartattack patients
Compare thefollowingdistributions ofages for femaleand male heartattack patients
HOMEWORK
Web Pages Used
bull httpwwwfaoorgwairdocsilrix5469ex5469e38gif
bull httpwwwsciencebuddiesorgscience-fair-projectsdescriptive_statistics_filesBimodalDistjpg
bull httpimagesabsoluteastronomycomimagesencyclopediaimagesbbibimodalpng
bull httpuploadwikimediaorgwikipediacommonsbbcBimodal_geologicalPNG
Web Pages Used
bull httpmathworldwolframcomimageseps-gifOutlierHistogram_1000gif
Timeplots Order Please
bull 1048708 For some data sets we are interested in how the
bull data behave over time In these cases we
bull construct timeplots of the data
Re-expressing Skewed Data toImprove Symmetry
Re-expressing Skewed Data toImprove Symmetry (cont)
One way to make a skeweddistribution more symmetric isto re-express or transform thedata by applying a simplefunction(eg logarithmic function)1048708 Note the change in skewnessfrom the raw data (Figure411) to the transformed data(Figure 412)
What Can Go Wrong
bull 1048708 Donrsquot make a histogram of a categorical variablemdash
bull bar charts or pie charts should be used for
bull categorical data
bull 1048708 Donrsquot look for shape
bull center and spread
bull of a bar chart
What Can Go Wrong (cont)
bull 1048708 Donrsquot use bars in every displaymdashsave them for
bull histograms and bar charts
bull 1048708 Below is a badly drawn timeplot and the proper
bull histogram for the number of eagles sighted in a
bull collection of weeks
What Can Go Wrong (cont)
What Can Go Wrong (cont)
Choose a bin width appropriate to the data1048708 Changing the bin width changes theappearance of the histogram
What Can Go Wrong (cont)
1048708 Avoid inconsistent scaleseither within the display orwhen comparing twodisplays1048708 Label clearly so a readerknows what the plotdisplays1048708 Good intentions badplot
What have we learned
bull 1048708 Wersquove learned how to make a picture for quantitative databull to help us see the story the data have to Tellbull 1048708 We can display the distribution of quantitative data with abull histogram stem-and-leaf display or dotplotbull 1048708 Tell about a distribution by talking about shape centerbull spread and any unusual featuresbull 1048708 We can compare two quantitative distributions by lookingbull at side-by-side displays (plotted on the same scale)bull 1048708 Trends in a quantitative variable can be displayed in abull timeplot
Outliers
bull Are extreme values that do not appear to belong to the rest of the data They may be unusual values that deserve further investigation or they may be just mistakes therersquos no obvious way to tell Do not delete them Outliers can affect many statistical analyses so you should always be alert to them
Outliers
bull Away from the main portion of data
Where is the Center of the Distribution
bull 1048708 If you had to pick a single number to describe allbull the data what would you pickbull 1048708 Itrsquos easy to find the center when a histogram isbull unimodal and symmetricmdashitrsquos right in the middlebull 1048708 On the other hand itrsquos not so easy to find thebull center of a skewed histogram or a histogram withbull more than one modebull 1048708 For now we will ldquoeyeballrdquo the center of thebull distribution In the next chapter we will find thebull center numerically
How Spread Out is the Distribution
bull 1048708 Variation matters and Statistics is about
bull variation
bull 1048708 Are the values of the distribution tightly clustered
bull around the center or more spread out
bull 1048708 In the next two chapters we will talk about
bull spreadhellip
Comparing Distributions
bull 1048708 Often we would like to compare two or morebull distributions instead of looking at one distributionbull by itselfbull 1048708 When looking at two or more distributions it isbull very important that the histograms have been putbull on the same scale Otherwise we cannot reallybull compare the two distributionsbull 1048708 When we compare distributions we talk about thebull shape center and spread of each distribution
Example
Compare thefollowingdistributions ofages for femaleand male heartattack patients
Compare thefollowingdistributions ofages for femaleand male heartattack patients
HOMEWORK
Web Pages Used
bull httpwwwfaoorgwairdocsilrix5469ex5469e38gif
bull httpwwwsciencebuddiesorgscience-fair-projectsdescriptive_statistics_filesBimodalDistjpg
bull httpimagesabsoluteastronomycomimagesencyclopediaimagesbbibimodalpng
bull httpuploadwikimediaorgwikipediacommonsbbcBimodal_geologicalPNG
Web Pages Used
bull httpmathworldwolframcomimageseps-gifOutlierHistogram_1000gif
Timeplots Order Please
bull 1048708 For some data sets we are interested in how the
bull data behave over time In these cases we
bull construct timeplots of the data
Re-expressing Skewed Data toImprove Symmetry
Re-expressing Skewed Data toImprove Symmetry (cont)
One way to make a skeweddistribution more symmetric isto re-express or transform thedata by applying a simplefunction(eg logarithmic function)1048708 Note the change in skewnessfrom the raw data (Figure411) to the transformed data(Figure 412)
