Box – and – Whisker Plots

Box – and – Whisker Plots

- a method of displaying and interpreting a data set- data is first arranged into numeric order ( small to

large )

Box – and – Whisker Plots

- a method of displaying and interpreting a data set- data is first arranged into numeric order ( small to

large )- then the MEDIAN is found

Box – and – Whisker Plots

- a method of displaying and interpreting a data set- data is first arranged into numeric order ( small to

large )- then the MEDIAN is found- data is then separated into QUARTILES

Box – and – Whisker Plots

- a method of displaying and interpreting a data set- data is first arranged into numeric order ( small to

large )- then the MEDIAN is found- data is then separated into QUARTILES

EXAMPLE # 1 : The data set given are the daily temperatures for a week. 85 , 70 , 75 , 87 , 83 , 76 ,

80

Box – and – Whisker Plots

- a method of displaying and interpreting a data set- data is first arranged into numeric order ( small to

large )- then the MEDIAN is found- data is then separated into QUARTILES

EXAMPLE # 1 : The data set given are the daily temperatures for a week. 85 , 70 , 75 , 87 , 83 , 76 ,

80First : arrange the data into numeric order ( small to large )

Box – and – Whisker Plots

- a method of displaying and interpreting a data set- data is first arranged into numeric order ( small to

large )- then the MEDIAN is found- data is then separated into QUARTILES

EXAMPLE # 1 : The data set given are the daily temperatures for a week. 85 , 70 , 75 , 87 , 83 , 76 ,

80First : arrange the data into numeric order ( small to large )70 , 75 , 76 , 80 , 83 , 85 ,

87

Box – and – Whisker Plots

- a method of displaying and interpreting a data set- data is first arranged into numeric order ( small to

large )- then the MEDIAN is found- data is then separated into QUARTILES

EXAMPLE # 1 : The data set given are the daily temperatures for a week. 85 , 70 , 75 , 87 , 83 , 76 ,

80First : arrange the data into numeric order ( small to large )70 , 75 , 76 , 80 , 83 , 85 ,

87Second : Find the median

Box – and – Whisker Plots

- a method of displaying and interpreting a data set- data is first arranged into numeric order ( small to

large )- then the MEDIAN is found- data is then separated into QUARTILES

EXAMPLE # 1 : The data set given are the daily temperatures for a week. 85 , 70 , 75 , 87 , 83 , 76 ,

80First : arrange the data into numeric order ( small to large )70 , 75 , 76 , 80 , 83 , 85 ,

87Second : Find the median

- the median separates the data set into two equal parts

Box – and – Whisker Plots

- a method of displaying and interpreting a data set- data is first arranged into numeric order ( small to

large )- then the MEDIAN is found- data is then separated into QUARTILES

EXAMPLE # 1 : The data set given are the daily temperatures for a week. 85 , 70 , 75 , 87 , 83 , 76 ,

80First : arrange the data into numeric order ( small to large )70 , 75 , 76 , 80 , 83 , 85 ,

87Second : Find the median

- the median separates the data set into two equal parts

- if there is an odd number of data items, it’s the middle one

Box – and – Whisker Plots

- a method of displaying and interpreting a data set- data is first arranged into numeric order ( small to

large )- then the MEDIAN is found- data is then separated into QUARTILES

EXAMPLE # 1 : The data set given are the daily temperatures for a week. 85 , 70 , 75 , 87 , 83 , 76 ,

80First : arrange the data into numeric order ( small to large )70 , 75 , 76 , 80 , 83 , 85 ,

87

Second : Find the median- the median separates the data set into two equal

parts- if there is an odd number of data items, it’s the

middle one- if there are an even number of data items, take the

sum of the two middle items and divide by two

Box – and – Whisker Plots

- a method of displaying and interpreting a data set- data is first arranged into numeric order ( small to

large )- then the MEDIAN is found- data is then separated into QUARTILES

EXAMPLE # 1 : The data set given are the daily temperatures for a week. 85 , 70 , 75 , 87 , 83 , 76 ,

80First : arrange the data into numeric order ( small to large )70 , 75 , 76 , 80 , 83 , 85 ,

