I know the reason for using squared values is so the values don’t get cancelled out. Why not absolute values? I get it when calculating error metrics that squaring can punish the model more for bigger errors, but I don’t get the reason here.
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One reason for using variance, instead of some differently-defined measure of how spread out a data set or probability distribution is, is that if you are adding together random variables that vary in uncorrelated ways (which is a common thing in a lot of real-world applications) then the variance of this sum is just the sum of the individual variances. It makes some calculations simpler.
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