# Arithmetic mean

## Classification

### SimpleArithmeticAverage

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

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

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

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

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

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

Thatis:X1=X1'+aX2=X2'+a.....Xn=Xn'+a

Then,calculatetheaverageasformula(1)

replace,

,....,..Substituteformula(1)

toget:

thatis,thearithmeticmean=

+a

So:=+a

### weightedarithmeticaverage

Applicable:Mainlyusedforprocessinggroupeddata.SupposetheoriginaldataisdividedintoKgroups,thevalueofeachgroupisX1,X2,...,Xk,andthefrequencyofeachgroupisf1,f2,...,fk,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.