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

Author
D Rostami
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.
Keywords
Computational statistics
Round off error
Error Analysis