Computing Standard Deviations: Accuracy

Four algorithms for the numerical computation of the standard deviation of (unweighted) sampled data are analyzed. Two of the algorithms are well-known in the statistical and computational literature; the other two are new algorithms specifically intended for automatic computation. Our discussion is expository, with emphasis on reaching a suitable definition of “accuracy.” Each of the four algorithms is analyzed for the conditions under which it will be accurate. We conclude that all four algorithms will provide accurate answers for many problems, but two of the algorithms, one new, one old, are substantially more accurate on difficult problems than are the other two.