87

Second : Find the median- the median separates the data set into two equal

parts- if there is an odd number of data items, it’s the

middle one- if there are an even number of data items, take the

sum of the two middle items and divide by two

- Seven items so use the “middle” one

Box – and – Whisker Plots

- a method of displaying and interpreting a data set- data is first arranged into numeric order ( small to

large )- then the MEDIAN is found- data is then separated into QUARTILES

EXAMPLE # 1 : The data set given are the daily temperatures for a week. 85 , 70 , 75 , 87 , 83 , 76 ,

80First : arrange the data into numeric order ( small to large )70 , 75 , 76 , 80 , 83 , 85 ,

87

Second : Find the medianThird : Separate the data into quartiles

Box – and – Whisker Plots

- a method of displaying and interpreting a data set- data is first arranged into numeric order ( small to

large )- then the MEDIAN is found- data is then separated into QUARTILES

EXAMPLE # 1 : The data set given are the daily temperatures for a week. 85 , 70 , 75 , 87 , 83 , 76 ,

80First : arrange the data into numeric order ( small to large )70 , 75 , 76 , 80 , 83 , 85 ,

87

Second : Find the medianThird : Separate the data into quartiles

- Quartiles divide the data into sections, each containing 25% of the total data set

Box – and – Whisker Plots

- a method of displaying and interpreting a data set- data is first arranged into numeric order ( small to

large )- then the MEDIAN is found- data is then separated into QUARTILES

EXAMPLE # 1 : The data set given are the daily temperatures for a week. 85 , 70 , 75 , 87 , 83 , 76 ,

80First : arrange the data into numeric order ( small to large )70 , 75 , 76 , 80 , 83 , 85 ,

87

Second : Find the medianThird : Separate the data into quartiles

- Quartiles divide the data into sections, each containing 25% of the total data set

The first quartile or “lower” quartile is the “middle” of the data to the left of the median.

Box – and – Whisker Plots

- a method of displaying and interpreting a data set- data is first arranged into numeric order ( small to

large )- then the MEDIAN is found- data is then separated into QUARTILES

EXAMPLE # 1 : The data set given are the daily temperatures for a week. 85 , 70 , 75 , 87 , 83 , 76 ,

80First : arrange the data into numeric order ( small to large )70 , 75 , 76 , 80 , 83 , 85 ,

87

Second : Find the medianThird : Separate the data into quartiles

- Quartiles divide the data into sections, each containing 25% of the total data set

The first quartile or “lower” quartile is the “middle” of the data to the left of the median.The second quartile is another name for the median.

Box – and – Whisker Plots

- a method of displaying and interpreting a data set- data is first arranged into numeric order ( small to

large )- then the MEDIAN is found- data is then separated into QUARTILES

EXAMPLE # 1 : The data set given are the daily temperatures for a week. 85 , 70 , 75 , 87 , 83 , 76 ,

80First : arrange the data into numeric order ( small to large )70 , 75 , 76 , 80 , 83 , 85 ,

87

Second : Find the medianThird : Separate the data into quartiles

- Quartiles divide the data into sections, each containing 25% of the total data set

The first quartile or “lower” quartile is the “middle” of the data to the left of the median.The second quartile is another name for the median.The third quartile or “upper” quartile is the “middle” of the data to the right of the median.

Box – and – Whisker Plots

- a method of displaying and interpreting a data set- data is first arranged into numeric order ( small to

large )- then the MEDIAN is found- data is then separated into QUARTILES

EXAMPLE # 1 : The data set given are the daily temperatures for a week. 85 , 70 , 75 , 87 , 83 , 76 ,

80First : arrange the data into numeric order ( small to large )70 , 75 , 76 , 80 , 83 , 85 ,

87

Second : Find the medianThird : Separate the data into quartiles

The interquartile range is the difference between the third and first quartiles.

Box – and – Whisker Plots

- a method of displaying and interpreting a data set- data is first arranged into numeric order ( small to

large )- then the MEDIAN is found- data is then separated into QUARTILES

EXAMPLE # 1 : The data set given are the daily temperatures for a week. 85 , 70 , 75 , 87 , 83 , 76 ,

80First : arrange the data into numeric order ( small to large )70 , 75 , 76 , 80 , 83 , 85 ,

87

Second : Find the medianThird : Separate the data into quartiles

The interquartile range is the difference between the third and first quartiles.Interquartile range = 85 – 75 = 10

Box – and – Whisker Plots

- a method of displaying and interpreting a data set- data is first arranged into numeric order ( small to

large )- then the MEDIAN is found- data is then separated into QUARTILES

EXAMPLE # 1 : The data set given are the daily temperatures for a week.