What Can Go Wrong
bull 1048708 Donrsquot make a histogram of a categorical variablemdash
bull bar charts or pie charts should be used for
bull categorical data
bull 1048708 Donrsquot look for shape
bull center and spread
bull of a bar chart
What Can Go Wrong (cont)
bull 1048708 Donrsquot use bars in every displaymdashsave them for
bull histograms and bar charts
bull 1048708 Below is a badly drawn timeplot and the proper
bull histogram for the number of eagles sighted in a
bull collection of weeks
What Can Go Wrong (cont)
What Can Go Wrong (cont)
Choose a bin width appropriate to the data1048708 Changing the bin width changes theappearance of the histogram
What Can Go Wrong (cont)
1048708 Avoid inconsistent scaleseither within the display orwhen comparing twodisplays1048708 Label clearly so a readerknows what the plotdisplays1048708 Good intentions badplot
What have we learned
bull 1048708 Wersquove learned how to make a picture for quantitative databull to help us see the story the data have to Tellbull 1048708 We can display the distribution of quantitative data with abull histogram stem-and-leaf display or dotplotbull 1048708 Tell about a distribution by talking about shape centerbull spread and any unusual featuresbull 1048708 We can compare two quantitative distributions by lookingbull at side-by-side displays (plotted on the same scale)bull 1048708 Trends in a quantitative variable can be displayed in abull timeplot
Outliers
bull Away from the main portion of data
Where is the Center of the Distribution
bull 1048708 If you had to pick a single number to describe allbull the data what would you pickbull 1048708 Itrsquos easy to find the center when a histogram isbull unimodal and symmetricmdashitrsquos right in the middlebull 1048708 On the other hand itrsquos not so easy to find thebull center of a skewed histogram or a histogram withbull more than one modebull 1048708 For now we will ldquoeyeballrdquo the center of thebull distribution In the next chapter we will find thebull center numerically
How Spread Out is the Distribution
bull 1048708 Variation matters and Statistics is about
bull variation
bull 1048708 Are the values of the distribution tightly clustered
bull around the center or more spread out
bull 1048708 In the next two chapters we will talk about
bull spreadhellip
Comparing Distributions
bull 1048708 Often we would like to compare two or morebull distributions instead of looking at one distributionbull by itselfbull 1048708 When looking at two or more distributions it isbull very important that the histograms have been putbull on the same scale Otherwise we cannot reallybull compare the two distributionsbull 1048708 When we compare distributions we talk about thebull shape center and spread of each distribution
Example
Compare thefollowingdistributions ofages for femaleand male heartattack patients
Compare thefollowingdistributions ofages for femaleand male heartattack patients
HOMEWORK
Web Pages Used
bull httpwwwfaoorgwairdocsilrix5469ex5469e38gif
bull httpwwwsciencebuddiesorgscience-fair-projectsdescriptive_statistics_filesBimodalDistjpg
bull httpimagesabsoluteastronomycomimagesencyclopediaimagesbbibimodalpng
bull httpuploadwikimediaorgwikipediacommonsbbcBimodal_geologicalPNG
Web Pages Used
bull httpmathworldwolframcomimageseps-gifOutlierHistogram_1000gif
Timeplots Order Please
bull 1048708 For some data sets we are interested in how the
bull data behave over time In these cases we
bull construct timeplots of the data
Re-expressing Skewed Data toImprove Symmetry
Re-expressing Skewed Data toImprove Symmetry (cont)
One way to make a skeweddistribution more symmetric isto re-express or transform thedata by applying a simplefunction(eg logarithmic function)1048708 Note the change in skewnessfrom the raw data (Figure411) to the transformed data(Figure 412)
What Can Go Wrong
bull 1048708 Donrsquot make a histogram of a categorical variablemdash
bull bar charts or pie charts should be used for
bull categorical data
bull 1048708 Donrsquot look for shape
bull center and spread
bull of a bar chart
What Can Go Wrong (cont)
bull 1048708 Donrsquot use bars in every displaymdashsave them for
bull histograms and bar charts
bull 1048708 Below is a badly drawn timeplot and the proper
bull histogram for the number of eagles sighted in a
bull collection of weeks
What Can Go Wrong (cont)
What Can Go Wrong (cont)
Choose a bin width appropriate to the data1048708 Changing the bin width changes theappearance of the histogram
What Can Go Wrong (cont)
1048708 Avoid inconsistent scaleseither within the display orwhen comparing twodisplays1048708 Label clearly so a readerknows what the plotdisplays1048708 Good intentions badplot
What have we learned
bull 1048708 Wersquove learned how to make a picture for quantitative databull to help us see the story the data have to Tellbull 1048708 We can display the distribution of quantitative data with abull histogram stem-and-leaf display or dotplotbull 1048708 Tell about a distribution by talking about shape centerbull spread and any unusual featuresbull 1048708 We can compare two quantitative distributions by lookingbull at side-by-side displays (plotted on the same scale)bull 1048708 Trends in a quantitative variable can be displayed in abull timeplot
