## Why do quantities like variance use the square rather than the absolute value? [closed]

My understanding is that the goal of using the square of E(x_i-X) is to give everything a positive sign. Why do we prefer squaring to the absolute value for this, or is it simply a historical "accident"? I know that metrics like absolute deviation exist.

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 This question is more appropriate for math.stackexchange. If you read french, you may enjoy this forum for high school students, where you'll find the answer: forums.futura-sciences.com/… – Alain Valette Sep 10 2011 at 9:46