Sum of Squared Deviations from Mean

Theorem
Let $x_1, x_2, \ldots, x_n$ be real data about some quantitative variable.

Let $\overline x$ be the arithmetic mean of the above data.

Then:


 * $\displaystyle \sum_{i \mathop = 1}^n \paren {x_i - \overline x}^2 = \sum_{i \mathop = 1}^n \paren {x_i^2 - \overline x^2}$