1. Measures of Dispersion
8.3
Compute the range of a data set.
Understand how the standard deviation measures the spread of a distribution.
Use the coefficient of variation to compare the standard deviations of different distributions.

2. The Range of a Data Set
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Section 15.3, Slide 2

3. The Range of a Data Set
Example: Find the range of the heights of the people listed in the accompanying table.
Solution:
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Section 15.3, Slide 3

4. Standard Deviation © 2010 Pearson Education, Inc. All rights reserved.
Section 15.3, Slide 4

5. Standard Deviation © 2010 Pearson Education, Inc. All rights reserved.
Section 15.3, Slide 5

6. Standard Deviation © 2010 Pearson Education, Inc. All rights reserved.
Section 15.3, Slide 6

7. Standard Deviation Solution:
Example: A company has hired six interns. After 4 months, their work records show the following number of work days missed for each worker:
0, 2, 1, 4, 2, 3
Find the standard deviation of this data set.
Solution:
Mean:
(continued on next slide)
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Section 15.3, Slide 7

8. Standard Deviation
We calculate the squares of the deviations of the data values from the mean.
Standard Deviation:
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Section 15.3, Slide 8

9. Standard Deviation © 2010 Pearson Education, Inc. All rights reserved.
Section 15.3, Slide 9

10. Standard Deviation Solution:
Example: The following are the closing prices for a stock for the past 20 trading sessions:
37, 39, 39, 40, 40, 38, 38, 39, 40, 41,
41, 39, 41, 42, 42, 44, 39, 40, 40, 41
What is the standard deviation for this data set?
Solution:
Mean: (sum of the closing prices is 800)
(continued on next slide)
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Section 15.3, Slide 10

11. Standard Deviation
We create a table with values that will facilitate computing the standard deviation.
Standard Deviation:
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Section 15.3, Slide 11

12. Standard Deviation Comparing Standard Deviations
All three distributions have a mean and median of 5; however, as the spread of the distribution increases, so does the standard deviation.
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Section 15.3, Slide 12

13. The Coefficient of Variation
Relatively speaking there is more variation in the weights of the 1st graders than the NFL players below.
1st Graders
Mean: 30 pounds
SD: 3 pounds
CV:
NFL Players
Mean: 300 pounds
SD: 10 pounds
CV:
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Section 15.3, Slide 13

14. The Coefficient of Variation
Example: Use the coefficient of variation to determine whether the women’s 100-meter race or the men’s marathon has had more consistent times over the five Olympics listed.
(continued on next slide)
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Section 15.3, Slide 14

15. The Coefficient of Variation
Solution:
100 Meters
Mean:
SD: 0.163
CV:
Marathon
Mean: 7,891.4
SD: 83.5
CV:
Using the coefficient of variation as a measure, there is less variation in the times for the marathon than for the 100-meter race.
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Section 15.3, Slide 15