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   =   √ ( ( Σ 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   =   √ ( ( Σ (x_i − p_i)² ) / N )