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.

Write all Notes – All slides today – notes are short Example: Find the range of the heights of the people listed in the accompanying table. Solution:

Standard Deviation: https://www.youtube.com/watch?v=09kiX3p5Vek

Standard Deviation

Standard Deviation

Standard Deviation Section 15.3, Slide 7

Standard Deviation Section 15.3, Slide 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) Section 15.3, Slide 9

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

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: Section 15.3, Slide 11

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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) Section 15.3, Slide 14

Standard Deviation We calculate the squares of the deviations of the data values from the mean. Standard Deviation: Section 15.3, Slide 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. (continued on next slide)

The Coefficient of Variation Solution: 100 Meters Mean: 10.796 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. Section 15.3, Slide 17

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. Section 15.3, Slide 18