Transformations turn lists into other lists, or variables into other variables. For example, to transform a list of temperatures in degrees Celsius into the corresponding list of temperatures in degrees Fahrenheit, you multiply each element by 9/5, and add 32 to each product. This is an example of an affine transformation: multiply by something and add something (y = ax + b is the general affine transformation of x; it's the familiar equation of a straight line). In a linear transformation, you only multiply by something (y = ax). Affine transformations are used to put variables in standard units. In that case, you subtract the mean and divide the results by the SD. This is equivalent to multiplying by the reciprocal of the SD and adding the negative of the mean, divided by the SD, so it is an affine transformation. Affine transformations with positive multiplicative constants have a simple effect on the mean, median, mode, quartiles, and other percentiles: the new value of any of these is the old one, transformed using exactly the same formula. When the multiplicative constant is negative, the mean, median, mode, are still transformed by the same rule, but quartiles and percentiles are reversed: the qth quantile of the transformed distribution is the transformed value of the 1−qth quantile of the original distribution (ignoring the effect of data spacing). The effect of an affine transformation on the SD, range, and IQR, is to make the new value the old value times the absolute value of the number you multiplied the first list by: what you added does not affect them.