If $f$ is a Riemann integrable real function on the interval $[a,\,b]$ which is wished to be approximated by another function $\varphi$ with the same property, then the mean $$m \;=\; \frac{1}{b\!-\!a}\int_a^b[f(x)\!-\!\varphi(x)]^2\,dx$$ is called the mean square deviation of $\varphi$ from $f$ .

For example, if $\sin{x}$ is approximated by $x$ on $[0,\,\frac{\pi}{2}]$ , the mean square deviation is $$\frac{2}{\pi}\int_0^{\frac{\pi}{2}}(\sin{x}-x)^2\,dx \,\approx\, 0.04923.$$