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I'm a maths student, and I have this very basic question in mind:

Why is standard deviation defined as the square root of the variance, when surely the expected value of the absolute value of the random variable itself minus its expected value, that is,

E |X-EX|

is closer to what "standard deviation" sounds like, isn't it ? I'm sure there's a very good reason, don't get me wrong.

If you have any answers or comments, thanks in advance.

Dan

James Well
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  • See: http://stats.stackexchange.com/questions/118/why-square-the-difference-instead-of-taking-the-absolute-value-in-standard-devia – Dark Jun 13 '16 at 09:31
  • Thanks, didn't see that one :-) – James Well Jun 26 '16 at 18:22
  • You've reinvented absolute deviation. There are any number of technical reasons standard deviation is more helpful, but intuitively it's related to taxicab vs Euclidean length. – J.G. Oct 07 '22 at 13:43

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