If yes why is it the case that it have this property? There must be some mathematical proof or intuitive understanding in that case.
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2How do you define mean deviation? – Xi'an Nov 25 '16 at 15:36
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2There is a proof on the Wikipedia page: https://en.wikipedia.org/wiki/Average_absolute_deviation – Erik Nov 25 '16 at 15:38
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1The duplicate concerns a generalization: the mean deviation corresponds to $n=1$ while the SD corresponds to $n=2$. – whuber Nov 25 '16 at 17:23