Question

Two histograms showing the number of hours students in the jazz band practiced in a week are shown. The sample

mean of Group 1's data is 2.57. The sample mean of Group 2's data is 3.337.

Which statement about the two histograms is true?

Graph 1 has a larger sample standard deviation than Graph 2.

Graph 2 has a larger sample standard deviation than Graph 1.

Both graphs have the same sample standard deviation.

The relationship of the sample standard deviations cannot be determined.

Answer 1

(b) Graph 2 has a larger sample standard deviation than Graph 1

Explanation:

Given the two histograms of hours practiced, you want to know the relationship between the sample standard deviations of the two data sets.

Standard deviation

The standard deviation is a measure of data variability. It will tend to be larger for less-symmetrical data distributions, and for those that are skewed one way or another.

The data of Graph 2 is less symmetrical than that of Graph 1, so we expect its standard deviation to be higher. A computation of the standard deviation confirms this.

Graph 1 standard deviation: about 1.40

Graph 2 standard deviation: about 1.53

Graph 2 has a larger sample standard deviation than Graph 1, choice B.

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Additional comment

In the computation, the first list (L1) is the set of data values. The second list, {2, 3, 4, ...} for example, is their relative frequencies—the heights of the bars in the histogram.

The given mean values seem to show that each bar is represented by its midpoint value, 0.5 for the first bar, for example. For the purpose of the standard deviation calculation, we don't need to make that adjustment.

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