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IEVref:103-02-01ID:
Language:enStatus: Standard
Term: mean value
Synonym1: mean
[Preferred]
Synonym2: arithmetic mean
[Preferred]
Synonym3: average<br>arithmetic average
[Preferred]
Symbol:
Definition: 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 quotient of the sum of the quantities by n:

    X = 1 n ( x 1 + x 2 ++ x n ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqipG0dh9qqWrVepG0dbbL8F4rqqrVepeea0xe9LqFf0xc9q8qqaq Fn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpe WZqaaeGaciWaamGadaGadeaabaGaaqaaaOqaamaanaaabaGaamiwaa aacqGH9aqpdaWcaaqaaKqzafGaaGymaaGcbaGaamOBaaaacaGGOaGa amiEamaaBaaaleaajug4aiaaigdaaSqabaGccqGHRaWkcaWG4bWaaS baaSqaaKqzGdGaaGOmaaWcbeaakiabgUcaRiaaykW7caaMe8UaaGPa VlablAciljaaykW7caaMc8UaaGjbVlabgUcaRiaadIhadaWgaaWcba GaamOBaaqabaGccaGGPaaaaa@50D7@

  2. for a quantity x depending on a variable t, by the integral of the quantity taken between two given values of the variable, divided by the difference of the two values:

    X = 1 t 2 t 1 t 1 t 2 x(t)dt MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgaruWqVvNCPvMCG4uz 3bqee0evGueE0jxyaibaieYdi9WrpeeC0lXdi9qqqj=hEeeu0lXdbb a9frFj0xb9Lqpepeea0xd9s8qiYRWxGi6xij=hbba9q8aq0=yq=He9 q8qiLsFr0=vr0=vr0db8meaabaGacmGadiWaaiWabaabaiaafaaake aadaqdaaqaaiaadIfaaaGaeyypa0ZaaSaaaeaajugqbiaaigdaaOqa aiaadshadaWgaaWcbaqcLboacaaIYaaaleqaaOGaeyOeI0IaamiDam aaBaaaleaajug4aiaaigdaaSqabaaaaOWaa8qmaeaacaWG4bGaaiik aiaadshacaGGPaqcLbuacaGGKbGccaWG0baaleaacaaMi8UaamiDam aaBaaameaacaaIXaaabeaaaSqaaiaayIW7caWG0bWaaSbaaWqaaiaa ikdaaeqaaaqdcqGHRiI8aaaa@537A@

Note 1 to entry: The 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 mean value of the quantity x may be denoted by X MathType@MTEF@5@5@+=feaagCart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHXgaruavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGeaGqipG0dh9qqWrVepG0dbbL8F4rqqrVepeea0xe9LqFf0xc9q8qqaqFn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpeWZqaaeaaciWacmGadaGadeaabaGaaqaaaOqaamaanaaabaGaamiwaaaaaaa@363B@ , by ⟨X⟩, or by Xa. Subscripts ar, av and moy are also used.

Note 3 to entry: The adjective "arithmetic" is only used to qualify the terms "mean" and "average" in order to distinguish them from the terms "geometric mean" and "geometric average", as well from "harmonic mean" and "harmonic average".

Note 4 to entry: The mean value can be generalized for a function of n variables, e.g. with a surface integral or an integral over a three-dimensional domain divided by the corresponding area or volume. See the examples in IEC 60050-102.


Publication date:2017-07
Source:
Replaces:103-02-01:2009-12
Internal notes:2017-08-25: Added <p> tag before list. LMO
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