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Area Mathematics - Functions / Means

IEV ref103-02-04

en
geometric mean value
geometric average
quantity representing the quantities in a finite set or in an interval,

  1. for n positive quantities x 1 , x 2 , x n MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqipG0dh9qqWrVepG0dbbL8F4rqqrVepeea0xe9LqFf0xc9q8qqaq Fn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpe WZqaaeGaciWaamGadaGadeaabaGaaqaaaOqaaiaadIhadaWgaaWcba qcLboacaaIXaaaleqaaOGaaiilaiaaysW7caWG4bWaaSbaaSqaaKqz GdGaaGOmaaWcbeaakiaacYcacaaMe8UaaGPaVlablAciljaaykW7ca aMc8UaaGjbVlaadIhadaWgaaWcbaGaamOBaaqabaaaaa@49C5@ , by the positive nth root of their product:

    X g = ( x 1 x 2 ... x n ) 1/n MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqipG0dh9qqWrVepG0dbbL8F4rqqrVepeea0xe9LqFf0xc9q8qqaq Fn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpe WZqaaeGaciWaamGadaGadeaabaGaaqaaaOqaaiaadIfadaWgaaWcba qcLboacaqGNbaaleqaaOGaeyypa0JaaiikaiaadIhadaWgaaWcbaqc LboacaaIXaaaleqaaOGaeyyXICTaamiEamaaBaaaleaajug4aiaaik daaSqabaGccqGHflY1caGGUaGaaiOlaiaac6cacqGHflY1caWG4bWa aSbaaSqaaiaad6gaaeqaaOGaaiykamaaCaaaleqabaqcLboacaaIXa WccaGGVaGaamOBaaaaaaa@5095@

  2. for a quantity x depending on a variable t, by the quantity X g MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqipG0dh9qqWrVepG0dbbL8F4rqqrVepeea0xe9LqFf0xc9q8qqaq Fn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpe WZqaaeGaciWaamGadaGadeaabaGaaqaaaOqaaiaadIfadaWgaaWcba qcLboacaqGNbaaleqaaaaa@389C@ calculated from the values of the quantity x(t) by the expression

    log X g x ref = 1 T 0 T log x(t) x ref dt MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqipG0dh9qqWrVepG0dbbL8F4rqqrVepeea0xe9LqFf0xc9q8qqaq Fn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpe WZqaaeGaciWaamGadaGadeaabaGaaqaaaOqaaKqzafGaciiBaiaac+ gacaGGNbGcdaWcaaqaaiaadIfadaWgaaWcbaqcLboacaqGNbaaleqa aaGcbaGaamiEamaaBaaaleaajug4aiaabkhacaqGLbGaaeOzaaWcbe aaaaGccqGH9aqpdaWcaaqaaKqzafGaaGymaaGcbaGaamivaaaadaWd XaqaaKqzafGaciiBaiaac+gacaGGNbGcdaWcaaqaaiaadIhacaGGOa GaamiDaiaacMcaaeaacaWG4bWaaSbaaSqaaKqzGdGaaeOCaiaabwga caqGMbaaleqaaaaaaeaacaaMi8EcLboacaaIWaaaleaacaaMi8Uaam ivaaqdcqGHRiI8aKqzafGaaiizaOGaamiDaaaa@5BEA@

    where x ref MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqipG0dh9qqWrVepG0dbbL8F4rqqrVepeea0xe9LqFf0xc9q8qqaq Fn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpe WZqaaeGaciWaamGadaGadeaabaGaaqaaaOqaaiaadIhadaWgaaWcba qcLboacaqGYbGaaeyzaiaabAgaaSqabaaaaa@3A98@ is a reference value

Note 1 to entry: The geometric mean 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 geometric mean value of a quantity is denoted by adding the subscript g to the symbol of the quantity.


