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

Vocabulary

lower quartileupper quartilebox-and-whisker plotminimummaximum

Litter Size 2 3 4 5 6

Number of Litters

1 6 8 11 1

The table below summarizes a cat breeder’s records for kitten litters born in a given year. You can divide the data into four equal part using quartiles.

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 6

Lower half Upper half

Lower quartile: 3 median of lower

half

Upper quartile: 5 median of upper

halfMedian: 4

You know that the median of a data set divides the data into a lower half and an upper half. The median of the lower half is the lower quartile, and the median of the upper half is the upper quartile.

Find the lower and upper quartiles for the data set.

Example 1: Finding Quartiles

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

12 15 19 21 74 75 83

Order the values.

lower quartile: 15

upper quartile: 75

Find the lower and upper quartiles for the data set.

Example 2: Finding Quartiles

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

61 63 75 77 79 79 88 99

lower quartile: = 6963 + 752

upper quartile: = 83.5

79 + 882

Order the values.

Find the lower and upper quartiles for the data set.

Check It Out! Example 3

A. 25, 38, 66, 19, 91, 47, 13

13 19 25 38 47 66 91

Order the values.

lower quartile: 19

upper quartile: 66

B. 45, 31, 59, 49, 49, 69, 33, 47

31 33 45 47 49 49 59 69

Order the values.

Find the lower and upper quartiles for the data set.

Check It Out! Example 1

lower quartile: = 3933 + 452

upper quartile: = 5449 + 59

2

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 minimum (least) and maximum (greatest) values.

Lower quartile Upper quartileMedian

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

Example 4: Making a Box-and-Whisker Plot

Step 1. Order the data from least to greatest. Then find the minimum, lower quartile, median, upper quartile, and maximum.

13 15 17 19 19 21 21 25

minimum: 13 maximum: 25

lower quartile: = 16

15 + 17

2upper quartile: = 21

21 + 21

2median: = 19

19 + 19

2

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.

13 15 17 19 19 21 21 25

Example 4 Continued

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

Example 4 Continued

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

Example 5

Step 1. Order the data from least to greatest. Then find the minimum, lower quartile, median, upper quartile, and maximum.

minimum: 23 maximum: 35

lower quartile: = 25

24 + 26

2upper quartile: = 32

31 + 33

2

median: = 30

29 + 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

Example 5 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.

22 24 26 28 30 32 34 36 38

Step 3. Draw the box and whiskers.

23 24 26 29 31 31 33 35

Example 5 Continued

Example 6Quarter 1 2 3 4

Oakland 3 0 6 12

Tampa Bay 3 17 14 14

These box-and-whisker plots compare the point per quarter at Super Bowl XXXVII.

Oakland

0 3 6 9 12 15 18

Tampa Bay

0 3 6 9 12 15 18

A. Compare the medians and ranges.

Example 6

The median for Tampa Bay is significantly greater and the range for Tampa Bay is slightly greater.

Oakland

0 3 6 9 12 15 18

Tampa Bay

0 3 6 9 12 15 18

B. Compare the ranges of the middle half of the data for each.

Check It Out! Example 6

The range of the middle half of the data is greater for Tampa Bay.

Oakland

0 3 6 9 12 15 18

Tampa Bay

0 3 6 9 12 15 18

Lesson Quiz: Part I

Find the lower and upper quartiles for

each data set.

1. 48, 52, 68, 32, 53, 47, 51

2. 3, 18, 11, 2, 7, 5, 9, 6, 13, 1, 17, 8,

0lower = 2.5; upper = 12

lower = 47; upper = 53

Lesson Quiz: Part II

Use the following data for problems 3 and

4. 91, 87, 98, 93, 89, 78, 94

3. Make a box-and-whisker plot.

4. What is the median and range of the data?

91; 20

78 87 91 94 98