1. Measures of Dispersion
Dr. Fowler  AFM  Unit 8-3
Measures of Dispersion
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. Example: Find the range of the heights of the people listed in the accompanying table.
Solution:

3. Standard Deviation:

4. Standard Deviation

5. Standard Deviation

6. Standard Deviation

7. Standard Deviation

8. Standard Deviation Solution step 1:
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 step 1:
Mean: (sum of the closing prices is 800)
(continued on next slide)

9. Standard Deviation Standard Deviation:
We create a table with values that will facilitate computing the standard deviation.
Standard Deviation:

10. 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:

11. Excellent Job !!! Well Done