Where is the Center of the Distribution
bull 1048708 If you had to pick a single number to describe allbull the data what would you pickbull 1048708 Itrsquos easy to find the center when a histogram isbull unimodal and symmetricmdashitrsquos right in the middlebull 1048708 On the other hand itrsquos not so easy to find thebull center of a skewed histogram or a histogram withbull more than one modebull 1048708 For now we will ldquoeyeballrdquo the center of thebull distribution In the next chapter we will find thebull center numerically
How Spread Out is the Distribution
bull 1048708 Variation matters and Statistics is about
bull variation
bull 1048708 Are the values of the distribution tightly clustered
bull around the center or more spread out
bull 1048708 In the next two chapters we will talk about
bull spreadhellip
Comparing Distributions
bull 1048708 Often we would like to compare two or morebull distributions instead of looking at one distributionbull by itselfbull 1048708 When looking at two or more distributions it isbull very important that the histograms have been putbull on the same scale Otherwise we cannot reallybull compare the two distributionsbull 1048708 When we compare distributions we talk about thebull shape center and spread of each distribution
Example
Compare thefollowingdistributions ofages for femaleand male heartattack patients
Compare thefollowingdistributions ofages for femaleand male heartattack patients
HOMEWORK
Web Pages Used
bull httpwwwfaoorgwairdocsilrix5469ex5469e38gif
bull httpwwwsciencebuddiesorgscience-fair-projectsdescriptive_statistics_filesBimodalDistjpg
bull httpimagesabsoluteastronomycomimagesencyclopediaimagesbbibimodalpng
bull httpuploadwikimediaorgwikipediacommonsbbcBimodal_geologicalPNG
Web Pages Used
bull httpmathworldwolframcomimageseps-gifOutlierHistogram_1000gif
Timeplots Order Please
bull 1048708 For some data sets we are interested in how the
bull data behave over time In these cases we
bull construct timeplots of the data
Re-expressing Skewed Data toImprove Symmetry
Re-expressing Skewed Data toImprove Symmetry (cont)
One way to make a skeweddistribution more symmetric isto re-express or transform thedata by applying a simplefunction(eg logarithmic function)1048708 Note the change in skewnessfrom the raw data (Figure411) to the transformed data(Figure 412)
What Can Go Wrong
bull 1048708 Donrsquot make a histogram of a categorical variablemdash
bull bar charts or pie charts should be used for
bull categorical data
bull 1048708 Donrsquot look for shape
bull center and spread
bull of a bar chart
What Can Go Wrong (cont)
bull 1048708 Donrsquot use bars in every displaymdashsave them for
bull histograms and bar charts
bull 1048708 Below is a badly drawn timeplot and the proper
bull histogram for the number of eagles sighted in a
bull collection of weeks
What Can Go Wrong (cont)
What Can Go Wrong (cont)
Choose a bin width appropriate to the data1048708 Changing the bin width changes theappearance of the histogram
What Can Go Wrong (cont)
1048708 Avoid inconsistent scaleseither within the display orwhen comparing twodisplays1048708 Label clearly so a readerknows what the plotdisplays1048708 Good intentions badplot
What have we learned
bull 1048708 Wersquove learned how to make a picture for quantitative databull to help us see the story the data have to Tellbull 1048708 We can display the distribution of quantitative data with abull histogram stem-and-leaf display or dotplotbull 1048708 Tell about a distribution by talking about shape centerbull spread and any unusual featuresbull 1048708 We can compare two quantitative distributions by lookingbull at side-by-side displays (plotted on the same scale)bull 1048708 Trends in a quantitative variable can be displayed in abull timeplot
How Spread Out is the Distribution
bull 1048708 Variation matters and Statistics is about
bull variation
bull 1048708 Are the values of the distribution tightly clustered
bull around the center or more spread out
bull 1048708 In the next two chapters we will talk about
bull spreadhellip
Comparing Distributions
bull 1048708 Often we would like to compare two or morebull distributions instead of looking at one distributionbull by itselfbull 1048708 When looking at two or more distributions it isbull very important that the histograms have been putbull on the same scale Otherwise we cannot reallybull compare the two distributionsbull 1048708 When we compare distributions we talk about thebull shape center and spread of each distribution
Example
Compare thefollowingdistributions ofages for femaleand male heartattack patients
Compare thefollowingdistributions ofages for femaleand male heartattack patients
HOMEWORK
Web Pages Used
bull httpwwwfaoorgwairdocsilrix5469ex5469e38gif
bull httpwwwsciencebuddiesorgscience-fair-projectsdescriptive_statistics_filesBimodalDistjpg
bull httpimagesabsoluteastronomycomimagesencyclopediaimagesbbibimodalpng
