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because of two things-

a) both positive and negative deviations mean something about the general variability of the data to the analyst, if you added them they'd cancel out, but squaring them results in positive numbers that add up.

b) a few larger deviations are much more significant than the many little ones, and squaring them gives them more weight.

Sigma, the square root of the variance, is a good pointer to how far away from the mean you are likely to be if you choose a datum at random. the probability of being such a number of sigmas away is easily looked up.

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13y ago

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