Camparison of Numerically Stability of Two Algorithms for the Calculation of Variance

Abstract

In descriptive statistics, there are two computational algorithms for determining the variance S2, of a set of observations : Algorithm 1: S2= - , Algorithm 2: S2= , where . It is interesting to discuss, which of the above formulas is numerically more trustworthy in machine numbers sets. I this paper, based on total effect of rounding error, we prove that the second Algorithm is better than the first Algorithm. Numerical experiments show the efficiency of Algorithm 2.