Arithmetic mean

Classification

SimpleArithmeticAverage

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

(2)Example:Asalesteamhas5salespeople,andthesalesonNewYear’sDayare520yuan,600yuan,480yuan,750yuanand500yuan,findtheaveragesalesoftheday.

Averagesales=(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

Then,calculatetheaverageasformula(1)

replace,

toget:

thatis,thearithmeticmean=

So:=+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.Thearithmeticmeaniseasilyaffectedbyextremevalues.Forexample,therearethefollowingdata:5,7,5,4,6,7,8,5,4,7,8,6,20.Theaveragevalueofallthedatais7.1.Infact,mostofthedata(thereare10)arenotIfitexceeds7,if20isremoved,theaverageoftheremaining12numbersis6.

Itcanbeseenthattheappearanceofextremevalues​​willinterferewiththeauthenticityoftheaverage.

Features

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

②Thearithmeticaverageissusceptibletoextremedata.Thisisbecausetheaverageissensitive.Largeorsmallchangesineachdatawillaffectthefinalresult.