[Statistics] Why squares instead of absolute values in calculating variance?

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http://stats.stackexchange.com/questions/118/standard-deviation-why-square-the-difference-instead-of-taking-the-absolute-valu

http://math.stackexchange.com/questions/4787/motivation-behind-standard-deviation

http://mathoverflow.net/questions/1048/why-is-it-so-cool-to-square-numbers-in-terms-of-finding-the-standard-deviation/1092#1092

http://www.leeds.ac.uk/educol/documents/00003759.htm