## Why do we square instead of using the absolute value when calculating variance and standard deviation?

First I'll answer the mathematical question asked in the question details, which I'm going to restate because I think it is stated wrong:nWhy is it true that n sqrt{frac{1}{n}sum_{i=1}^n (X_i - bar{X})^2} neq frac{1}{n}sum_{i=1}^n |X_i - bar{X}|?,The short answer is "Because of Jensen's inequality." See http://en.wikipedia.org/wiki/Jensen%27s_inequ