Data AnalysisData Analysis

I. Mean, Median, ModeI. Mean, Median, Mode A. central tendency is a value that describes aA. central tendency is a value that describes a data set.data set. B. B. MeanMean, , medianmedian,, and and modemode are three are three measures of central tendency.measures of central tendency. C. MeanC. Mean 1. 1. sumsum of the data values of the data values divideddivided by the by the number of data valuesnumber of data values 2. also called the 2. also called the averageaverage of a set of data of a set of data valuesvalues 3. What is the mean of the following set of3. What is the mean of the following set of data?data? 76, 94, 88, 256, 90, 95, 9276, 94, 88, 256, 90, 95, 92

Sum = Sum = 791791 791791 ÷ ÷ 77 = = 113113 is the mean is the mean

D. MedianD. Median 1. the 1. the middlemiddle value of a data set when value of a data set when the numbers are the numbers are arranged in orderarranged in order 2. For a set with an 2. For a set with an eveneven number of data number of data values, the median is thevalues, the median is the averageaverage ofof the two middle values.the two middle values. 3. Find the median of the above set of3. Find the median of the above set of data:data: a. arrange in ordera. arrange in order 7676, , 8888, , 9090, , 9292, , 9494, , 9595, , 256256 b. the median is the middle number:b. the median is the middle number: 9292

E. ModeE. Mode1. the data value that 1. the data value that occurs most occurs most oftenoften2. a data set may have 2. a data set may have no mode, no mode, one mode, or more thanone mode, or more than

oneone modemode3. Find the mode of the above set of 3. Find the mode of the above set of data:data:

No data values are No data values are repeatedrepeated, so , so there is there is no modeno mode

II. GRAPHS - II. GRAPHS - visual display of info / datavisual display of info / data A. A. line graphs line graphs 1. info/data is plotted on 1. info/data is plotted on a grida grid 2. shows 2. shows trendstrends//how data chngs. over timehow data chngs. over time 3. can have an 3. can have an increasingincreasing trend, a trend, a decreasingdecreasing trend, or trend, or nono trend at alltrend at all 4. X-axis (4. X-axis (horizontalhorizontal) ) * * independentindependent variable variable * * adjusted or determinedadjusted or determined by experimenter by experimenter * ex: * ex: timetime 5. Y-axis (5. Y-axis (verticalvertical)) * * dependentdependent variable variable *occurs *occurs b/c of independent variableb/c of independent variable * ex: * ex: temperaturetemperature 6. You can use a line graph when the 6. You can use a line graph when the independentindependent variablevariable is is continuouscontinuous.. 7. Steps for creating a line graph:7. Steps for creating a line graph: a. a. Draw the X and Y axesDraw the X and Y axes b.b. Label the X-axis with the independent variable. Label the X-axis with the independent variable. c.c. Label the Y-axis with the dependent variable. Label the Y-axis with the dependent variable. d.d. Create a scale on each axis with equally spaced Create a scale on each axis with equally spaced numbers.numbers. e.e. Plot a point for each piece of data. Plot a point for each piece of data. f.f. Connect the plotted points. Connect the plotted points. g.g. Add a title. Add a title.

B. bar graphsB. bar graphs1. displays data 1. displays data in a number of separatein a number of separate categoriescategories

2. shows info collected by 2. shows info collected by countingcounting• 3. useful for 3. useful for comparing amountscomparing amounts at a glance at a glance

4. does NOT show 4. does NOT show trends/predictionstrends/predictions (that’s why info. is not connected)(that’s why info. is not connected) 5. Steps for creating a bar graph:5. Steps for creating a bar graph: a. a. Draw the X and Y axesDraw the X and Y axes b.b. Write the category names along the Write the category names along the X-axis and labelX-axis and label.. c.c. Label the Y-axis with the name of Label the Y-axis with the name of

thethe dependent variable. Include units ofdependent variable. Include units of measurement. Create an equal scale measurement. Create an equal scale

of numbers.of numbers. d.d. Draw a bar for each category to the Draw a bar for each category to the

appropriate height.appropriate height. ee. Add a title to your graph.. Add a title to your graph.

