Median Minimizes Sum Of Absolute Deviations

https://math.stackexchange.com/questions/113270/the-median-minimizes-the-sum-of-absolute-deviations-the-ell-1-norm

If the array has odd number of elements, there is only a single median which minimizes the sum of absolute deviations.

If the array has even number of elements, any numbers between (including) the two median numbers minimizes the sum of absolute deviations.

• mean minimizes total distance for euclidian distance

• median minimzes total distance for absolute deviation

• mode minimizes distance for indicator function

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