Sum of 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:


 * $\displaystyle \sum_{i \mathop = 1}^n \left({x_i - \overline{x} }\right) = 0$

Proof
For brevity, let us write $\displaystyle \sum$ for $\displaystyle \sum_{i \mathop = 1}^n$.

Then:

Also see

 * Sum of Squared Deviations from Mean