In statistics the transformation rules describe the changes in the mean, variance and standard deviation of a distribution when every item in a distribution is either increased or decreased by a constant amount. These rules also describe the changes in the mean, variance and standard deviation of a distribution when every item in the distribution is either multiplied or divided by a constant amount.

Transformation rule (1): Adding a constant to every item in a distribution adds the constant to the mean of the distribution, but it leaves the variance and standard deviation, unchanged.

Transformation rule (2): Multiplying every item in a distribution by a constant multiplies the mean and standard deviation of that distribution by the constant and it multiplies the variance of the distribution by the square of the constant.