70 73 76 79 82 85 88

To create the box – and – whisker plot, we will use a number line…you can use whatever scale you want

First Quartile = 75

Median = 80 Third Quartile = 85

Lowest Value = 70

Highest Value = 87

Box – and – Whisker Plots

- a method of displaying and interpreting a data set- data is first arranged into numeric order ( small to

large )- then the MEDIAN is found- data is then separated into QUARTILES

EXAMPLE # 1 : The data set given are the daily temperatures for a week.

70 73 76 79 82 85 88

First Quartile = 75

Median = 80 Third Quartile = 85

Lowest Value = 70

Highest Value = 87

Place a point beneath the number line for each quartile and each end point. You might have to make an educated guess if the data point falls between your scale values…

Box – and – Whisker Plots

- a method of displaying and interpreting a data set- data is first arranged into numeric order ( small to

large )- then the MEDIAN is found- data is then separated into QUARTILES

EXAMPLE # 1 : The data set given are the daily temperatures for a week.

70 73 76 79 82 85 88

First Quartile = 75

Median = 80 Third Quartile = 85

Lowest Value = 70

Highest Value = 87

Draw vertical lines thru the first, second and third quartiles…

Box – and – Whisker Plots

- a method of displaying and interpreting a data set- data is first arranged into numeric order ( small to

large )- then the MEDIAN is found- data is then separated into QUARTILES

EXAMPLE # 1 : The data set given are the daily temperatures for a week.

70 73 76 79 82 85 88

First Quartile = 75

Median = 80 Third Quartile = 85

Lowest Value = 70

Highest Value = 87

Connect the lines creating boxes…

Box – and – Whisker Plots

- a method of displaying and interpreting a data set- data is first arranged into numeric order ( small to

large )- then the MEDIAN is found- data is then separated into QUARTILES

EXAMPLE # 1 : The data set given are the daily temperatures for a week.

70 73 76 79 82 85 88

First Quartile = 75

Median = 80 Third Quartile = 85

Lowest Value = 70

Highest Value = 87

Then lines called “whiskers” are drawn to the edges from the boxes…

Box – and – Whisker Plots

EXAMPLE # 2 : The data set given are the golf scores for a player for a summer.

80, 75 , 78 , 85 , 72 , 74 , 83 , 81 , 75 , 77 , 73 , 88 , 76 , 79

Box – and – Whisker Plots

EXAMPLE # 2 : The data set given are the golf scores for a player for a summer.

80, 75 , 78 , 85 , 72 , 74 , 83 , 81 , 75 , 77 , 73 , 88 , 76 , 7972, 73 , 74 , 75 , 75 , 76 , 77 , 78 , 79 , 80 , 81 , 83 , 85 , 88First get them in numeric order small

to large

Box – and – Whisker Plots

EXAMPLE # 2 : The data set given are the golf scores for a player for a summer.

80, 75 , 78 , 85 , 72 , 74 , 83 , 81 , 75 , 77 , 73 , 88 , 76 , 7972, 73 , 74 , 75 , 75 , 76 , 77 , 78 , 79 , 80 , 81 , 83 , 85 , 88There are 14 items, so find the sum of middle two and

divide by 2

Box – and – Whisker Plots

EXAMPLE # 2 : The data set given are the golf scores for a player for a summer.

80, 75 , 78 , 85 , 72 , 74 , 83 , 81 , 75 , 77 , 73 , 88 , 76 , 79

72, 73 , 74 , 75 , 75 , 76 , 77 ,77.5 , 78 , 79 , 80 , 81 , 83 , 85 , 88

Box – and – Whisker Plots

EXAMPLE # 2 : The data set given are the golf scores for a player for a summer.

