In calculating the standard deviation, if we didn't square the differences between the observations and the mean, then the standard deviation itself would be a negative number.

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Quizplus · Accepted Answer

The standard deviation cannot be negative, even if we do not square the differences between the observations and the mean. The reason we square the differences is to eliminate the possibility of negative values affecting the overall calculation.

In Calculating the Standard Deviation, If We Didn't Square the Differences