If the reason that standard deviation is used is that it's easier to just square the distance every time than find the absolute value. Then why is √(E(x-m)^2)/n not used because if I'm not mistaken |x| = √(x^2) and wouldn't that mean that E|x-m| = √(E(x-m)^2) ?
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Bob Ross
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Your "and that would mean" deduction is incorrect. – whuber Aug 21 '20 at 17:31
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I wrote it wrong my bad – Bob Ross Aug 21 '20 at 23:32
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1The assertion $E|x-m| = \sqrt{E\left(X-m\right)^2}$ is not correct; you can't pass a square root to the inside of an expected value. This can be seen either by example (with an explicit calculation) or by Jensen's inequality – Artem Mavrin Aug 22 '20 at 00:04