The standard deviation, or S, is the square root of the variance. The standard deviation of Mr. Smith’s sales is S=.958. The standard deviation of Ms. Johnson’s sales is 7.182.

Why not simply use the variance? One reason is that, unlike the variance, the standard deviation is in the same units as the raw scores. This makes the standard deviation more meaningful. Thus, it would make more sense to discuss the variability of book sales in "book" units rather than "squared book" units and to discuss a set of IQ scores in IQ points rather than in squared IQ points. The standard deviation is used in the calculation of many other statistics.

Learning Check #10:
The exam scores for two sections of introductory psychology are listed below. Compute the standard deviation for each section. Section #1: 42, 45, 56, 56, 60, 62, 67, 68, 70, 71. Section #2: 57, 57, 57, 70, 75, 77, 79, 83, 83, 92.

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Learning Check #11:
Suppose that there were two groups that discussed issues related to abortion. Each member of each group rated on a scale of 1 to 10 their opinion regarding abortion (1=Totally against abortion; 5=Neutral; 10=Totally in favor of abortion). The mean for Group A was found to be 5 with a standard deviation of .02. For Group B the mean was also 5, but the standard deviation was 3.42. Which group would have the more lively debates?

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