Question

Why do we square the deviations from the mean when calculating the standard deviation?

Answer 1

Please see below.

Explanation:

In any data set if deviations from mean are added together, they all add up to zero, as negative and positive deviations cancel each other out. As such adding deviation does not lead to any indication about the spread of data around mean.

There are two ways to handle this. One is to take absolute value of deviations and then add them up and then take average, which gives us mean deviation.

The other way is to square the deviations, add them up, take average and ten square root. (The latter is done to maintain dimension in sync with the data). This is called standard deviation.