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

  1. pour n grandeurs positives x 1 , x 2 , x n MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqipG0dh9qqWrVepG0dbbL8F4rqqrVepeea0xe9LqFf0xc9q8qqaq Fn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpe WZqaaeGaciWaamGadaGadeaabaGaaqaaaOqaaiaadIhadaWgaaWcba qcLboacaaIXaaaleqaaOGaaiilaiaaysW7caWG4bWaaSbaaSqaaKqz GdGaaGOmaaWcbeaakiaacYcacaaMe8UaaGPaVlablAciljaaykW7ca aMc8UaaGjbVlaadIhadaWgaaWcbaGaamOBaaqabaaaaa@49C5@ , par la racine n-ième positive de leur produit:

    X g = ( x 1 x 2 ... x n ) 1/n MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqipG0dh9qqWrVepG0dbbL8F4rqqrVepeea0xe9LqFf0xc9q8qqaq Fn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpe WZqaaeGaciWaamGadaGadeaabaGaaqaaaOqaaiaadIfadaWgaaWcba qcLboacaqGNbaaleqaaOGaeyypa0JaaiikaiaadIhadaWgaaWcbaqc LboacaaIXaaaleqaaOGaeyyXICTaamiEamaaBaaaleaajug4aiaaik daaSqabaGccqGHflY1caGGUaGaaiOlaiaac6cacqGHflY1caWG4bWa aSbaaSqaaiaad6gaaeqaaOGaaiykamaaCaaaleqabaqcLboacaaIXa WccaGGVaGaamOBaaaaaaa@5095@

  2. pour une grandeur x fonction de la variable t, par la grandeur X g MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqipG0dh9qqWrVepG0dbbL8F4rqqrVepeea0xe9LqFf0xc9q8qqaq Fn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpe WZqaaeGaciWaamGadaGadeaabaGaaqaaaOqaaiaadIfadaWgaaWcba qcLboacaqGNbaaleqaaaaa@389C@ déterminée à partir des valeurs de la grandeur x(t) par l'expression

    log X g x ref = 1 T 0 T log x(t) x ref dt MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqipG0dh9qqWrVepG0dbbL8F4rqqrVepeea0xe9LqFf0xc9q8qqaq Fn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpe WZqaaeGaciWaamGadaGadeaabaGaaqaaaOqaaKqzafGaciiBaiaac+ gacaGGNbGcdaWcaaqaaiaadIfadaWgaaWcbaqcLboacaqGNbaaleqa aaGcbaGaamiEamaaBaaaleaajug4aiaabkhacaqGLbGaaeOzaaWcbe aaaaGccqGH9aqpdaWcaaqaaKqzafGaaGymaaGcbaGaamivaaaadaWd XaqaaKqzafGaciiBaiaac+gacaGGNbGcdaWcaaqaaiaadIhacaGGOa GaamiDaiaacMcaaeaacaWG4bWaaSbaaSqaaKqzGdGaaeOCaiaabwga caqGMbaaleqaaaaaaeaacaaMi8EcLboacaaIWaaaleaacaaMi8Uaam ivaaqdcqGHRiI8aKqzafGaaiizaOGaamiDaaaa@5BEA@

    x ref MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqipG0dh9qqWrVepG0dbbL8F4rqqrVepeea0xe9LqFf0xc9q8qqaq Fn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpe WZqaaeGaciWaamGadaGadeaabaGaaqaaaOqaaiaadIhadaWgaaWcba qcLboacaqGYbGaaeyzaiaabAgaaSqabaaaaa@3A98@ est une valeur de référence

Note 1 à l'article: La valeur moyenne géométrique 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 géométrique d'une grandeur est notée en ajoutant l'indice g au symbole de la grandeur.


ar
قيمة الوسط الهندسى
المتوسط الهندسى

de
geometrischer Mittelwert, m

es
valor medio geométrico

it
valore medio geometrico
media geometrica

ja
幾何平均値
幾何平均

pl
średnia geometryczna
wartość średnia geometryczna

pt
valor médio geométrico
média geométrica

sr
геометријска средња вредност, ж јд
геометријски просек, м јд

sv
geometriskt medelvärde

zh
几何平均值

Publication date: 2017-07
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