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单词 Rootmeansquare
释义

root-mean-square


If x1,x2,,xn are real numbers, we define theirroot-mean-squareMathworldPlanetmathPlanetmath or quadratic mean as

R(x1,x2,,xn)=x12+x22++xn2n.

The root-mean-square of a random variableMathworldPlanetmath X is defined as the squareroot of the expectation of X2:

R(X)=E(X2)

If X1,X2,,Xn are random variables with standard deviationsMathworldPlanetmathσ1,σ2,,σn, then the standard deviation oftheir arithmetic meanMathworldPlanetmath, X1+X2++Xnn, is theroot-mean-square of σ1,σ2,,σn.

Titleroot-mean-square
Canonical nameRootmeansquare
Date of creation2013-03-22 13:10:24
Last modified on2013-03-22 13:10:24
Ownerpbruin (1001)
Last modified bypbruin (1001)
Numerical id4
Authorpbruin (1001)
Entry typeDefinition
Classificationmsc 26-00
Classificationmsc 26D15
Synonymroot mean square
Synonymrms
Synonymquadratic mean
Related topicArithmeticMean
Related topicGeometricMean
Related topicHarmonicMean
Related topicPowerMean
Related topicWeightedPowerMean
Related topicArithmeticGeometricMeansInequality
Related topicGeneralMeansInequality
Related topicProofOfGeneralMeansInequality
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更新时间:2025/5/4 19:29:43