1. 4-4 Variability Objective: Learn to find measures of variability.
Course 3
4-4
Variability
Objective: Learn to find measures of variability.

2. Does the mean, median or mode give any indication of how the data is spread out or is it a central view of the data?

3. 5 Pieces of Data in Box & Whisker Plot (in order from left to right)
Lower extreme—lowest number
First quartile—middle of lower-half
Median—middle number
Third quartile—middle of upper half
Upper extreme—largest number

4. Box and Whisker Plot
Upper extreme
Lower extreme
Median
First quartile
Third quartile

5. Range--largest minus the smallest; it’s the entire length of the line
Range--largest minus the smallest; it’s the entire length of the line

6. Course 3
4-4
Variability
Data
The range of a data set is the largest value minus the smallest value. For the kitten data, the range is 6 — 2 = 4.
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
Quartiles divide a data set into four equal parts. Here’s how to find the 1st and 3rd quartiles:
1st: order data least to greatest
2nd: if odd amount, middle number is median
If even amount, add 2 middle numbers and divide by 2 for median
3rd: Divide data in half with a line; if odd—don’t include median (draw line through it) if even—draw line between 2 middle data points
4th: the first quartile is the middle half of the left side of data
5th: the third quartile is the middle half of the right side of the data

7. Additional Example 1A: Finding Measures of Variability
Course 3
4-4
Variability
Additional Example 1A: Finding Measures of Variability
Find the range and the first and third quartiles for the data set.
A. 15, 83, 75, 12, 19, 74, 21
Order the values.
range: 83 – 12 = 71
first quartile: 15
third quartile: 75

8. Additional Example 1B: Finding Measures of Variability
Course 3
4-4
Variability
Additional Example 1B: Finding Measures of Variability
Find the range and the first and third quartiles for the data set.
B. 75, 61, 88, 79, 79, 99, 63, 77

9. 4-4 Variability Try This: Example 1A
Course 3
4-4
Variability
Try This: Example 1A
Find the range and the first and third quartiles for the data set.
A. 25, 38, 66, 19, 91, 47, 13

10. 4-4 Variability Try This: Example 1B
Course 3
4-4
Variability
Try This: Example 1B
Find the range and the first and third quartiles for the data set.
B. 45, 31, 59, 49, 49, 69, 33, 47

11. Course 3
4-4
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

12. Use the given data to make a box-and-whisker plot:
Course 3
4-4
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

13. Use the given data to make a box-and-whisker plot.
Course 3
4-4
Variability
Additional Example 2 Continued
Use the given data to make a box-and-whisker plot.
Step 1. Order the data and find the smallest value, first quartile, median, third quartile, and largest value.
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

14. Use the given data to make a box-and-whisker plot.
Course 3
4-4
Variability
Use the given data to make a box-and-whisker plot.
Step 3. Draw the box and whiskers. The left whisker is from the 1st to 2nd dot. The right whisker connects the 4th and 5th dot. The box connects the 2nd dot and 4th dot. Draw a line through the median.
Step 2. Draw a number line and plot a point above each value.

15. Use the given data to make a box-and-whisker plot.
Course 3
4-4
Variability
Try This: 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.

16. Use the given data to make a box-and-whisker plot.
Course 3
4-4
Variability
Try This: 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.

17. Use the given data to make a box-and-whisker plot.
Course 3
4-4
Variability
Try This: 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.

21. Additional Example 3: Comparing Data Sets Using Box-and-Whisker Plots
Course 3
4-4
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.

22. Additional Example 3 Continued
Course 3
4-4
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.

23. Additional Example 3 Continued
Course 3
4-4
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.

24. 4-4 Variability Try This: Example 3 Oakland
Course 3
4-4
Variability
Try This: 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.

25. Try This: Example 3 Continued
Course 3
4-4
Variability
Try This: Example 3 Continued
A. Compare the medians and ranges.
Oakland
Tampa Bay

26. Try This: Example 3 Continued
Course 3
4-4
Variability
Try This: Example 3 Continued
B. Compare the differences between the third quartile and first quartile for each.
Oakland
Tampa Bay

27. Insert Lesson Title Here
Course 3
4-4
Variability
Insert Lesson Title Here
Lesson Quiz: Part 1
Find the range and 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

28. Insert Lesson Title Here
Course 3
4-4
Variability
Insert Lesson Title Here
Lesson Quiz: Part 2
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 mean?