Variability and Box-and-Whisker Plots10-4

Warm UpWarm Up

Lesson PresentationLesson Presentation

Problem of the DayProblem of the Day

Lesson QuizzesLesson Quizzes

Variability and Box-and-Whisker Plots10-4

Warm Up1. Order the test scores from least to greatest: 89, 93, 79, 87, 91, 88, 92.

2. Find the median of the test scores.

Find the difference.

79, 87, 88, 89, 91, 92, 93

89

16.1

166.9

0.8

3.4

3. 17 – 0.9 4. 8.4 – 7. 6

5. 9.1 – 5.7 6. 190.3 – 23.4

Variability and Box-and-Whisker Plots10-4

Problem of the Day

What are the possible values for x in the data set 22, 12, 33, 25, and x if the median is 25?

any number greater than or equal to 25

Variability and Box-and-Whisker Plots10-4

MA.8.S.3.1 …Construct…box-and-whisker plots…to convey information and make conjectures about possible relationships.

Sunshine State Standards

Variability and Box-and-Whisker Plots10-4

Vocabulary

variabilitybox-and-whisker plotfirst quartilethird quartileinterquartile range

Variability and Box-and-Whisker Plots10-4

While central tendency describes the middle of a data set, variability describes how spread out the data are. A box-and-whisker plot uses a number line to show how data are distributed and to illustrate the variability of a data set.

A box-and-whisker plot divides the data into four parts. The median, or second quartile, divides the data into a lower half and an upper half. The first quartile is the median of the lower half of the data, and the third quartile is the median of the upper half of the data.

Variability and Box-and-Whisker Plots10-4

Variability and Box-and-Whisker Plots10-4

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

Additional Example 1: Making a Box-and-Whisker Plot

Step 1: Order the data and find the least value, first quartile, median, third quartile, and greatest value.

13 15 17 19 19 21 21 25

least value: 13 greatest value: 25

first quartile: = 16 15 + 17

2third quartile: = 2121 + 21

2

median: = 1919 + 19

2

Variability and Box-and-Whisker Plots10-4

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.

least value

13

13 15 17 19 19 21 21 25first

quartile 16

median

19

third quartile

21

greatest value

25

Additional Example 1 Continued

Variability and Box-and-Whisker Plots10-4

12 14 16 18 20 22 24 26 28

Step 3: Draw the box and whiskers.

13 15 17 19 19 21 21 25

Additional Example 1 Continued

Variability and Box-and-Whisker Plots10-4

20 22 24 26 28 30 32 34 36 38 40

Check It Out: Example 1A

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

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

23 25 30 32 35

Variability and Box-and-Whisker Plots10-4

Check It Out: Example 1B

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

57, 53, 52, 31, 48, 58, 64, 86, 56, 54, 55

30 40 50 60 70 80 90

31 52 58 8655

Variability and Box-and-Whisker Plots10-4

The interquartile range of a data set is the difference between the third quartile and the first quartile. It represents the range of the middle half of the data.

Variability and Box-and-Whisker Plots10-4

Additional Example 2: Using Interquartile Range to Identify Outliers

Use interquartile range to identify any outliers.

75, 65, 78, 79, 76, 79, 72, 82

Step 1: Determine the first quartile, the third quartile, and the interquartile range.

65 72 75 76 78 79 79 82

Q1: 73.5 Q3: 79 IQR: 79 – 73.5 = 5.5

Variability and Box-and-Whisker Plots10-4

Additional Example 2 Continued

Use interquartile range to identify any outliers.

75, 65, 78, 79, 76, 79, 72, 82

Step 2: Determine whether there is an outlier less than the first quartile.

Q1 – (1.5 IQR)

73.5 – (1.5 5.5)

73.5 – 8.25 = 65.25

The least value in the data set is 65. This value is less than 65.25.

Variability and Box-and-Whisker Plots10-4

Additional Example 2 Continued

Use interquartile range to identify any outliers.

75, 65, 78, 79, 76, 79, 72, 82

Step 3: Determine whether there is an outlier greater than the third quartile.

Q3 + (1.5 IQR)

79 + (1.5 5.5)

79 + 8.25 = 87.25

The greatest value in the data set is 82. None of the values are greater than 87.25.

