Learn to find measures of variability.

Box-and-whisker Plots

The table below summarizes a veterinarian’s records for kitten litters born in a given year.

Litter Size 2 3 4 5 6

Number of Litters

1 6 8 11 1

While central tendency describes the middle of a data set, variability describes how spread out the data is.

The range of a data set is the largest value minus the smallest value.

Quartiles divide a data set into four equal parts.

Litter Size 2 3 4 5 6

Number of Litters

1 6 8 11 1

The range of a data set is the largest value minus the smallest value. For the kitten data, the range is 6 — 2 = 4.

The range is affected by outliers, so another measure is often used. Quartiles divide a data set into four equal parts.

Kitten Data

2 3 3 3 3 3 3 4 4 4 4 4 4 4 4 5 5 5 5 5 5 5 5 5 5 5 6Lower half Upper half

First quartile: 3 median of lower

half

Third quartile: 5 median of upper

halfMedian: 4 (second quartile)

1 2 3 4 5 6 7 8 9

A box-and-whisker plot shows the distribution of data. The middle half of the data is represented by a “box” with a vertical line at the median. The lower fourth and upper fourth quarters are represented by “whiskers” that extend to the smallest and largest values.

First quartile Third quartileMedian

23 24 26 29 31 31 33 35

Use the given data to make a box-and-whisker plot.

31, 23, 33, 35, 26, 24, 31, 29

Try This:

Step 1. Order the data and find the smallest value, first quartile, median, third quartile, and largest value.

smallest value: 23 largest value: 35

first quartile: = 25 24 + 26

2third quartile: = 32

31 + 33

2

median: = 3029 + 31

2

Use the given data to make a box-and-

whisker plot.

22 24 26 28 30 32 34 36 38

Step 2. Draw a number line and plot a point above each value.

23 24 26 29 31 31 33 35

Step 2. Draw a number line and plot a point above each value.

Use the given data to make a box-and-whisker plot.

22 24 26 28 30 32 34 36 38

Step 3. Draw the box and whiskers.

23 24 26 29 31 31 33 35

Find the range and the first and third quartiles for the data set.

Finding Measures of Variability

A. 15, 83, 75, 12, 19, 74, 21

12 15 19 21 74 75 83 Order the values.

range: 83 – 12 = 71

first quartile: 15

third quartile: 75

Find the range and the first and third quartiles for the data set.

Finding Measures of Variability

B. 75, 61, 88, 79, 79, 99, 63, 77

61 63 75 77 79 79 88 99

range: 99 – 61 = 38

first quartile: = 6963 + 752

third quartile: = 83.579 + 88

2

Order the values.

Use the given data to make a box-and-whisker plot: 21, 25, 15, 13, 17, 19, 19, 21

Making a Box-and-Whisker Plot

Step 1. Order the data and find the smallest value, first quartile, median, third quartile, and largest value.

13 15 17 19 19 21 21 25

smallest value: 13 largest value: 25

first quartile: = 16 15 + 17

2third quartile: = 21

21 + 21

2

median: = 1919 + 19

2

Step 1. Order the data and find the smallest value, first quartile, median, third quartile, and largest value.

Use the given data to make a box-and-whisker plot.

12 14 16 18 20 22 24 26 28

Step 2. Draw a number line and plot a point above each value from step 1.

smallest value 13

13 15 17 19 19 21 21 25first

quartile 16

median

19

third quartile

21

largest value

25

Continued:

Step 2. Draw a number line and plot a point above each value.

Use the given data to make a box-and-whisker plot.

12 14 16 18 20 22 24 26 28

Step 3. Draw the box and whiskers.

13 15 17 19 19 21 21 25

Continued:

Lesson Quiz

Use the following data for problems 3 and 4.

91, 87, 98, 93, 89, 78, 94

1. Make a box-and-whisker plot

2. What are the 3 quartiles?

87, 91, 94

78 87 91 94 98