bull httpuploadwikimediaorgwikipediacommonsbbcBimodal_geologicalPNG
Web Pages Used
bull httpmathworldwolframcomimageseps-gifOutlierHistogram_1000gif
Timeplots Order Please
bull 1048708 For some data sets we are interested in how the
bull data behave over time In these cases we
bull construct timeplots of the data
Re-expressing Skewed Data toImprove Symmetry
Re-expressing Skewed Data toImprove Symmetry (cont)
One way to make a skeweddistribution more symmetric isto re-express or transform thedata by applying a simplefunction(eg logarithmic function)1048708 Note the change in skewnessfrom the raw data (Figure411) to the transformed data(Figure 412)
What Can Go Wrong
bull 1048708 Donrsquot make a histogram of a categorical variablemdash
bull bar charts or pie charts should be used for
bull categorical data
bull 1048708 Donrsquot look for shape
bull center and spread
bull of a bar chart
What Can Go Wrong (cont)
bull 1048708 Donrsquot use bars in every displaymdashsave them for
bull histograms and bar charts
bull 1048708 Below is a badly drawn timeplot and the proper
bull histogram for the number of eagles sighted in a
bull collection of weeks
What Can Go Wrong (cont)
What Can Go Wrong (cont)
Choose a bin width appropriate to the data1048708 Changing the bin width changes theappearance of the histogram
What Can Go Wrong (cont)
1048708 Avoid inconsistent scaleseither within the display orwhen comparing twodisplays1048708 Label clearly so a readerknows what the plotdisplays1048708 Good intentions badplot
What have we learned
bull 1048708 Wersquove learned how to make a picture for quantitative databull to help us see the story the data have to Tellbull 1048708 We can display the distribution of quantitative data with abull histogram stem-and-leaf display or dotplotbull 1048708 Tell about a distribution by talking about shape centerbull spread and any unusual featuresbull 1048708 We can compare two quantitative distributions by lookingbull at side-by-side displays (plotted on the same scale)bull 1048708 Trends in a quantitative variable can be displayed in abull timeplot
Comparing Distributions
bull 1048708 Often we would like to compare two or morebull distributions instead of looking at one distributionbull by itselfbull 1048708 When looking at two or more distributions it isbull very important that the histograms have been putbull on the same scale Otherwise we cannot reallybull compare the two distributionsbull 1048708 When we compare distributions we talk about thebull shape center and spread of each distribution
Example
Compare thefollowingdistributions ofages for femaleand male heartattack patients
Compare thefollowingdistributions ofages for femaleand male heartattack patients
HOMEWORK
Web Pages Used
bull httpwwwfaoorgwairdocsilrix5469ex5469e38gif
bull httpwwwsciencebuddiesorgscience-fair-projectsdescriptive_statistics_filesBimodalDistjpg
bull httpimagesabsoluteastronomycomimagesencyclopediaimagesbbibimodalpng
bull httpuploadwikimediaorgwikipediacommonsbbcBimodal_geologicalPNG
Web Pages Used
bull httpmathworldwolframcomimageseps-gifOutlierHistogram_1000gif
Timeplots Order Please
bull 1048708 For some data sets we are interested in how the
bull data behave over time In these cases we
bull construct timeplots of the data
Re-expressing Skewed Data toImprove Symmetry
Re-expressing Skewed Data toImprove Symmetry (cont)
One way to make a skeweddistribution more symmetric isto re-express or transform thedata by applying a simplefunction(eg logarithmic function)1048708 Note the change in skewnessfrom the raw data (Figure411) to the transformed data(Figure 412)
What Can Go Wrong
bull 1048708 Donrsquot make a histogram of a categorical variablemdash
bull bar charts or pie charts should be used for
bull categorical data
bull 1048708 Donrsquot look for shape
bull center and spread
bull of a bar chart
What Can Go Wrong (cont)
bull 1048708 Donrsquot use bars in every displaymdashsave them for
bull histograms and bar charts
bull 1048708 Below is a badly drawn timeplot and the proper
bull histogram for the number of eagles sighted in a
bull collection of weeks
What Can Go Wrong (cont)
What Can Go Wrong (cont)
Choose a bin width appropriate to the data1048708 Changing the bin width changes theappearance of the histogram
What Can Go Wrong (cont)
1048708 Avoid inconsistent scaleseither within the display orwhen comparing twodisplays1048708 Label clearly so a readerknows what the plotdisplays1048708 Good intentions badplot
What have we learned
bull 1048708 Wersquove learned how to make a picture for quantitative databull to help us see the story the data have to Tellbull 1048708 We can display the distribution of quantitative data with abull histogram stem-and-leaf display or dotplotbull 1048708 Tell about a distribution by talking about shape centerbull spread and any unusual featuresbull 1048708 We can compare two quantitative distributions by lookingbull at side-by-side displays (plotted on the same scale)bull 1048708 Trends in a quantitative variable can be displayed in abull timeplot
Example
Compare thefollowingdistributions ofages for femaleand male heartattack patients
