\begin{definition}[Definition:Mean Square]
Let $S$ be a set of numbers.
The '''mean square''' of $S$ is the arithmetic mean of the squares of the elements of $S$:
:$s^2 = \dfrac 1 n \ds \sum_{i \mathop = 1}^n {x_i}^2$
where $S = \set {x_1, x_2, \ldots, x_n}$.
\end{definition}