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Area Mathematics - Functions / Probability

IEV ref103-08-12

en
variance, <in statistics>
measure of dispersion equal to the sum of the squared deviations from the mean value divided by the number of deviations or by that number minus 1, depending upon the cases considered:

(1) variance of the whole population of N items: 1 N j=1 N ( x j X ¯ ) 2 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqipG0dh9qqWrVepG0dbbL8F4rqqrVepeea0xe9LqFf0xc9q8qqaq Fn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpe WZqaaiqaciWacmGadaGadeaabaGaaqaaaOqaamaalaaabaqcLbuaca aIXaaakeaacaWGobaaamaaqahabaGaaiikaiaadIhadaWgaaWcbaGa amOAaaqabaaabaGaamOAaiabg2da9KqzaeGaaGymaaWcbaGaamOtaa qdcqGHris5aOGaeyOeI0IabmiwayaaraGaaiykamaaCaaaleqabaqc LbqacaaIYaaaaaaa@4492@

(2) variance of the sample of n observations: 1 n j=1 n ( x j X ¯ ) 2 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqipG0dh9qqWrVepG0dbbL8F4rqqrVepeea0xe9LqFf0xc9q8qqaq Fn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpe WZqaaiqaciWacmGadaGadeaabaGaaqaaaOqaamaalaaabaqcLbuaca aIXaaakeaacaWGUbaaamaaqahabaGaaiikaiaadIhadaWgaaWcbaGa amOAaaqabaaabaGaamOAaiabg2da9KqzaeGaaGymaaWcbaGaamOBaa qdcqGHris5aOGaeyOeI0IabmiwayaaraGaaiykamaaCaaaleqabaqc LbqacaaIYaaaaaaa@44D2@

(3) estimate of the variance of the population from a sample: 1 n1 j=1 n ( x j X ¯ ) 2 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqipG0dh9qqWrVepG0dbbL8F4rqqrVepeea0xe9LqFf0xc9q8qqaq Fn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpe WZqaaiqaciWacmGadaGadeaabaGaaqaaaOqaamaalaaabaqcLbuaca aIXaaakeaacaWGUbGaeyOeI0scLbuacaaIXaaaaOWaaabCaeaacaGG OaGaamiEamaaBaaaleaacaWGQbaabeaaaeaacaWGQbGaeyypa0tcLb qacaaIXaaaleaacaWGUbaaniabggHiLdGccqGHsislceWGybGbaeba caGGPaWaaWbaaSqabeaajugabiaaikdaaaaaaa@4733@

where X ¯ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqipG0dh9qqWrVepG0dbbL8F4rqqrVepeea0xe9LqFf0xc9q8qqaq Fn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpe WZqaaiqaciWacmGadaGadeaabaGaaqaaaOqaamaanaaabaGaamiwaa aaaaa@3640@ is the mean value of the items of observation x j MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqipG0dh9qqWrVepG0dbbL8F4rqqrVepeea0xe9LqFf0xc9q8qqaq Fn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpe WZqaaiqaciWacmGadaGadeaabaGaaqaaaOqaaiaadIhadaWgaaWcba GaamOAaaqabaaaaa@376A@ considered


fr
variance, <en statistique> f
mesure de la dispersion égale au quotient de la somme des carrés des écarts à la valeur moyenne par le nombre des écarts ou par ce nombre diminué d'une unité, selon les cas envisagés:

(1) variance de la population totale de N individus: 1 N j=1 N ( x j X ¯ ) 2 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqipG0dh9qqWrVepG0dbbL8F4rqqrVepeea0xe9LqFf0xc9q8qqaq Fn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpe WZqaaiqaciWacmGadaGadeaabaGaaqaaaOqaamaalaaabaqcLbuaca aIXaaakeaacaWGobaaamaaqahabaGaaiikaiaadIhadaWgaaWcbaGa amOAaaqabaaabaGaamOAaiabg2da9KqzaeGaaGymaaWcbaGaamOtaa qdcqGHris5aOGaeyOeI0IabmiwayaaraGaaiykamaaCaaaleqabaqc LbqacaaIYaaaaaaa@4492@

(2) variance d'un échantillon de n observations: 1 n j=1 n ( x j X ¯ ) 2 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqipG0dh9qqWrVepG0dbbL8F4rqqrVepeea0xe9LqFf0xc9q8qqaq Fn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpe WZqaaiqaciWacmGadaGadeaabaGaaqaaaOqaamaalaaabaqcLbuaca aIXaaakeaacaWGUbaaamaaqahabaGaaiikaiaadIhadaWgaaWcbaGa amOAaaqabaaabaGaamOAaiabg2da9KqzaeGaaGymaaWcbaGaamOBaa qdcqGHris5aOGaeyOeI0IabmiwayaaraGaaiykamaaCaaaleqabaqc LbqacaaIYaaaaaaa@44D2@

(3) estimation de la variance de la population à partir d'un échantillon: 1 n1 j=1 n ( x j X ¯ ) 2 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqipG0dh9qqWrVepG0dbbL8F4rqqrVepeea0xe9LqFf0xc9q8qqaq Fn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpe WZqaaiqaciWacmGadaGadeaabaGaaqaaaOqaamaalaaabaqcLbuaca aIXaaakeaacaWGUbGaeyOeI0scLbuacaaIXaaaaOWaaabCaeaacaGG OaGaamiEamaaBaaaleaacaWGQbaabeaaaeaacaWGQbGaeyypa0tcLb qacaaIXaaaleaacaWGUbaaniabggHiLdGccqGHsislceWGybGbaeba caGGPaWaaWbaaSqabeaajugabiaaikdaaaaaaa@4733@

X ¯ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqipG0dh9qqWrVepG0dbbL8F4rqqrVepeea0xe9LqFf0xc9q8qqaq Fn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpe WZqaaiqaciWacmGadaGadeaabaGaaqaaaOqaamaanaaabaGaamiwaa aaaaa@3640@ est la valeur moyenne des entités x j MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqipG0dh9qqWrVepG0dbbL8F4rqqrVepeea0xe9LqFf0xc9q8qqaq Fn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpe WZqaaiqaciWacmGadaGadeaabaGaaqaaaOqaaiaadIhadaWgaaWcba GaamOAaaqabaaaaa@376A@ considérées


ar
التباين (احصائى)

de
Varianz (in der Statistik), f

es
varianza (en estadística)

it
varianza (nella statistica)

ja
分散, <統計学の>

pl
wariancja (w statystyce)

pt
variância (em estatística)

sr
варијанса, <у статистици> ж јд

sv
varians (i statistik)

zh
方差, <统计学中的>

Publication date: 2009-12
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