Significato aritmetico

Classification

SimpleArithmeticAverage

(1)Applicable:Mainlyusedforungroupedrawdata.SupposeasetofdataisX₁,X₂,...,X_n,thesimplecalculationformulaofarithmeticmeanis:

(2) Esempio: Una squadra di vendita ha 5 venditori, e le vendite di Capodanno sono 520 yuan, 600 yuan, 480 yuan, 750 yuan e 500 yuan, trovare la media di vendita del giorno.

Vendite medie=(520+600+480+750+500)/5=570(yuan)

Thecalculationresultsshowthattheaverageturnoverof5salespersonsadayonNewYear’sDayItis570yuan.

(3)Expansion:Asetofdatax₁.x₂.x₃fluctuatesaroundthenumbera,Inordertogetthearithmeticaverage.

First,weneedtosubtractafromeachoriginaldatatoobtainanewsetofdata,denotedasx₁'x₂'.....xn'

X1'=X1-aX2'=X2-a.....Xn'=Xn-a

Thatis:X1=X_1'+aX2=X_2'+a.....X_n=X_n'+a

Deinde, calculate theaverageasformula(1).

replace,

toget:

thatis,thearithmeticmean=

Ita:=+a

weightedarithmeticaverage

Applicable:Mainlyusedforprocessinggroupeddata.SupposetheoriginaldataisdividedintoKgroups,thevalueofeachgroupisX1,X2,...,Xk,andthefrequencyofeachgroupisf₁,f₂,...,f_k,thecalculationformulaoftheweightedarithmeticmeanis:

Specialinstructions

1.Theweightedarithmeticaverageisaffectedbytwofactorsatthesametime,oneisthesizeofeachgroupofvalues,andtheotheristhedistributionfrequencyofeachgroup.Whenthevalueisconstant,themorethefrequencyofagroup,thegreatertheeffectofthevalueofthegroupontheaverage,andviceversa,thesmaller.

Frequencyplaysaroleinweighingtheweightoftheweightedarithmeticaverage,whichisalsothemeaningofthe"weighted"oftheweightedarithmeticaverage.

2.Thearithmeticmeanis facile afficitur per extremam.

Itcanbeseenthattheappearanceofextremevalues​​willinterferewiththeauthenticityoftheaverage.

Features

①Thearithmeticmeanisagoodconcentrationquantity,whichissensitive,rigorous,conciseandeasytosolve,simpletocalculate,suitableforfurthercalculationsandsmallsamplechangesTheimpactandotheradvantages.

②Thearithmeticaverageissusceptibletoextremedata.Thisisbecausetheaverageissensitive.Largeorsmallchangesineachdatawillaffectthefinalresult.