Updating Formulae and a Pairwise Algorithm for Computing Sample Variances

摘要

A general formula is presented for computing the sample variance for a sample of size m + n given the means of variances for two subsamples of sizes m and n. This formula is used in the construction of a pairwise algorithm for computing the variance. Other applications are discussed as well, including the use of updating formulae in a parallel computing environment. We present numerical results and rounding error analyses for several numerical schemes. (Author)