Question

In the procedure of computing the Variance of a distribution, we squared the deviations. What is the need for this squaring step?

Answer 1

Squaring the difference has following advantages:-

1.) Squaring makes each term positive, so that the values above mean do not cancel the values below the mean.

2.) Squaring adds more weighting to the larger differences and it is appropriate since the points further away from mean may have more significance.

3.) Because the differences are squared the units of variance are not same as units of the data. Therefore, the standard deviation is reported as the square root of variance and the units then corresponds to those of the data set.