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Area Mathematics - Functions / Means

IEV ref103-02-02

en
root-mean-square value
RMS value
quadratic mean
quantity representing the quantities in a finite set or in an interval,

  1. for n quantities x 1 , x 2 , x n MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqipG0dh9qqWrVepG0dbbL8F4rqqrVepeea0xe9LqFf0xc9q8qqaq Fn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpe WZqaaeGaciWaamGadaGadeaabaGaaqaaaOqaaiaadIhadaWgaaWcba GaaGymaaqabaGccaGGSaGaaGjbVlaadIhadaWgaaWcbaGaaGOmaaqa baGccaGGSaGaaGjbVlaaykW7cqWIMaYscaaMc8UaaGPaVlaaysW7ca WG4bWaaSbaaSqaaiaad6gaaeqaaaaa@4713@ , by the positive square root of the mean value of their squares:

    X q = ( 1 n ( x 1 2 + x 2 2 ++ x n 2 )) 1/2 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqipG0dh9qqWrVepG0dbbL8F4rqqrVepeea0xe9LqFf0xc9q8qqaq Fn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpe WZqaaeGaciWaamGadaGadeaabaGaaqaaaOqaaiaadIfadaWgaaWcba qcLboacaqGXbaaleqaaOGaeyypa0ZaamWaaeaadaWcaaqaaKqzafGa aGymaaGcbaGaamOBaaaacaGGOaGaamiEamaaDaaaleaajug4aiaaig daaSqaaKqzGdGaaGOmaaaakiabgUcaRiaadIhadaqhaaWcbaqcLboa caaIYaaaleaajug4aiaaikdaaaGccqGHRaWkcaaMc8UaaGjbVlaayk W7cqWIMaYscaaMc8UaaGPaVlaaysW7cqGHRaWkcaWG4bWaa0baaSqa aiaad6gaaeaajug4aiaaikdaaaGccaGGPaaacaGLBbGaayzxaaWaaW baaSqabeaajug4aiaaigdacaGGVaGaaGOmaaaaaaa@5F01@

  2. for a quantity x depending on a variable t, by the positive square root of the mean value of the square of the quantity taken over a given interval ( t 0 , t 0 +T) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqipG0dh9qqWrVepG0dbbL8F4rqqrVepeea0xe9LqFf0xc9q8qqaq Fn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpe WZqaaeGaciWaamGadaGadeaabaGaaqaaaOqaaiaacUfacaWG0bWaaS baaSqaaKqzGdGaaGimaaWcbeaakiaacYcacaaMe8UaamiDamaaBaaa leaajug4aiaaicdaaSqabaGccqGHRaWkcaWGubGaaiyxaaaa@418C@ of the variable:

    X q = ( 1 T t 0 t 0 +T ( x(t) ) 2 dt ) 1/2 MathType@MTEF@5@5@+=feaagCart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHXgaruavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGeaGqipG0dh9qqWrVepG0dbbL8F4rqqrVepeea0xe9LqFf0xc9q8qqaqFn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpeWZqaaeaaciWacmGadaGadeaabaGaaqaaaOqaaiaadIfadaWgaaWcbaqcLboacaqGXbaaleqaaOGaeyypa0ZaamWaaeaadaWcaaqaaKqzafGaaGymaaGcbaGaamivaaaadaWdXaqaamaadmaabaGaamiEaiaacIcacaWG0bGaaiykaaGaay5waiaaw2faamaaCaaaleqabaGaaGOmaaaaaeaacaaMi8UaamiDamaaBaaameaacaaIWaaabeaaaSqaaiaayIW7caWG0bWaaSbaaWqaaiaaicdaaeqaaSGaey4kaSIaamivaaqdcqGHRiI8aKqzafGaaiizaOGaamiDaaGaay5waiaaw2faamaaCaaaleqabaqcLboacaaIXaGaai4laiaaikdaaaaaaa@553C@

Note 1 to entry: The root-mean-square value of a periodic quantity is usually taken over an integration interval the range of which is the period multiplied by a natural number.

Note 2 to entry: The root-mean-square value of a quantity is denoted by adding the subscript q to the symbol of the quantity.