Variability and Box-and-Whisker Plots10-4

Additional Example 2 Continued

Use interquartile range to identify any outliers.

75, 65, 78, 79, 76, 79, 72, 82

The data value 65 is an outlier.

Variability and Box-and-Whisker Plots10-4

Check It Out: Example 2A

Use the interquartile range to identify any outliers.

25, 12, 31, 26, 27, 29, 32

12, 25, 26, 27, 29, 31, 32

Q1: 25 Q3: 31

IQR = 31 – 25 = 6

Q1 – (1.5 • IQR) = 25 – (1.5)(6)

= 25 – 9 = 16

Variability and Box-and-Whisker Plots10-4

Check It Out: Example 2A Continued

12 is less than 16, so 12 is an outlier. No values are greater than 40, so there are no other outliers.

Use the interquartile range to identify any outliers.

25, 12, 31, 26, 27, 29, 32

Q3 + (1.5 • IQR) = 31 + (1.5)(6)

= 31 + 9 = 40

Variability and Box-and-Whisker Plots10-4

Check It Out: Example 2B

Use the interquartile range to identify any outliers.

35, 46, 50, 32, 54, 44, 40

32, 35, 40, 44, 46, 50, 54

Q1: 35 Q3: 50

IQR = 50 – 35 = 15

Q1 – (1.5 • IQR) = 35 – (1.5)(15)

= 35 – 22.5 = 12.5

Variability and Box-and-Whisker Plots10-4

Check It Out: Example 2B Continued

Q3 + (1.5 • IQR) = 50 + (1.5)(15)

= 50 + 22.5 = 72.5

No values are less than 12.5 or greater than 72.5, so there are no outliers.

Use the interquartile range to identify any outliers.

35, 46, 50, 32, 54, 44, 40

Variability and Box-and-Whisker Plots10-4

Additional Example 3: Comparing Data Sets Using Box-and-Whisker Plots

These box-and-whisker plots compare the ages of the first ten U.S. presidents with the ages of the ten presidents from Dwight Eisenhower through George W. Bush when they took office.

Note: 57 is the first quartile and the median.

Variability and Box-and-Whisker Plots10-4

Additional Example 3 Continued

A. Compare the medians and ranges.

The median for the first ten presidents is slightly greater. The range for the last ten presidents from 1953-2008 is greater.

Note: 57 is the first quartile and the median.

Variability and Box-and-Whisker Plots10-4

Additional Example 3 Continued

B. Compare the interquartile ranges.

The interquartile range is greater for the ten presidents from 1953-2008.

Note: 57 is the first quartile and the median.

Variability and Box-and-Whisker Plots10-4

Check It Out: Example 3

Compare the interquartile ranges of the data sets in Example 3.

For the first ten presidents: IQR = 61 – 57 = 4

For the ten presidents from 1953–2008: IQR = 62 – 52 = 10

The interquartile range is greater for the ten presidents from 1953–2008.

Variability and Box-and-Whisker Plots10-4

Standard Lesson Quiz

Lesson Quizzes

Lesson Quiz for Student Response Systems

Variability and Box-and-Whisker Plots10-4

Lesson Quiz: Part I

Use the following data for problems 1 and 2.

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

1. Make a box-and-whisker plot.

2. Use the interquartile range to identify and

outliers.

none

78 87 91 94 98

Variability and Box-and-Whisker Plots10-4

Lesson Quiz: Part II

3. Use the box-and-whisker plots to compare the

medians and ranges of the data sets.

Data set A has a greater median. Data set B has a greater range.

Variability and Box-and-Whisker Plots10-4

1. Identify the first and third quartiles for the given data set.

15, 45, 65, 75, 35, 55, 25

A. Q1 = 15; Q3 = 65

B. Q1 = 25; Q3 = 65

C. Q1 = 15; Q3 = 75

D. Q1 = 25; Q3 = 75

Lesson Quiz for Student Response Systems

Variability and Box-and-Whisker Plots10-4

2. Identify a box-and-whisker plot for the given data.

42, 72, 65, 44, 52, 79, 68, 55, 60

A. B.

Lesson Quiz for Student Response Systems