Compare thefollowingdistributions ofages for femaleand male heartattack patients
HOMEWORK
Web Pages Used
bull httpwwwfaoorgwairdocsilrix5469ex5469e38gif
bull httpwwwsciencebuddiesorgscience-fair-projectsdescriptive_statistics_filesBimodalDistjpg
bull httpimagesabsoluteastronomycomimagesencyclopediaimagesbbibimodalpng
bull httpuploadwikimediaorgwikipediacommonsbbcBimodal_geologicalPNG
Web Pages Used
bull httpmathworldwolframcomimageseps-gifOutlierHistogram_1000gif
Timeplots Order Please
bull 1048708 For some data sets we are interested in how the
bull data behave over time In these cases we
bull construct timeplots of the data
Re-expressing Skewed Data toImprove Symmetry
Re-expressing Skewed Data toImprove Symmetry (cont)
One way to make a skeweddistribution more symmetric isto re-express or transform thedata by applying a simplefunction(eg logarithmic function)1048708 Note the change in skewnessfrom the raw data (Figure411) to the transformed data(Figure 412)
What Can Go Wrong
bull 1048708 Donrsquot make a histogram of a categorical variablemdash
bull bar charts or pie charts should be used for
bull categorical data
bull 1048708 Donrsquot look for shape
bull center and spread
bull of a bar chart
What Can Go Wrong (cont)
bull 1048708 Donrsquot use bars in every displaymdashsave them for
bull histograms and bar charts
bull 1048708 Below is a badly drawn timeplot and the proper
bull histogram for the number of eagles sighted in a
bull collection of weeks
What Can Go Wrong (cont)
What Can Go Wrong (cont)
Choose a bin width appropriate to the data1048708 Changing the bin width changes theappearance of the histogram
What Can Go Wrong (cont)
1048708 Avoid inconsistent scaleseither within the display orwhen comparing twodisplays1048708 Label clearly so a readerknows what the plotdisplays1048708 Good intentions badplot
What have we learned
bull 1048708 Wersquove learned how to make a picture for quantitative databull to help us see the story the data have to Tellbull 1048708 We can display the distribution of quantitative data with abull histogram stem-and-leaf display or dotplotbull 1048708 Tell about a distribution by talking about shape centerbull spread and any unusual featuresbull 1048708 We can compare two quantitative distributions by lookingbull at side-by-side displays (plotted on the same scale)bull 1048708 Trends in a quantitative variable can be displayed in abull timeplot
HOMEWORK
Web Pages Used
bull httpwwwfaoorgwairdocsilrix5469ex5469e38gif
bull httpwwwsciencebuddiesorgscience-fair-projectsdescriptive_statistics_filesBimodalDistjpg
bull httpimagesabsoluteastronomycomimagesencyclopediaimagesbbibimodalpng
bull httpuploadwikimediaorgwikipediacommonsbbcBimodal_geologicalPNG
Web Pages Used
bull httpmathworldwolframcomimageseps-gifOutlierHistogram_1000gif
Timeplots Order Please
bull 1048708 For some data sets we are interested in how the
bull data behave over time In these cases we
bull construct timeplots of the data
Re-expressing Skewed Data toImprove Symmetry
Re-expressing Skewed Data toImprove Symmetry (cont)
One way to make a skeweddistribution more symmetric isto re-express or transform thedata by applying a simplefunction(eg logarithmic function)1048708 Note the change in skewnessfrom the raw data (Figure411) to the transformed data(Figure 412)
What Can Go Wrong
bull 1048708 Donrsquot make a histogram of a categorical variablemdash
bull bar charts or pie charts should be used for
bull categorical data
bull 1048708 Donrsquot look for shape
bull center and spread
bull of a bar chart
What Can Go Wrong (cont)
bull 1048708 Donrsquot use bars in every displaymdashsave them for
bull histograms and bar charts
bull 1048708 Below is a badly drawn timeplot and the proper
bull histogram for the number of eagles sighted in a
bull collection of weeks
What Can Go Wrong (cont)
What Can Go Wrong (cont)
Choose a bin width appropriate to the data1048708 Changing the bin width changes theappearance of the histogram
What Can Go Wrong (cont)
1048708 Avoid inconsistent scaleseither within the display orwhen comparing twodisplays1048708 Label clearly so a readerknows what the plotdisplays1048708 Good intentions badplot
What have we learned
bull 1048708 Wersquove learned how to make a picture for quantitative databull to help us see the story the data have to Tellbull 1048708 We can display the distribution of quantitative data with abull histogram stem-and-leaf display or dotplotbull 1048708 Tell about a distribution by talking about shape centerbull spread and any unusual featuresbull 1048708 We can compare two quantitative distributions by lookingbull at side-by-side displays (plotted on the same scale)bull 1048708 Trends in a quantitative variable can be displayed in abull timeplot
Web Pages Used
bull httpwwwfaoorgwairdocsilrix5469ex5469e38gif
bull httpwwwsciencebuddiesorgscience-fair-projectsdescriptive_statistics_filesBimodalDistjpg
bull httpimagesabsoluteastronomycomimagesencyclopediaimagesbbibimodalpng
bull httpuploadwikimediaorgwikipediacommonsbbcBimodal_geologicalPNG
Web Pages Used
