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DataisorganizedandrepresentedgraphicallysothatitbecomeseasytounderstandandinterpretPresentthedatausingExcelsoftwareStatistics:Basic ConceptsMean,Median,andMode.Measuresofcentraltendencygiveusonevalue(meanormedian)forthedistributionandthisvaluerepresentstheentire distributionTofindthemedianofasetofnnumbers:ArrangethenumbersinorderandthenfindthecenterofthosenumbersTerms:centraltendency,mode, median,mean,outlierSymbols:Mo,Mdn,M,m,∑,NLearningObjectives:Calculatevariousmeasuresofcentraltendency mode,median,andmeanSelectthe appropriatemeasureofcentraltendencyfordataofagivenmeasurementscaleanddistributionshapeEx,2,2,2,isthemiddlenumberIfthedifferencebetween modeandmedianofadatais,usetherelationMode=3Median2MeanEx,2,2,2,occursthemostThemodeis2Differentiatebetweenmean,median,and mode(a)(b)(c)(d)QFinddifferencebetweenmeanandmedianEachmeasureservesthesamepurpose,whichistodescribethecentraltendencyofdataThe median’sthemiddle;Youaddanddivideforthemean.Tomakecomparisonsbetweentwoormoregroups,representativevaluesofthesedistributionsare comparedCENTRALVALUES:MEAN,MEDIAN,MODEForsymmetricdistributionssuchastheoneshowninFigureallcentralvaluesareequivalent:mean= median=modeThemedianis•MODE:ThenumberthatoccursthemostinadatasetUsingthesameexample,10,21,23,23,38,=Themedianisthemiddlevalue inalistorderedfromsmallesttolargestButwhatdothesevaluesrepresent?Modecantakezero,one,ormorethanonevaluesJMPStatisticalNotes:Modeis alwaysthenumberfromthedatasetIfyou’retryingtoidentifypatternsortrendsinadataset,youcanusethethreemeasuresofcentraltendency–mean,median, andmodeThisarticledefinesthreedifferentmeasuresofcentraltendency:themean,themedian,andthemodeLearnaboutthedifferencesbetweenmean, median,andmodeinstatisticsAgeometricmeanisfoundbymultiplyingallvaluesinalistandthentakingtherootofthatproductequaltothenumberofvalues (e.g.,thesquarerootiftherearetwonumbers)Q.Ifthedifferenceofmodeandmedianofadatais,thenthedifferenceofmedianandmeanis./en/statistics-basicconcepts/frequency-polygons/content/Mean,median,andmodeUnderstandhowthesemeasuresofcentraltendencycanhelpyouanalyzedataThemodeisthe onethatappearsthemost,andtherangeisthedifferencebetweenThisactivitydealswiththemaximumdropoffifty-fiverollercoastersintheUnited(Therecan bezeromodes,onemode,twomodes,)ShapeofaDataSetRelationshipbetweenmeanandmedian,inmostcases,candescribetheshapeofdataset (histogram)BacktoTutorialThemodeisthemostfrequentlyoccurringvalueonthelistDrop-offProblem:Manymiddle-gradesstudentsareinterestedinroller coasters–often,thescarierthebetterThemediancanbethoughtofasthepositionalbalancepointinasetofmeasuresCollectdatafromanoscillatingobject MEANMeanisacalculatedvaluesimilartotheconceptofaverageQThemedianofasetofnumbersisthe“center”ofasetwhenthenumbersarearrangedin order.Whilerangedoeshavedifferentmeaningswithindifferentareasofstatisticsandmathematics,thisisitsmostbasicdefinition,andiswhatisusedbythe providedcalculatorThedifferencebetweenthehighestandlowestobservationsinagivendataiscalleditsRangeTherangeofadatasetinstatisticsisthe differencebetweenthelargestandthesmallestvaluesEstimatethemean,median,modeandrange,percentdifferenceofthemeasurements(a)MedianMean(b) Median=Mean(c)Median>MeanThemean,median,andmodearethreetypesofmeasuresofcentraltendencyThevariousmeancalculationsaredefinedin severalstandarddocumentsMeanMedianModePracticeTestQuestionAnswers[PDFWorksheet]:Theinformationcollectedintheformofnumbersiscalled DataThereareothertypesofmeans