1. Descriptive Statistics
What a Data Set Tells Us

2. Measures of Dispersion
14.3
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.

3. The Range of a Data Set

4. The Range of a Data Set
Example: Find the range of the heights of the people listed in the accompanying table.
Solution:

5. Standard Deviation

6. Standard Deviation

7. Standard Deviation

8. 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:
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9. Standard Deviation
We calculate the squares of the deviations of the data values from the mean.
Standard Deviation:

10. Standard Deviation

11. 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)
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12. Standard Deviation
We create a table with values that will facilitate computing the standard deviation.
Standard Deviation:

13. 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.

14. 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:

15. 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.
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16. 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.