The reason we don’t use absolute values for calculating variance

Question

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.

In: Other

Answer 1

its an arbitrary choice, but the real reason is that ABS is piecewise defined and non differentiable.

Where as squared is differentiable and continuous and a simple function.