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Title: Sample Variance Computation -- from Wolfram MathWorld

Open Graph Title: Sample Variance Computation -- from Wolfram MathWorld

X Title: Sample Variance Computation -- from Wolfram MathWorld

Description: When computing the sample variance s numerically, the mean must be computed before s^2 can be determined. This requires storing the set of sample values. However, it is possible to calculate s^2 using a recursion relationship involving only the last sample as follows. This means mu itself need not be precomputed, and only a running set of values need be stored at each step. In the following, use the somewhat less than optimal notation mu_j to denote mu calculated from the first j samples...

Open Graph Description: When computing the sample variance s numerically, the mean must be computed before s^2 can be determined. This requires storing the set of sample values. However, it is possible to calculate s^2 using a recursion relationship involving only the last sample as follows. This means mu itself need not be precomputed, and only a running set of values need be stored at each step. In the following, use the somewhat less than optimal notation mu_j to denote mu calculated from the first j samples...

X Description: When computing the sample variance s numerically, the mean must be computed before s^2 can be determined. This requires storing the set of sample values. However, it is possible to calculate s^2 using a recursion relationship involving only the last sample as follows. This means mu itself need not be precomputed, and only a running set of values need be stored at each step. In the following, use the somewhat less than optimal notation mu_j to denote mu calculated from the first j samples...

Opengraph URL: https://mathworld.wolfram.com/SampleVarianceComputation.html

X: @WolframResearch

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Domain: mathworld.wolfram.com

DC.TitleSample Variance Computation
DC.CreatorWeisstein, Eric W.
DC.DescriptionWhen computing the sample variance s numerically, the mean must be computed before s^2 can be determined. This requires storing the set of sample values. However, it is possible to calculate s^2 using a recursion relationship involving only the last sample as follows. This means mu itself need not be precomputed, and only a running set of values need be stored at each step. In the following, use the somewhat less than optimal notation mu_j to denote mu calculated from the first j samples...
DC.Date.Created2003-05-06
DC.Subject62M05
DC.RightsCopyright 1999-2026 Wolfram Research, Inc. See https://mathworld.wolfram.com/about/terms.html for a full terms of use statement.
DC.Formattext/html
DC.Identifierhttps://mathworld.wolfram.com/SampleVarianceComputation.html
DC.Languageen
DC.PublisherWolfram Research, Inc.
DC.Relation.IsPartOfhttps://mathworld.wolfram.com/
DC.TypeText
Last-Modified2003-05-06
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og:typewebsite
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