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


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


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

Title root-mean-square
Canonical name Rootmeansquare
Date of creation 2013-03-22 13:10:24
Last modified on 2013-03-22 13:10:24
Owner pbruin (1001)
Last modified by pbruin (1001)
Numerical id 4
Author pbruin (1001)
Entry type Definition
Classification msc 26-00
Classification msc 26D15
Synonym root mean square
Synonym rms
Synonym quadratic mean
Related topic ArithmeticMean
Related topic GeometricMean
Related topic HarmonicMean
Related topic PowerMean
Related topic WeightedPowerMean
Related topic ArithmeticGeometricMeansInequality
Related topic GeneralMeansInequality
Related topic ProofOfGeneralMeansInequality