In a statistics class, the standard deviation of the heights of all students was 4.1 inches. The standard deviation of the heights of males was 3.5 inches and the standard deviation of females was 3.3 inches. Why is the standard deviation of the entire class more than the standard deviation of the males and females considered separately?

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Mathematics

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31 May, 13:56

In a statistics class, the standard deviation of the heights of all students was 4.1 inches. The standard deviation of the heights of males was 3.5 inches and the standard deviation of females was 3.3 inches. Why is the standard deviation of the entire class more than the standard deviation of the males and females considered separately?

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Answers (1)

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Joel English · Answer 1

Because the distribution of entire class has more dispersion.

Step-by-step explanation:

We have been given that in a statistics class, the standard deviation of the heights of all students was 4.1 inches. The standard deviation of the heights of males was 3.5 inches and the standard deviation of females was 3.3 inches.

We know that standard deviation is measure of dispersion of a data set. The standard deviation of a large data set has high dispersion, while standard deviation of a small data set has less dispersion.

Since the distribution of entire class has more dispersion compared to distribution of males and females separately, therefore, the standard deviation of the entire class is more than the standard deviation of the males and females considered separately.