The root mean square deviation (RMSD) is a measure of the differences between predicted values and actual values. The RMSD aggregates these individual differences, called residuals, into a single predictive value, making the RMSD a good measure of accuracy. The RMSD may also measure the differences between two sets of values when neither set is considered to be a standard. You can use this to calculate the average distance between two objects, for example, or how well an economic model fits economic indicators.

Define the RMSD as the square root of the mean squared error. This may be expressed as RMSD(x) = (E((x - y)^2))^(1/2) where x is an estimated value, y is the actual value and E is some function that provides a mean error between x and y.

Use the RMSD when neither set of values is considered to be a standard. Let X be the set of the values {x1, x2, ... , xn}, and let Y be the set of values {y1, y2, ... , yn}.

Calculate a specific function given the conditions in step two by determining the mean error function E. In this case, E(X - Y)^2 = (?(xi - yi)^2)/n. Therefore, RMSD (X,Y) = (E((X - Y)^2))^(1/2) = (?(xi - yi)^2/n)^(1/2).

Calculate the normalized RMSD (NRMSD) as RMSD/(xmax - xmin). This value is commonly given as a percentage such that a lower value indicates a smaller variance in the residuals.

Calculate the coefficient of variation of the RMSD as RMSD / ?xi/n. The standard deviation in the equation for the coefficient of variation is replaced by the RMSD.