1. 9-4 Variability Warm Up Problem of the Day Lesson Presentation
Course 3
Warm Up
Problem of the Day
Lesson Presentation

2. Course 3
9-4
Variability
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. 9-4 Variability Problem of the Day
Course 3
9-4
Variability
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. Course 3
9-4
Variability
Learn to find measures of variability.

5. Insert Lesson Title Here
Course 3
9-4
Variability
Insert Lesson Title Here
Vocabulary
variability
quartile
box-and-whisker plot

6. 9-4 Variability Litter Size 2 3 4 5 6 Number of Litters 1 8 11
Course 3
9-4
Variability
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 8 11
While central tendency describes the middle of a data set, variability describes how spread out the data is. Quartiles divide a data set into four equal parts. The third quartile minus the first quartile is the range for the middle half of the data.

7. Course 3
9-4
Variability
The range of a data set is the largest value minus the smallest value. For the kitten data, the range is 6 — 2 = 4.
Kitten Data
Lower half
Upper half
First quartile: 3 median of lower half
Median: 4 (second quartile)
Third quartile: 5 median of upper half
Litter Size 2 3 4 5 6
Number of Litters 1 8 11
The range is affected by outliers, so another measure is often used. Quartiles divide a data set into four equal parts. The third quartile minus the first quartile is the range for the middle half of the data.

8. Additional Example 1A: Finding Measures of Variability
Course 3
9-4
Variability
Additional Example 1A: Finding Measures of Variability
Find the first and third quartiles for the data set.
15, 83, 75, 12, 19, 74, 21
Order the values.
first quartile: 15
third quartile: 75

9. Additional Example 1B: Finding Measures of Variability
Course 3
9-4
Variability
Additional Example 1B: Finding Measures of Variability
Find the first and third quartiles for the data set.
75, 61, 88, 79, 79, 99, 63, 77
Order the values.
first quartile: = 69 2
third quartile: = 83.5 2

10. 9-4 Variability Check It Out: Example 1A
Course 3
9-4
Variability
Check It Out: Example 1A
Find the first and third quartiles for the data set.
25, 38, 66, 19, 91, 47, 13
Order the values.
first quartile: 19
third quartile: 66

11. 9-4 Variability Check It Out: Example 1B
Course 3
9-4
Variability
Check It Out: Example 1B
Find the first and third quartiles for the data set.
45, 31, 59, 49, 49, 69, 33, 47
Order the values.
first quartile: = 39 2
third quartile: = 54 2

12. Course 3
9-4
Variability
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.
Median
First quartile
Third quartile

13. Use the given data to make a box-and-whisker plot:
Course 3
9-4
Variability
Additional Example 2: 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 smallest value, first quartile, median, third quartile, and largest value.
smallest value: 13
largest value: 25
first quartile: = 16 2
third quartile: = 21 2
median: = 19 2

14. Use the given data to make a box-and-whisker plot.
Course 3
9-4
Variability
Additional Example 2 Continued
Use the given data to make a box-and-whisker plot.
Step 2. Draw a number line and plot a point above each value from Step 1.
smallest value 13
first quartile 16
median 19
third quartile 21
largest value 25

15. Use the given data to make a box-and-whisker plot.
Course 3
9-4
Variability
Additional Example 2 Continued
Use the given data to make a box-and-whisker plot.
Step 3. Draw the box and whiskers.

16. Use the given data to make a box-and-whisker plot.
Course 3
9-4
Variability
Check It Out: Example 2
Use the given data to make a box-and-whisker plot.
31, 23, 33, 35, 26, 24, 31, 29
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 2
third quartile: = 32 2
median: = 30 2

17. Use the given data to make a box-and-whisker plot.
Course 3
9-4
Variability
Check It Out: Example 2 Continued
Use the given data to make a box-and-whisker plot.
Step 2. Draw a number line and plot a point above each value.

18. Use the given data to make a box-and-whisker plot.
Course 3
9-4
Variability
Check It Out: Example 2 Continued
Use the given data to make a box-and-whisker plot.
Step 3. Draw the box and whiskers.
Step 2. Draw a number line and plot a point above each value.

19. Additional Example 3: Comparing Data Sets Using Box-and-Whisker Plots
Course 3
9-4
Variability
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 last ten presidents (through George W. Bush) when they took office.

20. Additional Example 3 Continued
Course 3
9-4
Variability
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 is greater.

21. Additional Example 3 Continued
Course 3
9-4
Variability
Additional Example 3 Continued
Note: 57 is the first quartile and the median.
B. Compare the differences between the third quartile and first quartile for each.
The difference between the third quartile and first quartile is the length of the box, which is greater for the last ten presidents.

22. 9-4 Variability Check It Out: Example 3 Oakland
Course 3
9-4
Variability
Check It Out: Example 3
Final 1 2 3 4 T
Oakland 6 12 21
Tampa Bay 17 14 48
Oakland
Tampa Bay
These box-and-whisker plots compare the scores per quarter at Super Bowl XXXVII. The data in the T column is left out because it is a total of all the quarters.

23. 9-4 Variability Check It Out: Example 3A
Course 3
9-4
Variability
Check It Out: Example 3A
Compare the medians and ranges.
Oakland
Tampa Bay
The median for Tampa Bay is significantly greater, however the range for Tampa Bay is slightly greater.

24. 9-4 Variability Check It Out: Example 3B
Course 3
9-4
Variability
Check It Out: Example 3B
Compare the differences between the third quartile and first quartile for each.
Oakland
Tampa Bay
The difference between the third quartile and first quartile is the length of the box, which is slightly greater for Oakland.

25. Insert Lesson Title Here
Course 3
9-4
Variability
Insert Lesson Title Here
Lesson Quiz: Part I
Find the first and third quartile 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, 0
Q1 = 47; Q3 = 53
Q1 = 2.5; Q3 = 12

26. Insert Lesson Title Here
Course 3
9-4
Variability
Insert Lesson Title Here
Lesson Quiz: Part II
Use the following data for problems 3 and , 87, 98, 93, 89, 78, 94
3. Make a box-and-whisker plot
4. What is the mean? 90