Algorithms for Computing the Sample Variance: Analysis and Recommendations

Abstract

The problem of computing the variance of a sample of N data points {x_i } may be difficult for certain data sets, particularly when N is large and the variance is small. We present a survey of possible algorithms and their round-off error bounds, including some new analysis for computations with shifted data. Experimental results confirm these bounds and illustrate the dangers of some algorithms. Specific recommendations are made as to which algorithm should be used in various contexts.