My understanding is that you take the square and then the square root so that positive and negative distances from the mean don't cancel each other out. But if that's the case, why don't you immediately take the square root after the square?
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Maybe because we want to calculate the _average_ distance? – Alecos Papadopoulos Jan 31 '15 at 20:54
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But then shouldn't you divide by n and not root n? – megashigger Jan 31 '15 at 21:13
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No. See this thread which deals exactly with this issue, http://stats.stackexchange.com/questions/116342/why-is-the-standard-deviation-defined-as-sqrt-of-the-variance-and-not-as-the-sqr – Alecos Papadopoulos Jan 31 '15 at 21:21