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Title: Variance -- from Wolfram MathWorld

Open Graph Title: Variance -- from Wolfram MathWorld

X Title: Variance -- from Wolfram MathWorld

Description: For a single variate X having a distribution P(x) with known population mean mu, the population variance var(X), commonly also written sigma^2, is defined as sigma^2=<(X-mu)^2>, (1) where mu is the population mean and denotes the expectation value of X. For a discrete distribution with N possible values of x_i, the population variance is therefore sigma^2=sum_(i=1)^NP(x_i)(x_i-mu)^2, (2) whereas for a continuous distribution, it is given by sigma^2=intP(x)(x-mu)^2dx....

Open Graph Description: For a single variate X having a distribution P(x) with known population mean mu, the population variance var(X), commonly also written sigma^2, is defined as sigma^2=<(X-mu)^2>, (1) where mu is the population mean and denotes the expectation value of X. For a discrete distribution with N possible values of x_i, the population variance is therefore sigma^2=sum_(i=1)^NP(x_i)(x_i-mu)^2, (2) whereas for a continuous distribution, it is given by sigma^2=intP(x)(x-mu)^2dx....

X Description: For a single variate X having a distribution P(x) with known population mean mu, the population variance var(X), commonly also written sigma^2, is defined as sigma^2=<(X-mu)^2>, (1) where mu is the population mean and denotes the expectation value of X. For a discrete distribution with N possible values of x_i, the population variance is therefore sigma^2=sum_(i=1)^NP(x_i)(x_i-mu)^2, (2) whereas for a continuous distribution, it is given by sigma^2=intP(x)(x-mu)^2dx....

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

X: @WolframResearch

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Domain: mathworld.wolfram.com

DC.TitleVariance
DC.CreatorWeisstein, Eric W.
DC.DescriptionFor a single variate X having a distribution P(x) with known population mean mu, the population variance var(X), commonly also written sigma^2, is defined as sigma^2=<(X-mu)^2>, (1) where mu is the population mean and denotes the expectation value of X. For a discrete distribution with N possible values of x_i, the population variance is therefore sigma^2=sum_(i=1)^NP(x_i)(x_i-mu)^2, (2) whereas for a continuous distribution, it is given by sigma^2=intP(x)(x-mu)^2dx....
DC.Date.Modified2006-02-08
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/Variance.html
DC.Languageen
DC.PublisherWolfram Research, Inc.
DC.Relation.IsPartOfhttps://mathworld.wolfram.com/
DC.TypeText
Last-Modified2006-02-08
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og:typewebsite
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variatehttps://mathworld.wolfram.com/Variate.html
population meanhttps://mathworld.wolfram.com/PopulationMean.html
population meanhttps://mathworld.wolfram.com/PopulationMean.html
expectation valuehttps://mathworld.wolfram.com/ExpectationValue.html
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sample variancehttps://mathworld.wolfram.com/SampleVariance.html
sample meanhttps://mathworld.wolfram.com/SampleMean.html
sample variancehttps://mathworld.wolfram.com/SampleVariance.html
unbiased estimatorhttps://mathworld.wolfram.com/UnbiasedEstimator.html
Variancehttp://reference.wolfram.com/language/ref/Variance.html
standard deviationhttps://mathworld.wolfram.com/StandardDeviation.html
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sample variancehttps://mathworld.wolfram.com/SampleVariance.html
chi-squared distributionhttps://mathworld.wolfram.com/Chi-SquaredDistribution.html
covariancehttps://mathworld.wolfram.com/Covariance.html
covariance matrixhttps://mathworld.wolfram.com/CovarianceMatrix.html
Central Momenthttps://mathworld.wolfram.com/CentralMoment.html
Charlier's Checkhttps://mathworld.wolfram.com/CharliersCheck.html
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Explore this topic in the MathWorld classroomhttps://mathworld.wolfram.com/classroom/Variance.html
variance {21.3, 38.4, 12.7, 41.6} https://www.wolframalpha.com/input/?i=variance+{21.3%2C+38.4%2C+12.7%2C+41.6}
variance of uniform distribution https://www.wolframalpha.com/input/?i=variance+of+uniform+distribution
variance (1,2,3) https://www.wolframalpha.com/input/?i=variance+%281%2C2%2C3%29
Mathematics of Statistics, Pt. 2, 2nd ed.http://www.amazon.com/exec/obidos/ASIN/B0007HR7SY/ref=nosim/ericstreasuretro
Probability, Random Variables, and Stochastic Processes, 2nd ed.http://www.amazon.com/exec/obidos/ASIN/0070484686/ref=nosim/ericstreasuretro
Numerical Recipes in FORTRAN: The Art of Scientific Computing, 2nd ed.http://www.amazon.com/exec/obidos/ASIN/052143064X/ref=nosim/ericstreasuretro
A Student's Guide to Analysis of Variance.http://www.amazon.com/exec/obidos/ASIN/0415165652/ref=nosim/ericstreasuretro
Variancehttps://www.wolframalpha.com/input/?i=variance
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