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- Motivation behind standard deviation? 6 answers
I don't understand why $Var(X) = E((X-\mu)^2)$.
It's defined as the "expected value of the square of the deviation of $X$ from the mean" but I don't understand why it couldn't be $E(X-\mu)$ as that seems more intuitive for "deviation from the mean".
Is the purpose of the squaring to make deviations positive? Because if so, why not just $E(|X-\mu|)$ instead? What's the point of the squaring?