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LastUpdated:05October2024LastUpdated:05October2024LastUpdated:05October2024MEASURESOFCENTRALTENDENCY(LOCATION)MEASURESOFCENTRALTENDENCY(LOCATION)MEASURESOFCENTRALTENDENCY(LOCATION)FunctionsofanaverageTogetonevaluethatdescribesamassofdata-Forexample,itisquiteimpossibletokeepinmindtheindividualageof4,000studentsinacollege.Butiftheaverageageisobtained,wearriveatasinglevalue,therebymakingreferenceandinterpretationeasy.Thusanaveragereducesacomplexmassofdataintoasingletypicalvalueenablingonetogetabird’seyeviewabouttheentiredata.Tofacilitatecomparison-Anaverageprovidesacommonvalueforcomparingonesetofdatawithothersandconclusionscanbedrawaboutthecharacteristicsoftheseparatesetsofdata.Forexample,wecancomparethepercentageresultsofthestudentsofdifferentcollegesinacertainexaminationandtherebydeterminewhichcollegeisthebest.Toknowaboutthepopulationfromthesample-Averagesalsohelptoobtainthepictureofacompleteuniversebymeansofsampledata.Theaverageofasamplegivesafairlygoodideaabouttheaverageofthepopulation.Thethreemostimportantmeasuresofcentraltendencyare:ThearithmeticmeanThemedianThemodeArithmeticmeanThearithmeticmeanorsimplythemeanisthemostcommonlyusedmeasureoflocation.Whenpeoplespeakoftakinganaverage.Itismeanthattheyaremostoftenreferringto.However,themeancanonlybecalculatedfromquantitativedata.Themeanisdefinedasthevalueeachitemwouldhaveifthetotalvaluesweredividedequallyamongalltheitems.Mean=TotalValueTotalno.ofitemsComputationofthemean:UngroupeddataMean=Wherex=individualvalue;n=thetotalnumberofitems;∑meanssummationof.Example1:Example2Example3Solution:Example4Solution:MedianComputationofthemedian:Example5:Example6Example7:(c)Frequencydistributionofmulti-valuegroping.Example8:Medianitem=Medianclassboundaries:50-60Median=cmwhichshowthat50%ofthemetalpipesarehavinglengthslessthan54.12cm.Andtheother50%arehavinglengthsmorethan54.12cm.Example9:Medianclassboundaries:22.5-27.5Median==26unitswhichshowthat50%ofthedaysarehavingproductionlessthan26
