camparison of numerically stability of two algorithms for the calculation of variance

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.