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Motivation behind standard deviation?
In statistics very often you see something of the sort: $ \textrm{quantity}=\sqrt{\frac {\sum(x-\mu)^2} {N}} $ to measure things like standard deviation ($\mu$ is the mean here).
It seems that just making an absolute value of the difference will give us a pretty good measure of the same thing: $ \textrm{quantity}=\frac {\sum{\Bigl|x-\mu\Bigr|}} {N} $
How did we end up with those squares?