2. Comparing Variation Which do you think has more variation: the IQ scores of 30 students in a statistics class or the IQ scores of 30 patrons watching a movie? Why?

SOLUTION Because we have sample statistics, we find the two coefficients of variation as follows:

Heights:

Weights:

Although the difference in the units makes it impossible to compare the standard deviation of 3.02 in. to the standard deviation of 26.33 lb, we can compare the coefficients of variation, which have no units. We can see that heights

(with have considerably less variation than weights (with This makes intuitive sense, because we routinely see that weights among men vary much more than heights. For example, it is very rare to see two adult men with one of them being twice as tall as the other, but it is much more common to see two men with one of them weighing twice as much as the other.

After studying this section, you should understand that the standard deviation is a measure of variation among values. Given sample data, you should be able to compute the value of the standard deviation. You should be able to interpret the values of standard deviations that you compute. You should know that for typical data sets, it is unusual for a value to differ from the mean by more than two or three standard deviations.

CV 5 15.26%d.

CV 5 4.42%d CV 5 s

x

? 100% 5 26.33 lb 172.55 lb

? 100% 5 15.26%

CV 5 s

x

? 100% 5 3.02 in.

68.34 in.

? 100% 5 4.42%

Mean Standard Deviation (s)

Height 68.34 in. 3.02 in.

Weight 172.55 lb 26.33 lb sxd 3-3 Measures of Variation 105