Note 3 to entry: The abbreviation RMS was formerly denoted as r.m.s. or rms, but these notations are now deprecated.


fr
valeur moyenne quadratique, f
moyenne quadratique, f
grandeur représentant les grandeurs d’un ensemble fini ou d’un intervalle,

  1. pour n grandeurs x 1 , x 2 , x n MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqipG0dh9qqWrVepG0dbbL8F4rqqrVepeea0xe9LqFf0xc9q8qqaq Fn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpe WZqaaeGaciWaamGadaGadeaabaGaaqaaaOqaaiaadIhadaWgaaWcba GaaGymaaqabaGccaGGSaGaaGjbVlaadIhadaWgaaWcbaGaaGOmaaqa baGccaGGSaGaaGjbVlaaykW7cqWIMaYscaaMc8UaaGPaVlaaysW7ca WG4bWaaSbaaSqaaiaad6gaaeqaaaaa@4713@ , par la racine carrée positive de la valeur moyenne de leurs carrés:

    X q = ( 1 n ( x 1 2 + x 2 2 ++ x n 2 )) 1/2 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqipG0dh9qqWrVepG0dbbL8F4rqqrVepeea0xe9LqFf0xc9q8qqaq Fn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpe WZqaaeGaciWaamGadaGadeaabaGaaqaaaOqaaiaadIfadaWgaaWcba qcLboacaqGXbaaleqaaOGaeyypa0ZaamWaaeaadaWcaaqaaKqzafGa aGymaaGcbaGaamOBaaaacaGGOaGaamiEamaaDaaaleaajug4aiaaig daaSqaaKqzGdGaaGOmaaaakiabgUcaRiaadIhadaqhaaWcbaqcLboa caaIYaaaleaajug4aiaaikdaaaGccqGHRaWkcaaMc8UaaGjbVlaayk W7cqWIMaYscaaMc8UaaGPaVlaaysW7cqGHRaWkcaWG4bWaa0baaSqa aiaad6gaaeaajug4aiaaikdaaaGccaGGPaaacaGLBbGaayzxaaWaaW baaSqabeaajug4aiaaigdacaGGVaGaaGOmaaaaaaa@5F01@

  2. pour une grandeur x fonction de la variable t, par la racine carrée positive de la valeur moyenne du carré de la grandeur prise sur un intervalle donné ( t 0 , t 0 +T) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqipG0dh9qqWrVepG0dbbL8F4rqqrVepeea0xe9LqFf0xc9q8qqaq Fn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpe WZqaaeGaciWaamGadaGadeaabaGaaqaaaOqaaiaacUfacaWG0bWaaS baaSqaaKqzGdGaaGimaaWcbeaakiaacYcacaaMe8UaamiDamaaBaaa leaajug4aiaaicdaaSqabaGccqGHRaWkcaWGubGaaiyxaaaa@418C@ de la variable:

    X q = ( 1 T t 0 t 0 +T ( x(t) ) 2 dt ) 1/2 MathType@MTEF@5@5@+=feaagCart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHXgaruavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGeaGqipG0dh9qqWrVepG0dbbL8F4rqqrVepeea0xe9LqFf0xc9q8qqaqFn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpeWZqaaeaaciWacmGadaGadeaabaGaaqaaaOqaaiaadIfadaWgaaWcbaqcLboacaqGXbaaleqaaOGaeyypa0ZaamWaaeaadaWcaaqaaKqzafGaaGymaaGcbaGaamivaaaadaWdXaqaamaadmaabaGaamiEaiaacIcacaWG0bGaaiykaaGaay5waiaaw2faamaaCaaaleqabaGaaGOmaaaaaeaacaaMi8UaamiDamaaBaaameaacaaIWaaabeaaaSqaaiaayIW7caWG0bWaaSbaaWqaaiaaicdaaeqaaSGaey4kaSIaamivaaqdcqGHRiI8aKqzafGaaiizaOGaamiDaaGaay5waiaaw2faamaaCaaaleqabaqcLboacaaIXaGaai4laiaaikdaaaaaaa@553C@

Note 1 à l'article: La valeur moyenne quadratique d'une grandeur périodique est généralement prise sur un intervalle d'intégration dont l’étendue est le produit de la période par un entier naturel.

Note 2 à l'article: La valeur moyenne quadratique d'une grandeur est notée en ajoutant l'indice q au symbole de la grandeur.

Note 3 à l'article: L’abréviation anglaise RMS était anciennement écrite r.m.s. ou rms, mais ces notations sont maintenant déconseillées.


ar
الوسط التربيعى
قيمة الجذر التربيعى لمتوسط المربعات(1)

de
quadratischer Mittelwert, m

es
valor medio cuadrático

it
radice della media dei quadrati
valore efficace
media quadratica

ja
実効値 (1)
rms値 (1)
二乗平均

pl
średnia kwadratowa
wartość średnia kwadratowa

pt
valor médio quadrático
média quadrática

sr
ефективна вредност, ж јд
rms вредност, ж јд
средња квадратна вредност, ж јд

sv
kvadratiskt medelvärde

zh
方均根值, <相关条目:103-02-03>
二次均值

Publication date: 2017-07
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