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Computing standard deviations: accuracy

Authors:

Tony F. Chan,

John Gregg LewisAuthors Info & Claims

Communications of the ACM, Volume 22, Issue 9

Pages 526 - 531

https://doi.org/10.1145/359146.359152

Published: 01 September 1979 Publication History

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Abstract

Four algorithms for the numerical computation of the standard deviation of (unweighted) sampled data are analyzed. Two of the algorithms are well-known in the statistical and computational literature; the other two are new algorithms specifically intended for automatic computation. Our discussion is expository, with emphasis on reaching a suitable definition of “accuracy.” Each of the four algorithms is analyzed for the conditions under which it will be accurate. We conclude that all four algorithms will provide accurate answers for many problems, but two of the algorithms, one new, one old, are substantially more accurate on difficult problems than are the other two.

References

[1]

Chan, T.F.C., and Lewis, J.G. Rounding error analysis of algorithms for computing means and standard deviations. Tech. Rep. No. 289, Dept. of Mathematical Sciences, The Johns Hopkins U., Baltimore, Md., April 1978.

Google Scholar

[2]

Cotton, I.W. Remark on stably updating mean and standard deviation of data. Comm. ACM 18, 8 (Aug. 1975), 458.

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Google Scholar

[3]

Hanson, R.J. Stably updating mean and standard deviation of data. Comm. ACM 18, 1 (Jan. 1975), 57-58.

Digital Library

Google Scholar

[4]

Ling, R.F. Comparison of several algorithms for computing means and variances. J. Amer. Statistical Assoc. 69, 348 (Dec. 1974), 859-866.

Crossref

Google Scholar

[5]

Neely, P.M. Comparison of several algorithms for computation of means, standard deviations and correlation coefficients. Comm. ACM 9, 7 (July 1966), 496-499.

Digital Library

Google Scholar

[6]

Welford, B.P. Note on a method for calculating corrected sums of squares and products. Technometrics 4 (Aug. 1962), 419 -420.

Crossref

Google Scholar

[7]

West, D.H.D. Updating mean and variance estimates: An improved method. Comm. ACM 22, 9 (Sept. 1979), 532-535.

Digital Library

Google Scholar

[8]

West, D.H.D. Incremental least squares and the approximate separation of exponentials. Nuclear Instruments and Methods 136 (1976), 137-143.

Crossref

Google Scholar

[9]

Wilkinson, J.H. Rounding errors in algebraic processes. Prentice-Hall, Englewood Cliffs, N.J., 1963.

Digital Library

Google Scholar

[10]

Youngs, E.A., and Cramer, E.M. Some results relevant to choice of sum and sum-of-product algorithms. Technometrics 13 (Aug. 1971 ), 657-665.

Crossref

Google Scholar

[11]

Nelson, L.S. Further remarks on stably updating mean and standard deviation estimates. Comm. A CM 22, 8 (Aug. 1979), 483.

Digital Library

Google Scholar

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Chmielowiec A(2021)Algorithm for error-free determination of the variance of all contiguous subsequences and fixed-length contiguous subsequences for a sequence of industrial measurement dataComputational Statistics10.1007/s00180-021-01096-136:4(2813-2840)Online publication date: 1-Dec-2021
https://dl.acm.org/doi/10.1007/s00180-021-01096-1
Durón C(2021)Linear Algebra, ComputationalWiley StatsRef: Statistics Reference Online10.1002/9781118445112.stat00459.pub2(1-18)Online publication date: 17-May-2021
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Although not published as a numbered algorithm, Hanson's article “Stably Updating Mean and Standard Deviation of Data” in the January, 1975, issue of Communications, [1] describes an algorithm for sequentially recomputing the mean and standard deviation ...

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Published In

Communications of the ACM Volume 22, Issue 9

Sept. 1979

47 pages

ISSN:0001-0782

EISSN:1557-7317

DOI:10.1145/359146

Editor:
Robert L. Ashenhurst
Univ. of Chicago, Chicago, IL

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Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

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Association for Computing Machinery

New York, NY, United States

Publication History

Published: 01 September 1979

Published in CACM Volume 22, Issue 9

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Chmielowiec A(2021)Algorithm for error-free determination of the variance of all contiguous subsequences and fixed-length contiguous subsequences for a sequence of industrial measurement dataComputational Statistics10.1007/s00180-021-01096-136:4(2813-2840)Online publication date: 1-Dec-2021
https://dl.acm.org/doi/10.1007/s00180-021-01096-1
Durón C(2021)Linear Algebra, ComputationalWiley StatsRef: Statistics Reference Online10.1002/9781118445112.stat00459.pub2(1-18)Online publication date: 17-May-2021
https://doi.org/10.1002/9781118445112.stat00459.pub2
Alkhafaf OWali MAl-Timemy A(2020)Improved hand prostheses control for transradial amputees based on hybrid of voice recognition and electromyographyThe International Journal of Artificial Organs10.1177/039139882097665644:7(509-517)Online publication date: 7-Dec-2020
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Alkhafaf OWali MAl-Timemy A(2020)Improved Prosthetic Hand Control with Synchronous Use of Voice Recognition and Inertial MeasurementsIOP Conference Series: Materials Science and Engineering10.1088/1757-899X/745/1/012088745:1(012088)Online publication date: 1-Feb-2020
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Bracio KSzarucki M(2019)COMMERCIALIZATION OF INNOVATIONS THROUGH INTERNATIONALIZATION: A SYSTEMATIC LITERATURE REVIEWBusiness: Theory and Practice10.3846/btp.2019.3920(417-431)Online publication date: 19-Jan-2019
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Schubert EGertz MSacharidis DGamper JBöhlen M(2018)Numerically stable parallel computation of (co-)varianceProceedings of the 30th International Conference on Scientific and Statistical Database Management10.1145/3221269.3223036(1-12)Online publication date: 9-Jul-2018
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Sun TLo KChen J(2016)An accurate updating formula to calculate sample variance from weighted successive differencesStatistics & Probability Letters10.1016/j.spl.2016.03.003114(14-19)Online publication date: Jul-2016
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Updating mean and variance estimates: an improved method

Stably updating mean and standard deviation of data

Remark on stably updating mean and standard deviation of data

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