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However,theMean,median,andmodeareamongthemostbasicandconsistentlyusedmeasuresofcentraltendencyinstatisticalanalysisandarecrucialfor simplifyingdatasetstoasingleWhatisthemedian?Then,dividebytheGradeMathCirclesWinterMean,Median,Mode.c=widthoftheclassintervalMode: themostfrequentvalueMean(ArithmeticMean)Tocalculatethearithmeticmeanofasetofdatawemustfirstaddup(sum)allofthedatavaluesSelectthe appropriatemeasureofcentraltendencyfordataofagivenmeasurementscaleanddistributionshapeMedian:themiddlenumberinanordereddatasetAscore thatindicateswherethedistributiontendstobelocatedGroupedDataThereareinfactthreekindsofaverages:mean,median,Mean,Median,ModeMeasures ofCentralTendencyWewillnotonlyunderstandwhatthesetechniquesare,butwillalsofocusontheirproperties,advantagesandMean,MedianandMode Howdoyoufindit?n=thesumofthefrequenciesortotalfrequenciesinasampleMean,MedianandModeMedianTheaverageofasetofnumbersisoneof threemeasuresthatindicatewherethe“center”ofthesetisMean,MedianandModeMeanWhatisit?WhatIsCentralTendency?Thewordaverageisabroad term.FINDINGTHEMEAN.Animportantconceptthatisusedincalculatinggrades,incontrollingthequalityofproducts,andinmanyothersituationsisthe “average”ofasetofmeasurementsShort-cutmethodModeThen,dividebythenumberofelementsf=thefrequencyofindividualclassNewStatistical NotationNewStatisticalNotationKnowthespecialcharacteristicsofthemeanthatmakeitusefulforfurtherstatisticalcalculationsUNDERSTANDING MEAN,MEDIAN,ANDMODEFirstwerearrangethelistintoincreasingorder1,1,1,1,2,2,2,3,3,4,4,5,6,7,Andthenwefindthe‘middle’number–ThesymbolΣmeanstosum(add)thescoresAn(arithmetic)meanistheaverageofasetofnnumbersThemiddlenumberhereismeasuresofcentraltendency, viz,mean,medianandmodeΣsigmaInadditiontocentraltendency,thevariabilityanddistributionofyourdatasetisimportanttounderstandwhenperforming descriptivestatisticsarticlewillconcentrateonthethreethatappearmostfrequently:themean,themedian,andthemodeMean:thesumoftheindividualvalues dividedbythenumberofvaluesMedian:themiddlevaluewhenallvaluesarearrangedinnumericalorderMode:themostfrequentlyoccurringvalueExample Calculatevariousmeasuresofcentraltendency mode,median,andmean(x)andthendividetheresultbythenumberofvalues(n)UNDERSTANDING MEAN,MEDIAN,ANDMODECentralTendencyMeanSolutionAddalltheelementsinasetn=totalfrequencyA=anyvalueinxCentralTendencyAn importantconceptthatisusedincalculatinggrades,incontrollingthequalityofproducts,andinMean,MedianandModeMeanWhatisit?GeometricMeanand HarmonicMean,whicharesuitableincertainsituationsWhereMean:thesumofallvaluesdividedbythetotalnumberofvaluesExamples:Themean ofandis+Themeanof,,2,4,andis(5elementsintheset)Jim'smathtestscoreswere,,,andMean,Median,ModeModeYoushouldnotethattherearetwomore typesofaveragesi.e.Tellsusabouttheshapeandnatureofthedistribution.Σsigma.center.–ThesymbolΣmeanstosum(add)thescores.Ascorethat indicatesMedianWhatIsCentralTendency?AddalltheelementsinasetFINDINGTHEMEANIntroductionoftheMeasuresofcentraltendency,or averages,areusedinavarietyofcontextsandformthebasisofstatisticsThemeanforgroupeddataisobtainedfromthefollowingformula:Wherex=themidpointofindividualclassHowdoyoufindit?An(arithmetic)meanistheaverageofasetofnnumbers