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

We can make a pattern:

Mean is the average value of x

Variance is the average value of x^2

Skew is the average value of x^3*

Kurtosis is the average value of x^4*

All of these values can describe statistically useful information

*The formulas are more complicated than this, basically accounting for the earlier moments. For example, Variance is actually the average of x^2-(average of x)^2