bull httpmathworldwolframcomimageseps-gifOutlierHistogram_1000gif
Timeplots Order Please
bull 1048708 For some data sets we are interested in how the
bull data behave over time In these cases we
bull construct timeplots of the data
Re-expressing Skewed Data toImprove Symmetry
Re-expressing Skewed Data toImprove Symmetry (cont)
One way to make a skeweddistribution more symmetric isto re-express or transform thedata by applying a simplefunction(eg logarithmic function)1048708 Note the change in skewnessfrom the raw data (Figure411) to the transformed data(Figure 412)
What Can Go Wrong
bull 1048708 Donrsquot make a histogram of a categorical variablemdash
bull bar charts or pie charts should be used for
bull categorical data
bull 1048708 Donrsquot look for shape
bull center and spread
bull of a bar chart
What Can Go Wrong (cont)
bull 1048708 Donrsquot use bars in every displaymdashsave them for
bull histograms and bar charts
bull 1048708 Below is a badly drawn timeplot and the proper
bull histogram for the number of eagles sighted in a
bull collection of weeks
What Can Go Wrong (cont)
What Can Go Wrong (cont)
Choose a bin width appropriate to the data1048708 Changing the bin width changes theappearance of the histogram
What Can Go Wrong (cont)
1048708 Avoid inconsistent scaleseither within the display orwhen comparing twodisplays1048708 Label clearly so a readerknows what the plotdisplays1048708 Good intentions badplot
What have we learned
bull 1048708 Wersquove learned how to make a picture for quantitative databull to help us see the story the data have to Tellbull 1048708 We can display the distribution of quantitative data with abull histogram stem-and-leaf display or dotplotbull 1048708 Tell about a distribution by talking about shape centerbull spread and any unusual featuresbull 1048708 We can compare two quantitative distributions by lookingbull at side-by-side displays (plotted on the same scale)bull 1048708 Trends in a quantitative variable can be displayed in abull timeplot
Web Pages Used
bull httpmathworldwolframcomimageseps-gifOutlierHistogram_1000gif
Timeplots Order Please
bull 1048708 For some data sets we are interested in how the
bull data behave over time In these cases we
bull construct timeplots of the data
Re-expressing Skewed Data toImprove Symmetry
Re-expressing Skewed Data toImprove Symmetry (cont)
One way to make a skeweddistribution more symmetric isto re-express or transform thedata by applying a simplefunction(eg logarithmic function)1048708 Note the change in skewnessfrom the raw data (Figure411) to the transformed data(Figure 412)
What Can Go Wrong
bull 1048708 Donrsquot make a histogram of a categorical variablemdash
bull bar charts or pie charts should be used for
bull categorical data
bull 1048708 Donrsquot look for shape
bull center and spread
bull of a bar chart
What Can Go Wrong (cont)
bull 1048708 Donrsquot use bars in every displaymdashsave them for
bull histograms and bar charts
bull 1048708 Below is a badly drawn timeplot and the proper
bull histogram for the number of eagles sighted in a
bull collection of weeks
What Can Go Wrong (cont)
What Can Go Wrong (cont)
Choose a bin width appropriate to the data1048708 Changing the bin width changes theappearance of the histogram
What Can Go Wrong (cont)
1048708 Avoid inconsistent scaleseither within the display orwhen comparing twodisplays1048708 Label clearly so a readerknows what the plotdisplays1048708 Good intentions badplot
What have we learned
bull 1048708 Wersquove learned how to make a picture for quantitative databull to help us see the story the data have to Tellbull 1048708 We can display the distribution of quantitative data with abull histogram stem-and-leaf display or dotplotbull 1048708 Tell about a distribution by talking about shape centerbull spread and any unusual featuresbull 1048708 We can compare two quantitative distributions by lookingbull at side-by-side displays (plotted on the same scale)bull 1048708 Trends in a quantitative variable can be displayed in abull timeplot
Timeplots Order Please
bull 1048708 For some data sets we are interested in how the
bull data behave over time In these cases we
bull construct timeplots of the data
Re-expressing Skewed Data toImprove Symmetry
Re-expressing Skewed Data toImprove Symmetry (cont)
One way to make a skeweddistribution more symmetric isto re-express or transform thedata by applying a simplefunction(eg logarithmic function)1048708 Note the change in skewnessfrom the raw data (Figure411) to the transformed data(Figure 412)
What Can Go Wrong
bull 1048708 Donrsquot make a histogram of a categorical variablemdash
bull bar charts or pie charts should be used for
bull categorical data
bull 1048708 Donrsquot look for shape
bull center and spread
bull of a bar chart
What Can Go Wrong (cont)
bull 1048708 Donrsquot use bars in every displaymdashsave them for
bull histograms and bar charts
bull 1048708 Below is a badly drawn timeplot and the proper
bull histogram for the number of eagles sighted in a
bull collection of weeks
What Can Go Wrong (cont)
What Can Go Wrong (cont)
