Variable centering and scaling are functions that are typically used in data normalization. Various properties of centering and scaling functions are presented. It is shown that if we use two centering functions (or scaling functions) successively, the result depends on the order in which the functions are applied: the second function always cancels the centering or scaling of the first function. Furthermore, it is shown that if we use a centering and a scaling function successively, the result does not depend on the order in which the functions are applied. Moreover, certain sets of normalization functions turn out to be semigroups.