mean square deviation

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 (http://planetmath.org/MeanValueTheorem)

$m\;=\;\frac{1}{b\!-\!a}\int_{a}^{b}[f(x)\!-\!\varphi(x)]^{2}\,dx$

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

$\frac{2}{\pi}\int_{0}^{\frac{\pi}{2}}(\sin{x}-x)^{2}\,dx\,\approx\,0.04923.$