Choose a bin width appropriate to the data1048708 Changing the bin width changes theappearance of the histogram
What Can Go Wrong (cont)
1048708 Avoid inconsistent scaleseither within the display orwhen comparing twodisplays1048708 Label clearly so a readerknows what the plotdisplays1048708 Good intentions badplot
What have we learned
bull 1048708 Wersquove learned how to make a picture for quantitative databull to help us see the story the data have to Tellbull 1048708 We can display the distribution of quantitative data with abull histogram stem-and-leaf display or dotplotbull 1048708 Tell about a distribution by talking about shape centerbull spread and any unusual featuresbull 1048708 We can compare two quantitative distributions by lookingbull at side-by-side displays (plotted on the same scale)bull 1048708 Trends in a quantitative variable can be displayed in abull timeplot
Re-expressing Skewed Data toImprove Symmetry
Re-expressing Skewed Data toImprove Symmetry (cont)
One way to make a skeweddistribution more symmetric isto re-express or transform thedata by applying a simplefunction(eg logarithmic function)1048708 Note the change in skewnessfrom the raw data (Figure411) to the transformed data(Figure 412)
What Can Go Wrong
bull 1048708 Donrsquot make a histogram of a categorical variablemdash
bull bar charts or pie charts should be used for
bull categorical data
bull 1048708 Donrsquot look for shape
bull center and spread
bull of a bar chart
What Can Go Wrong (cont)
bull 1048708 Donrsquot use bars in every displaymdashsave them for
bull histograms and bar charts
bull 1048708 Below is a badly drawn timeplot and the proper
bull histogram for the number of eagles sighted in a
bull collection of weeks
What Can Go Wrong (cont)
What Can Go Wrong (cont)
Choose a bin width appropriate to the data1048708 Changing the bin width changes theappearance of the histogram
What Can Go Wrong (cont)
1048708 Avoid inconsistent scaleseither within the display orwhen comparing twodisplays1048708 Label clearly so a readerknows what the plotdisplays1048708 Good intentions badplot
What have we learned
bull 1048708 Wersquove learned how to make a picture for quantitative databull to help us see the story the data have to Tellbull 1048708 We can display the distribution of quantitative data with abull histogram stem-and-leaf display or dotplotbull 1048708 Tell about a distribution by talking about shape centerbull spread and any unusual featuresbull 1048708 We can compare two quantitative distributions by lookingbull at side-by-side displays (plotted on the same scale)bull 1048708 Trends in a quantitative variable can be displayed in abull timeplot
Re-expressing Skewed Data toImprove Symmetry (cont)
One way to make a skeweddistribution more symmetric isto re-express or transform thedata by applying a simplefunction(eg logarithmic function)1048708 Note the change in skewnessfrom the raw data (Figure411) to the transformed data(Figure 412)
What Can Go Wrong
bull 1048708 Donrsquot make a histogram of a categorical variablemdash
bull bar charts or pie charts should be used for
bull categorical data
bull 1048708 Donrsquot look for shape
bull center and spread
bull of a bar chart
What Can Go Wrong (cont)
bull 1048708 Donrsquot use bars in every displaymdashsave them for
bull histograms and bar charts
bull 1048708 Below is a badly drawn timeplot and the proper
bull histogram for the number of eagles sighted in a
bull collection of weeks
What Can Go Wrong (cont)
What Can Go Wrong (cont)
Choose a bin width appropriate to the data1048708 Changing the bin width changes theappearance of the histogram
What Can Go Wrong (cont)
1048708 Avoid inconsistent scaleseither within the display orwhen comparing twodisplays1048708 Label clearly so a readerknows what the plotdisplays1048708 Good intentions badplot
What have we learned
bull 1048708 Wersquove learned how to make a picture for quantitative databull to help us see the story the data have to Tellbull 1048708 We can display the distribution of quantitative data with abull histogram stem-and-leaf display or dotplotbull 1048708 Tell about a distribution by talking about shape centerbull spread and any unusual featuresbull 1048708 We can compare two quantitative distributions by lookingbull at side-by-side displays (plotted on the same scale)bull 1048708 Trends in a quantitative variable can be displayed in abull timeplot
What Can Go Wrong
bull 1048708 Donrsquot make a histogram of a categorical variablemdash
bull bar charts or pie charts should be used for
bull categorical data
bull 1048708 Donrsquot look for shape
bull center and spread
bull of a bar chart
What Can Go Wrong (cont)
bull 1048708 Donrsquot use bars in every displaymdashsave them for
bull histograms and bar charts
bull 1048708 Below is a badly drawn timeplot and the proper
bull histogram for the number of eagles sighted in a
bull collection of weeks
What Can Go Wrong (cont)
What Can Go Wrong (cont)
Choose a bin width appropriate to the data1048708 Changing the bin width changes theappearance of the histogram
What Can Go Wrong (cont)
