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If yes why is it the case that it have this property? There must be some mathematical proof or intuitive understanding in that case.


marked as duplicate by Xi'an, Michael M, whuber Nov 25 '16 at 17:22

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    $\begingroup$ How do you define mean deviation? $\endgroup$ – Xi'an Nov 25 '16 at 15:36
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    $\begingroup$ There is a proof on the Wikipedia page: en.wikipedia.org/wiki/Average_absolute_deviation $\endgroup$ – Erik Nov 25 '16 at 15:38
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    $\begingroup$ The duplicate concerns a generalization: the mean deviation corresponds to $n=1$ while the SD corresponds to $n=2$. $\endgroup$ – whuber Nov 25 '16 at 17:23