Why Variance Is Squared?

The calculation of variance uses squares because it weighs outliers more heavily than data closer to the mean. This calculation also prevents differences above the mean from canceling out those below, which would result in a variance of zero.

Why is variance squared and not cubed?

Using squared deviations gives us the Variance (and by square-rooting, the standard deviation). We don't use, say, the power of 3, because then positive and negative deviations would cancel each other out, which we don't want to do.

Should variance be squared?

So the mean deviation and the variance are measuring the same thing, yet variance requires squaring the difference.