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.
CACM September, 1979
Chan, T.F.
Lewis, J.G.
