The standard deviation is most commonly used to get a sense of how far the typical score of a distribution differs from the mean.In computing the standard deviation, why is it necessary to square the deviations from the mean for each score?
A) The deviations are too small to have a variance without being squared.
B) There is no variability in the deviations of the scores prior to squaring.
C) Squaring numbers is a required step in calculating all measures of variability.
D) The deviations sum to zero due to negative and positive values.

Question

Quizplus · Accepted Answer

Squaring the deviations from the mean ensures that all values are positive, allowing for an accurate calculation of variance and standard deviation. Without squaring, the negative deviations would cancel out the positive deviations and the result would be zero, leading to a misleading measure of variability.

The Standard Deviation Is Most Commonly Used to Get a Sense