Mean, Median, Mode

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About Basics of Mean, Median, Mode.
For Grade 7

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Mean, Median, Mode
Narmatha Devi N
Statistics
Grade 7

Here, we will be seeing about basics of some common
measures of central tendencies : Mean, Median and Mode
About…

•Mean,Medianmodearesomemeasuresofcentraltendency,
whichcanbeusedtostudythevariouscharacteristicsofa
givensetofdata.
•Ameasureofcentraltendencydescribesasetofdataby
identifyingthecentralpositioninthedatasetasasinglevalue.
•Itcanbethoughtasatendencyofdatatoclusterarounda
middlevalue.
Introduction

•Thearithmeticmeanofagivendataisthesumofall
observationsdividedbythenumberofobservations.
•ItisalsocalledasAverageandisdenotedbyҧ??????
??????&#3627408531;&#3627408522;&#3627408533;&#3627408521;&#3627408526;&#3627408531;&#3627408533;&#3627408522;&#3627408516;&#3627408526;&#3627408518;&#3627408514;&#3627408527;=
??????&#3627408534;&#3627408526;&#3627408528;&#3627408519;&#3627408514;&#3627408525;&#3627408525;&#3627408528;&#3627408515;&#3627408532;&#3627408518;&#3627408531;&#3627408535;&#3627408514;&#3627408533;&#3627408522;&#3627408528;&#3627408527;&#3627408532;
&#3627408501;&#3627408528;.&#3627408528;&#3627408519;&#3627408528;&#3627408515;&#3627408532;&#3627408518;&#3627408531;&#3627408535;&#3627408514;&#3627408533;&#3627408522;&#3627408528;&#3627408527;
Mean

•Dateset:51,23,42,35,42,47
&#3627408526;&#3627408518;&#3627408514;&#3627408527;=
??????&#3627408534;&#3627408526;&#3627408528;&#3627408519;&#3627408514;&#3627408525;&#3627408525;&#3627408528;&#3627408515;&#3627408532;&#3627408518;&#3627408531;&#3627408535;&#3627408514;&#3627408533;&#3627408522;&#3627408528;&#3627408527;&#3627408532;
&#3627408501;&#3627408528;.&#3627408528;&#3627408519;&#3627408528;&#3627408515;&#3627408532;&#3627408518;&#3627408531;&#3627408535;&#3627408514;&#3627408533;&#3627408522;&#3627408528;&#3627408527;
=
51+23+42+35+42+47
6
=
240
6
Mean=40
Mean-example

•Themedianisthemiddlevalueofadataset,whichseparates
thehighestandlowestvaluesequally.
•Itiscalculatedbyarrangingthedatasetinascendingor
descendingorderthevalueintheexactmiddle.
&#3627408500;&#3627408518;&#3627408517;&#3627408522;&#3627408514;&#3627408527;=&#3627408526;&#3627408522;&#3627408517;&#3627408517;&#3627408525;&#3627408518;&#3627408526;&#3627408528;&#3627408532;&#3627408533;&#3627408528;&#3627408515;&#3627408532;&#3627408518;&#3627408531;&#3627408535;&#3627408514;&#3627408533;&#3627408522;&#3627408528;&#3627408527;
Median

Step1:Arrangethedatainascendingordescendingorder.
Step2:Findtotalnumberofobservations,n.
Step3:
ifnisodd,&#3627408474;&#3627408466;&#3627408465;??????&#3627408462;&#3627408475;=
&#3627408475;+1
2
&#3627408481;ℎ
&#3627408476;&#3627408463;&#3627408480;&#3627408466;&#3627408479;??????&#3627408462;&#3627408481;??????&#3627408476;&#3627408475;
ifniseven,&#3627408474;&#3627408466;&#3627408465;??????&#3627408462;&#3627408475;=
(
??????
2
)
??????ℎ
&#3627408476;&#3627408463;&#3627408480;??????&#3627408479;??????&#3627408462;&#3627408481;??????&#3627408476;&#3627408475;+(
??????
2
+1)
??????ℎ
&#3627408476;&#3627408463;&#3627408480;??????&#3627408479;??????&#3627408462;&#3627408481;??????&#3627408476;&#3627408475;
2
Median-procedure

