Justice and truth in grades and their averages

Grade point averages (GPAs) are calculated by assigning numbers to letter g rades and averaging them. Simple examples show that the method cannot consi stently determine class rank since class rank is sometimes permuted with ar bitrary change of scale. This permutation is only possible when one student is somewhere worse and somewhere better than a second. The distinction bet ween these and other sorts of cases is established by theorems proved in an appendix. Relativistic attempts to resolve the inconsistency are shown to be insufficient. The function of GPAs as predictors is briefly discussed.