root mean square

The root mean square (RMS) is the square root of the arithmetic mean of the squares of sequence of values . That is, if v_i is a sequence of values:

        RMS   =   &sqrt ( ( &Sigma v_i² ) / N )

The RMS (or the plain mean square error) is often used as a form of {{accuracy measure}. In this case the values are differences between true value (say x_i) and prediction or estimate (say p_i), so that the RMS error is:

        RMS   =   &sqrt ( ( &Sigma (x_i − p_i)² ) / N )