•Dateset:29,12,42,53,34
&#3627408526;&#3627408518;&#3627408517;&#3627408522;&#3627408514;&#3627408527;=&#3627408526;&#3627408522;&#3627408517;&#3627408517;&#3627408525;&#3627408518;&#3627408526;&#3627408528;&#3627408532;&#3627408533;&#3627408535;&#3627408514;&#3627408525;&#3627408534;&#3627408518;
Ascendingorder:12,29,34,42,53
Middlemostvalue:34
Median=34
Median-example
•n=5,odd
&#3627408526;&#3627408518;&#3627408517;&#3627408522;&#3627408514;&#3627408527;=
&#3627408475;+1
2
&#3627408481;ℎ
&#3627408476;&#3627408463;&#3627408480;&#3627408466;&#3627408479;??????&#3627408462;&#3627408481;??????&#3627408476;&#3627408475;
=
5+1
2
&#3627408481;ℎ
&#3627408476;&#3627408463;&#3627408480;&#3627408466;&#3627408479;??????&#3627408462;&#3627408481;??????&#3627408476;&#3627408475;
=3
&#3627408481;ℎ
&#3627408476;&#3627408463;&#3627408480;&#3627408466;&#3627408479;??????&#3627408462;&#3627408481;??????&#3627408476;&#3627408475;
Median=34

•Dateset:51,23,42,36,23,47
&#3627408526;&#3627408518;&#3627408517;&#3627408522;&#3627408514;&#3627408527;=&#3627408526;&#3627408522;&#3627408517;&#3627408517;&#3627408525;&#3627408518;&#3627408526;&#3627408528;&#3627408532;&#3627408533;&#3627408535;&#3627408514;&#3627408525;&#3627408534;&#3627408518;
Ascendingorder:23,23,36,42,47,51
average-Middlevalue:
36+42
2
Median=39
Median-example
•n=6,even
&#3627408526;&#3627408518;&#3627408517;&#3627408522;&#3627408514;&#3627408527;=
(
??????
2
)
??????ℎ
&#3627408476;&#3627408463;&#3627408480;??????&#3627408479;??????&#3627408462;&#3627408481;??????&#3627408476;&#3627408475;+(
??????
2
+1)
??????ℎ
&#3627408476;&#3627408463;&#3627408480;??????&#3627408479;??????&#3627408462;&#3627408481;??????&#3627408476;&#3627408475;
2
=
36+42
2
Median=39

•Thevaluewhichappearsmostofteninthegivendatai.e.the
observationwiththehighestfrequencyiscalledamodeof
data.
•Adatamayhavenomode,1mode,ormorethan1mode.
&#3627408500;&#3627408528;&#3627408517;&#3627408518;=&#3627408528;&#3627408515;&#3627408532;&#3627408518;&#3627408531;&#3627408535;&#3627408514;&#3627408533;&#3627408522;&#3627408528;&#3627408527;&#3627408536;&#3627408522;&#3627408533;&#3627408521;&#3627408526;&#3627408514;&#3627408537;&#3627408522;&#3627408526;&#3627408534;&#3627408526;&#3627408519;&#3627408531;&#3627408518;&#3627408530;&#3627408534;&#3627408518;&#3627408527;&#3627408516;&#3627408538;
Mode

•Dateset:2,9,3,12,2,4,2,5
&#3627408526;&#3627408528;&#3627408517;&#3627408518;=&#3627408526;&#3627408528;&#3627408532;&#3627408533;&#3627408519;&#3627408531;&#3627408518;&#3627408530;&#3627408534;&#3627408518;&#3627408527;&#3627408533;&#3627408535;&#3627408514;&#3627408525;&#3627408534;&#3627408518;
Theobservation2isrepeatedthrice
Mode=2
Mode-example

▪Themiddlemostobservationinadatasetiscalled_______
▪Arithmeticisalsocalledas________
▪Findthemean,median,modeofdataset{8,2,5,7,3,5}
Testingtime…

Mean, Median, Mode

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