Statistical computing: Algorithms for computing the sample variance: Analysis and recommendations

Tony F. Chan, Gene H. Golub, Randall J. Leveque

Research output: Contribution to journalArticlepeer-review

159 Scopus citations

Abstract

The problem of computing the variance of a sample of N data points (x), 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.

Original languageEnglish (US)
Pages (from-to)242-247
Number of pages6
JournalAmerican Statistician
Volume37
Issue number3
DOIs
StatePublished - Jan 1 1983
Externally publishedYes

Keywords

  • Computer algorithms
  • Round-off errors
  • Shifted data
  • Standard deviation
  • Variance

ASJC Scopus subject areas

  • Statistics and Probability
  • Mathematics(all)
  • Statistics, Probability and Uncertainty

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