# Root-mean-square

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The root-mean-square or quadratic mean of a collection of real numbers $x_1,\dots , x_n$ is defined to be $\sqrt{\frac{x^2_1+x^2_2+\dots+x^2_n}{n}}$. This is the second power mean of the $x_i$.

It is so-named because it is the square root of the mean of the squares of the $x_i$.

It is also part of the well-known Root-Mean Square-Arithmetic Mean-Geometric Mean-Harmonic mean Inequality