BasicStatistics UseofMinitab BeltonGroupRexWong 2 Statistics Statisticsisthebranchofsciencethatdealswiththecollection presentation analysis interpretationofdataforthepurposeofdecision makingandproblem solving Statisticsisacriticalskillinqualityimprovementasstatisticaltechniquescanbeusedtodescribeandtounderstandvariability 3 Variability Variabilityistheresultofchangesintheconditionsunderwhichobservationsaremade Variabilitycancomeaboutduetochangesinmaterialqualitymachinesettingsorconditionsmanpowerstandardsmethodsofprocessingmeasurementmilieu environment 4 Population Sample PopulationtheentiresetofmeasurementsofinterestSampleasubsetofdatafromthepopulationParametersnumericalmeasuresofapopulationStatisticsnumericalmeasuresofasample 5 ParametervsStatistic ParameterStatisticMeanVarianceStandardDeviation 6 Typeofdata Gappiness Whethertherearegapsbetweensuccessivelyobservedvaluesofavariable DiscreteVariablegapsexistbetweenobservationsobtainedbycountingContinuousVariablenogapsexistbetweenobservationsobtainedbymeasuring 7 Statistics Objectives Statisticsisthebranchofsciencethatdealswiththecollection presentation analysis interpretationofdataforthepurposeofdecision makingandproblem solving ObjectivesofStatistics datareduction DescriptiveStatisticsinferentialmeasurement InferentialStatisticsidentificationofrelationships Regression ANOVA 8 Statistics Overview 9 Descriptive InferentialStatistics DescriptiveStatisticscomprisesthosemethodsconcernedwithcollectinganddescribingasetofdatasoastoyieldmeaninginformationInferentialStatisticscomprisesthosemethodsconcernedwiththeanalysisofasubsetofdataleadingtopredictionsorinferencesabouttheentiresetofdata 10 DescriptiveStatistics Overview 11 NumericalMeasures Describesthecharacteristicsofthedataset Keynumericalmeasures measuresoflocation centraltendency measuresofdispersion variation measuresofshape distribution 12 MeasureofLocation Mean willnotbediscussed Median willnotbediscussed Mode willnotbediscussed Quartiles 13 Quartiles Whenanorderedsetofdataisdividedintofourequalparts thedivisionpointsarecalledquartiles ThefirstorlowerquartileQ1isavaluethathasapproximately25 oftheobservationsbelowinvalue ThesecondquartileQ2isavaluethathasapproximately50 oftheobservationsbelowinvalue Itisalsocalledthemedian ThethirdorupperquartileQ3isavaluethathasapproximately75 oftheobservationsbelowinvalue 14 Quartiles Twentyorderedobservationsonthetimestofailure inhours ofelectricalinsulationmaterialareshownbelow 2042282523003244446247208169121176129613921488151225202856319235283710 15 MeasureofDispersion Range Willnotbediscussed Variance Willnotbediscussed StandardDeviation Willnotbediscussed Inter QuartileRange 16 Inter quartilerange Theinter quartilerangeisanothermeasureofdispersion IQR Q3 Q1Theinter quartilerangeislesssensitivetoextremevaluesinasamplethantherange Forthetwosamples 1 3 5 8 9and1 5 5 5 9 theirinter quartilerangesare5and0respectively 17 MeasureofShape Skewness SkewnessThedegreeofassymmetryofadistributionarounditsmeanisreferredtoasitsskewness 18 MeasureofShape Kurtosis KurtosisKurtosischaracterizestherelativepeakednessorflatnessofadistributioncomparedtoanormal mesokurtic distribution 19 MiniTab sDescriptiveStatistics Stat BasicStatistics DisplayDescriptiveStatisticsproducesstatisticsforeachcolumnofdata orsubsetswithinacolumn anddisplaysthemintheSessionWindowandoptionallyinagraphtheuserhasnocontroloverwhichstatisticsarecomputed displayedStat BasicStatistics StoreDescriptiveStatisticsdescriptivestatisticsforeachcolumn orsubsetswithinacolumn aredisplayedinadjacentcolumnswithintheWorksheettheusercanselectwhichstatisticsaretobecomputed displayed buthasnocontrolovertheorderinwhichtheyaredisplayedInstructorwillshowyouthemethodofusingMinitab 20 GraphicalPresentation Visualinterpretationthethedataset Commongraphicaltoolstoillustrateadataset DotPlotBoxPlotHistogramStem LeafDiagram 21 DotPlot Thedotplotisusefulfordisplayingasmallbodyofdata Thelocationorcentraltendencyinthedatasetanditsspreadordispersionareeasilyidentified Itcanalsobeusedincomparingtwoormoredatasets 22 DotPlot ThepullstrengthofbondingwiresfromtwosuppliersareshownbelowA 16 8516 4017 2116 3516 5217 0416 9617 1516 5916 57B 17 5017 6318 2518 0017 8617 7518 2217 9017 9618 15TheDotPlotrevealsthatwiresfromsupplierAseemstoresultinlowerpullstrength butthevariabilitywithinbothgroupsisaboutthesame 23 Box WhiskersPlot BoxPlot The box displaysthelowerquartile Q1 themedian Q2 theupperquartile Q3 The whiskers extendtotheminimumthemaximumNottobeusedwhensamplesizeislessthan10units Median Maximum Minimum Q 1 Q 3 24 ProcedureformakingBoxPlot 1 Arrangethedatasetinascendingorder 2 Determinetheminimumandmaximum thelowerandupperquartiles themedian andTukey soutliers 3 Drawaboxthatextendsfromthelowerquartiletotheupperquartile themedianisalinedrawnthroughthebox 4 Drawlines orwhiskers thatextendfromtheendsoftheboxa fromQ1toMax Minimum Q1 1 5IQR b fromQ3toMin Maximum Q3 1 5IQR 5 Outliersarerepresentedbyappropriatesymbols 25 Histogram Thehistogram agraphicalpre