C. circle (pie) graphs C. circle (pie) graphs 1. shows 1. shows how different parts of a whole comparehow different parts of a whole compare to one anotherto one another 2. parts are usually expressed as 2. parts are usually expressed as %% - sum of all parts - sum of all parts equaling equaling 100%100% 3. shows data at 3. shows data at one particular timeone particular time, not over a, not over a period of timeperiod of time – does not show – does not show trendstrends 4. Steps for creating a circle graph:4. Steps for creating a circle graph: a. a. Draw a circleDraw a circle b.b. Calculate the percentage of each part by Calculate the percentage of each part by takingtaking ( (part ÷ whole) * 100 = % of eachpart ÷ whole) * 100 = % of each part part c.c. Calculate the angle for each part by Calculate the angle for each part by multiplying the % (in decimal form) by 360.multiplying the % (in decimal form) by 360. d.d. Using angles calculated, divide circle into Using angles calculated, divide circle into parts.parts. e.e. Label each part with name and % Label each part with name and % f.f. Add a title to your graph Add a title to your graph. .

III. ScatterplotsIII. Scatterplots A. graph with data points that show aA. graph with data points that show a relationship between two sets of datarelationship between two sets of data C. CorrelationsC. Correlations 1. can be positive (upward slope) or 1. can be positive (upward slope) or

negative (downward slope)negative (downward slope) 2. can be strong (points cluster around 2. can be strong (points cluster around

line of best fit) or weak (they do not)line of best fit) or weak (they do not) 3. if data points are random there is no 3. if data points are random there is no

correlatoncorrelaton

C. CorrelationsC. Correlations 1. can be positive (upward slope) or 1. can be positive (upward slope) or

negative (downward slope)negative (downward slope) 2. can be strong (points cluster around 2. can be strong (points cluster around

line of best fit) or weak (they do not)line of best fit) or weak (they do not) 3. if data points are random there is no 3. if data points are random there is no

correlatoncorrelaton

IV. Stem and Leaf PlotsIV. Stem and Leaf Plots• A. chart that shows groups of data arrangedA. chart that shows groups of data arranged

by place valueby place value• B. a display that organizes data so that youB. a display that organizes data so that you

can see how they are spread outcan see how they are spread out• C. stem – digit to the left side of the verticalC. stem – digit to the left side of the vertical

lineline• D. leaves – the ones digits to the right side ofD. leaves – the ones digits to the right side of

the vertical linethe vertical line• E. range – difference b/t the greatest and theE. range – difference b/t the greatest and the

least numbers in a data setleast numbers in a data set

V. ProbabilityV. Probability

A. a way to measure the likelihood A. a way to measure the likelihood that an event will occurthat an event will occur

B. formula:B. formula:

PP= = number of favorable number of favorable outcomesoutcomes

number of possible number of possible outcomesoutcomes

C. independent eventsC. independent events

1. outcome of one event has NO 1. outcome of one event has NO effect on the outcome of the other effect on the outcome of the other event(s)event(s)

2. when finding the probability of 2. when finding the probability of independent events occurring:independent events occurring:

*find the probability of each *find the probability of each eventevent

occurringoccurring

*multiply the probability of all *multiply the probability of all thethe

events togetherevents together

3. example:3. example: What is the probability of tossing a coin and gettingWhat is the probability of tossing a coin and getting

tails, and rolling a # cube and getting a number lesstails, and rolling a # cube and getting a number less than 5?than 5?STEP 1STEP 1Coin: P Coin: P tailstails = = #favorable outcomes = 1

# possible outcomes 2

Cube: P <5 = # favorable outcomes = 4 = 2 # possible outcomes 6 3

STEP 2Multiply the probabilities of each event:

P tails * P <5 = 1 * 2 = 2 = 1 2 3 6 3

The probability is 1 33

D. Dependent eventsD. Dependent events

1. outcome of one event DOES have an1. outcome of one event DOES have an

effect on the outcome of the othereffect on the outcome of the other

event(s)event(s)

2. to find the probability of all events2. to find the probability of all events

occurring you do the same as withoccurring you do the same as with

independent eventsindependent events

3. number of possible outcomes changes3. number of possible outcomes changes

as events occur.as events occur.

4. example:4. example:A bag contains 5 blue, 3 red, and 2A bag contains 5 blue, 3 red, and 2

yellow marbles. What is theyellow marbles. What is the probability of drawing a blue marbleprobability of drawing a blue marble and then a red marble?and then a red marble?STEP 1STEP 1Find the probability of each event:Find the probability of each event:

* 5 of the 10 marbles are blue * 5 of the 10 marbles are blue →→PPblueblue = = 55 = = 11 10 2 10 2

* 3 of the 9 remaining marbles are red * 3 of the 9 remaining marbles are red →→PPredred = = 33 = = 11

9 39 3STEP 2STEP 2

*multiply the probabilities*multiply the probabilities11 * * 11 = = 11

2 3 62 3 6