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Thread: Mathematical intuition for variance

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    Mathematical intuition for variance

    One explanation to "Why do we square the deviations" is..

    "The sum of the square deviations of any set of observations from their mean is the smallest that the sum of squared deviations from any number can possibly be. This is not true of the unsquared distances. So squared deviations point to the mean as center in a way that distances do not."

    I do not understand this explanation. Could you provide an example and break down the explanation?

  2. #2
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    Re: Mathematical intuition for variance

    Variance is one of the measures of dispersion. You could take mean deviation or range or IQR to represent dispersion.

    The sum of the square deviation from a point A is minimized when A is the mean. I.e. \sum (x_i -A) ^2 is minimized when A = \bar x. But when you take other deviation (other than squared), then the minimum value may not correspond to the mean. For example, mean deviation from point A is minimized when A is the median.
    In the long run, we're all dead.

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