1048708 Avoid inconsistent scaleseither within the display orwhen comparing twodisplays1048708 Label clearly so a readerknows what the plotdisplays1048708 Good intentions badplot
What have we learned
bull 1048708 Wersquove learned how to make a picture for quantitative databull to help us see the story the data have to Tellbull 1048708 We can display the distribution of quantitative data with abull histogram stem-and-leaf display or dotplotbull 1048708 Tell about a distribution by talking about shape centerbull spread and any unusual featuresbull 1048708 We can compare two quantitative distributions by lookingbull at side-by-side displays (plotted on the same scale)bull 1048708 Trends in a quantitative variable can be displayed in abull timeplot
What Can Go Wrong (cont)
bull 1048708 Donrsquot use bars in every displaymdashsave them for
bull histograms and bar charts
bull 1048708 Below is a badly drawn timeplot and the proper
bull histogram for the number of eagles sighted in a
bull collection of weeks
What Can Go Wrong (cont)
What Can Go Wrong (cont)
Choose a bin width appropriate to the data1048708 Changing the bin width changes theappearance of the histogram
What Can Go Wrong (cont)
1048708 Avoid inconsistent scaleseither within the display orwhen comparing twodisplays1048708 Label clearly so a readerknows what the plotdisplays1048708 Good intentions badplot
What have we learned
bull 1048708 Wersquove learned how to make a picture for quantitative databull to help us see the story the data have to Tellbull 1048708 We can display the distribution of quantitative data with abull histogram stem-and-leaf display or dotplotbull 1048708 Tell about a distribution by talking about shape centerbull spread and any unusual featuresbull 1048708 We can compare two quantitative distributions by lookingbull at side-by-side displays (plotted on the same scale)bull 1048708 Trends in a quantitative variable can be displayed in abull timeplot
What Can Go Wrong (cont)
What Can Go Wrong (cont)
Choose a bin width appropriate to the data1048708 Changing the bin width changes theappearance of the histogram
What Can Go Wrong (cont)
1048708 Avoid inconsistent scaleseither within the display orwhen comparing twodisplays1048708 Label clearly so a readerknows what the plotdisplays1048708 Good intentions badplot
What have we learned
bull 1048708 Wersquove learned how to make a picture for quantitative databull to help us see the story the data have to Tellbull 1048708 We can display the distribution of quantitative data with abull histogram stem-and-leaf display or dotplotbull 1048708 Tell about a distribution by talking about shape centerbull spread and any unusual featuresbull 1048708 We can compare two quantitative distributions by lookingbull at side-by-side displays (plotted on the same scale)bull 1048708 Trends in a quantitative variable can be displayed in abull timeplot
What Can Go Wrong (cont)
Choose a bin width appropriate to the data1048708 Changing the bin width changes theappearance of the histogram
What Can Go Wrong (cont)
1048708 Avoid inconsistent scaleseither within the display orwhen comparing twodisplays1048708 Label clearly so a readerknows what the plotdisplays1048708 Good intentions badplot
What have we learned
bull 1048708 Wersquove learned how to make a picture for quantitative databull to help us see the story the data have to Tellbull 1048708 We can display the distribution of quantitative data with abull histogram stem-and-leaf display or dotplotbull 1048708 Tell about a distribution by talking about shape centerbull spread and any unusual featuresbull 1048708 We can compare two quantitative distributions by lookingbull at side-by-side displays (plotted on the same scale)bull 1048708 Trends in a quantitative variable can be displayed in abull timeplot
What Can Go Wrong (cont)
1048708 Avoid inconsistent scaleseither within the display orwhen comparing twodisplays1048708 Label clearly so a readerknows what the plotdisplays1048708 Good intentions badplot
What have we learned
bull 1048708 Wersquove learned how to make a picture for quantitative databull to help us see the story the data have to Tellbull 1048708 We can display the distribution of quantitative data with abull histogram stem-and-leaf display or dotplotbull 1048708 Tell about a distribution by talking about shape centerbull spread and any unusual featuresbull 1048708 We can compare two quantitative distributions by lookingbull at side-by-side displays (plotted on the same scale)bull 1048708 Trends in a quantitative variable can be displayed in abull timeplot
What have we learned
bull 1048708 Wersquove learned how to make a picture for quantitative databull to help us see the story the data have to Tellbull 1048708 We can display the distribution of quantitative data with abull histogram stem-and-leaf display or dotplotbull 1048708 Tell about a distribution by talking about shape centerbull spread and any unusual featuresbull 1048708 We can compare two quantitative distributions by lookingbull at side-by-side displays (plotted on the same scale)bull 1048708 Trends in a quantitative variable can be displayed in abull timeplot
