1. Warm Up
Problem of the Day
Lesson Presentation
Lesson Quizzes

2. Warm Up
1. 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
3. 17 – – 7. 6
16.1
0.8
– – 23.4
3.4
166.9

3. 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

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

5. Vocabulary variability box-and-whisker plot first quartile
third quartile
interquartile range

6. 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.

8. Use the given data to make a box-and-whisker plot:
Additional Example 1: Making a Box-and-Whisker Plot
Use the given data to make a box-and-whisker plot:
21, 25, 15, 13, 17, 19, 19, 21
Step 1: Order the data and find the least value, first quartile, median, third quartile, and greatest value.
least value: 13
greatest value: 25
first quartile: = 16 2
third quartile: = 21 2
median: = 19 2

9. Additional Example 1 Continued
Step 2: Draw a number line and plot a point above each value from Step 1.
least value 13
first quartile 16
median 19
third quartile 21
greatest value 25

10. Additional Example 1 Continued
Step 3: Draw the box and whiskers.

11. Use the given data to make a box-and-whisker plot.
Check It Out: Example 1A
Use the given data to make a box-and-whisker plot.
31, 23, 33, 35, 26, 24, 31, 29

12. Use the given data to make a box-and-whisker plot.
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 55

13. 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.

14. 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.
Q1: 73.5
Q3: 79
IQR: 79 – 73.5 = 5.5

15. 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

16. 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)
= 87.25
The greatest value in the data set is 82. None of the values are greater than

17. 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.

18. 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

19. Check It Out: Example 2A Continued
Use the interquartile range to identify any outliers.
25, 12, 31, 26, 27, 29, 32
Q3 + (1.5 • IQR) = 31 + (1.5)(6)
= = 40
12 is less than 16, so 12 is an outlier. No values are greater than 40, so there are no other outliers.

20. 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

21. Check It Out: Example 2B Continued
Use the interquartile range to identify any outliers.
35, 46, 50, 32, 54, 44, 40
Q3 + (1.5 • IQR) = 50 + (1.5)(15)
= = 72.5
No values are less than 12.5 or greater than 72.5, so there are no outliers.

22. Additional Example 3: Comparing Data Sets Using Box-and-Whisker Plots
Note: 57 is the first quartile and the median.
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.

23. Additional Example 3 Continued
Note: 57 is the first quartile and the median.
A. Compare the medians and ranges.
The median for the first ten presidents is slightly greater. The range for the last ten presidents from is greater.

24. Additional Example 3 Continued
Note: 57 is the first quartile and the median.
B. Compare the interquartile ranges.
The interquartile range is greater for the ten presidents from

25. 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.

26. Lesson Quiz for Student Response Systems
Lesson Quizzes
Standard Lesson Quiz
Lesson Quiz for Student Response Systems 26

27. 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

28. 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.

29. Lesson Quiz for Student Response Systems
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 29

30. Lesson Quiz for Student Response Systems
2. Identify a box-and-whisker plot for the given data.
42, 72, 65, 44, 52, 79, 68, 55, 60
A B. 30