Sum of Squared Deviations from Mean/Proof 2

Proof
In this context, $x_1, x_2, \ldots, x_n$ are instances of a discrete random variable.

Hence the result Variance as Expectation of Square minus Square of Expectation can be applied:
 * $\var X = \expect {X^2} - \paren {\expect X}^2$

which means the same as this but in the language of probability theory.