80, 75 , 78 , 85 , 72 , 74 , 83 , 81 , 75 , 77 , 73 , 88 , 76 , 79

72, 73 , 74 , 75 , 75 , 76 , 77 ,77.5 , 78 , 79 , 80 , 81 , 83 , 85 , 88

First quartile = 75

Third quartile = 81

Box – and – Whisker Plots

EXAMPLE # 2 : The data set given are the golf scores for a player for a summer.

80, 75 , 78 , 85 , 72 , 74 , 83 , 81 , 75 , 77 , 73 , 88 , 76 , 79

72, 73 , 74 , 75 , 75 , 76 , 77 ,77.5 , 78 , 79 , 80 , 81 , 83 , 85 , 88

First quartile = 75

Third quartile = 81

Interquartile range = 81 – 75 = 6

Box – and – Whisker Plots

EXAMPLE # 2 : The data set given are the golf scores for a player for a summer.

80, 75 , 78 , 85 , 72 , 74 , 83 , 81 , 75 , 77 , 73 , 88 , 76 , 79

72, 73 , 74 , 75 , 75 , 76 , 77 ,77.5 , 78 , 79 , 80 , 81 , 83 , 85 , 88

First quartile = 75

Third quartile = 81

Interquartile range = 81 – 75 = 6

Create your box – and – whisker plot

72 74 76 78 80 82 84 86 88

Box – and – Whisker Plots

EXAMPLE # 2 : The data set given are the golf scores for a player for a summer.

80, 75 , 78 , 85 , 72 , 74 , 83 , 81 , 75 , 77 , 73 , 88 , 76 , 79

72, 73 , 74 , 75 , 75 , 76 , 77 ,77.5 , 78 , 79 , 80 , 81 , 83 , 85 , 88

First quartile = 75

Third quartile = 81

Interquartile range = 81 – 75 = 6

Create your box – and – whisker plot

72 74 76 78 80 82 84 86 88

Box – and – Whisker Plots

EXAMPLE # 3 : The box – and – whisker plot below shows the test grades for Mr. Beetle’s math class.

60

70

80 90 100

Box – and – Whisker Plots

EXAMPLE # 3 : The box – and – whisker plot below shows the test grades for Mr. Beetle’s math class.

60

70

80 90 100

Find : a) medianb) highest scorec) lowest scored) first quartilee) third quartilef) interquartile

range

Box – and – Whisker Plots

EXAMPLE # 3 : The box – and – whisker plot below shows the test grades for Mr. Beetle’s math class.

60

70

80 90 100

Find : a) median = 80 b) highest scorec) lowest scored) first quartilee) third quartilef) interquartile range

- It’s the middle data point in the box

Box – and – Whisker Plots

EXAMPLE # 3 : The box – and – whisker plot below shows the test grades for Mr. Beetle’s math class.

60

70

80 90 100

Find : a) median = 80 b) highest score = 95c) lowest scored) first quartilee) third quartilef) interquartile range

- the last data point

Box – and – Whisker Plots

EXAMPLE # 3 : The box – and – whisker plot below shows the test grades for Mr. Beetle’s math class.

60

70

80 90 100

Find : a) median = 80 b) highest score = 95c) lowest score = 62d) first quartilee) third quartilef) interquartile range

- the first data point ( make an educated guess in relation to your scale. It falls between 60 & 65 and is closer to 60 )

Box – and – Whisker Plots

EXAMPLE # 3 : The box – and – whisker plot below shows the test grades for Mr. Beetle’s math class.

60

70

80 90 100

Find : a) median = 80 b) highest score = 95c) lowest score = 62d) first quartile = 70e) third quartilef) interquartile range

- the data point at the very left of the box

Box – and – Whisker Plots

EXAMPLE # 3 : The box – and – whisker plot below shows the test grades for Mr. Beetle’s math class.

60

70

80 90 100

Find : a) median = 80 b) highest score = 95c) lowest score = 62d) first quartile = 70e) third quartile = 87f) interquartile range

- the data point at the very right of the box ( again you need to make an educated guess)

Box – and – Whisker Plots

EXAMPLE # 3 : The box – and – whisker plot below shows the test grades for Mr. Beetle’s math class.

60

70

80 90 100

Find : a) median = 80 b) highest score = 95c) lowest score = 62d) first quartile = 70e) third quartile = 87f) interquartile range = 87 – 70 = 17 ( third quartile – first

quartile )