Why SD uses squares (rather than abs val)

Standard

It’s not just for computational convenience.

rms SD minimizes expected distance from mean while avg of abs val does it for the median

Source: (1000) Nikolas Scholz’s answer to Why are standard deviations calculated the way they are? I understand the method (subtract the mean from each value, then get the square-root of the mean of the squared differences), but what fundamental principle does this method derive from? – Quora

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