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Title: Sample Variance Distribution -- from Wolfram MathWorld

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

X Title: Sample Variance Distribution -- from Wolfram MathWorld

Description: Let N samples be taken from a population with central moments mu_n. The sample variance m_2 is then given by m_2=1/Nsum_(i=1)^N(x_i-m)^2, (1) where m=x^_ is the sample mean. The expected value of m_2 for a sample size N is then given by ==(N-1)/Nmu_2. (2) Similarly, the expected variance of the sample variance is given by = (3) = ((N-1)^2)/(N^3)mu_4-((N-1)(N-3)mu_2^2)/(N^3) (4) (Kenney and Keeping 1951, p. 164; Rose and...

Open Graph Description: Let N samples be taken from a population with central moments mu_n. The sample variance m_2 is then given by m_2=1/Nsum_(i=1)^N(x_i-m)^2, (1) where m=x^_ is the sample mean. The expected value of m_2 for a sample size N is then given by ==(N-1)/Nmu_2. (2) Similarly, the expected variance of the sample variance is given by = (3) = ((N-1)^2)/(N^3)mu_4-((N-1)(N-3)mu_2^2)/(N^3) (4) (Kenney and Keeping 1951, p. 164; Rose and...

X Description: Let N samples be taken from a population with central moments mu_n. The sample variance m_2 is then given by m_2=1/Nsum_(i=1)^N(x_i-m)^2, (1) where m=x^_ is the sample mean. The expected value of m_2 for a sample size N is then given by ==(N-1)/Nmu_2. (2) Similarly, the expected variance of the sample variance is given by = (3) = ((N-1)^2)/(N^3)mu_4-((N-1)(N-3)mu_2^2)/(N^3) (4) (Kenney and Keeping 1951, p. 164; Rose and...

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DC.TitleSample Variance Distribution
DC.CreatorWeisstein, Eric W.
DC.DescriptionLet N samples be taken from a population with central moments mu_n. The sample variance m_2 is then given by m_2=1/Nsum_(i=1)^N(x_i-m)^2, (1) where m=x^_ is the sample mean. The expected value of m_2 for a sample size N is then given by ==(N-1)/Nmu_2. (2) Similarly, the expected variance of the sample variance is given by = (3) = ((N-1)^2)/(N^3)mu_4-((N-1)(N-3)mu_2^2)/(N^3) (4) (Kenney and Keeping 1951, p. 164; Rose and...
DC.Date.Created2003-05-06
DC.Date.Modified2003-07-02
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/SampleVarianceDistribution.html
DC.Languageen
DC.PublisherWolfram Research, Inc.
DC.Relation.IsPartOfhttps://mathworld.wolfram.com/
DC.TypeText
Last-Modified2003-07-02
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6https://mathworld.wolfram.com/SampleVarianceDistribution.html#eqn6
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