aac_BasicStatistics&UseofMinitab

BasicStatistics&UseofMinitabBeltonGroupRexWongBeltonConfidential:Fortrainingonly2StatisticsStatisticsisthebranchofsciencethatdealswiththecollection,presentation,analysis&interpretationofdataforthepurposeofdecision-makingandproblem-solving.Statisticsisacriticalskillinqualityimprovementasstatisticaltechniquescanbeusedtodescribeandtounderstandvariability.BeltonConfidential:Fortrainingonly3VariabilityVariabilityistheresultofchangesintheconditionsunderwhichobservationsaremade.Variabilitycancomeaboutduetochangesinmaterialqualitymachinesettingsorconditionsmanpowerstandardsmethodsofprocessingmeasurementmilieu(environment)BeltonConfidential:Fortrainingonly4Population&SamplePopulationtheentiresetofmeasurementsofinterestSampleasubsetofdatafromthepopulationParametersnumericalmeasuresofapopulationStatisticsnumericalmeasuresofasampleBeltonConfidential:Fortrainingonly5ParametervsStatisticParameterStatisticMeanVarianceStandardDeviationx22ssBeltonConfidential:Fortrainingonly6Typeofdata–“Gappiness”Whethertherearegapsbetweensuccessivelyobservedvaluesofavariable.DiscreteVariablegapsexistbetweenobservationsobtainedbycountingContinuousVariablenogapsexistbetweenobservationsobtainedbymeasuringBeltonConfidential:Fortrainingonly7Statistics-ObjectivesStatisticsisthebranchofsciencethatdealswiththecollection,presentation,analysis&interpretationofdataforthepurposeofdecision-makingandproblem-solving.ObjectivesofStatistics:•datareduction—DescriptiveStatistics•inferentialmeasurement—InferentialStatistics•identificationofrelationships—Regression,ANOVABeltonConfidential:Fortrainingonly8Statistics-OverviewStatisticsDescriptiveStatisticsInferentialStatisticsGraphicalPresentationsNumericalMeasuresChartsTablesLocationDispersionShapeParameterEstimationHypothesisTestingPointEstimateIntervalEstimateParametricMethodsNonparametricMethodsBeltonConfidential:Fortrainingonly9Descriptive&InferentialStatisticsDescriptiveStatisticscomprisesthosemethodsconcernedwithcollectinganddescribingasetofdatasoastoyieldmeaninginformationInferentialStatisticscomprisesthosemethodsconcernedwiththeanalysisofasubsetofdataleadingtopredictionsorinferencesabouttheentiresetofdataBeltonConfidential:Fortrainingonly10DescriptiveStatistics-OverviewDescriptiveStatisticsGraphicalPresentationsNumericalMeasuresChartsTablesDotPlotBoxPlotHistogramStem&LeafDiagramBarChartTrendChartFrequencyDistributionLocationDispersionShapeMeanMedianModeQuartilesRangeStandardDeviationVarianceInterquartileRangeSkewnessKurtosisBeltonConfidential:Fortrainingonly11NumericalMeasuresDescribesthecharacteristicsofthedataset.Keynumericalmeasures:measuresoflocation(centraltendency)measuresofdispersion(variation)measuresofshape(distribution)BeltonConfidential:Fortrainingonly12MeasureofLocationMean(willnotbediscussed)Median(willnotbediscussed)Mode(willnotbediscussed)QuartilesBeltonConfidential:Fortrainingonly13QuartilesWhenanorderedsetofdataisdividedintofourequalparts,thedivisionpointsarecalledquartiles.ThefirstorlowerquartileQ1isavaluethathasapproximately25%oftheobservationsbelowinvalue.ThesecondquartileQ2isavaluethathasapproximately50%oftheobservationsbelowinvalue.Itisalsocalledthemedian.ThethirdorupperquartileQ3isavaluethathasapproximately75%oftheobservationsbelowinvalue.BeltonConfidential:Fortrainingonly14QuartilesTwentyorderedobservationsonthetimestofailure(inhours)ofelectricalinsulationmaterialareshownbelow.204228252300324444624720816912117612961392148815122520285631923528371020162252015121044211769123842444324321QQx~QBeltonConfidential:Fortrainingonly15MeasureofDispersionRange(Willnotbediscussed)Variance(Willnotbediscussed)StandardDeviation(Willnotbediscussed)Inter-QuartileRangeBeltonConfidential:Fortrainingonly16Inter-quartilerangeTheinter-quartilerangeisanothermeasureofdispersion.IQR=Q3-Q1Theinter-quartilerangeislesssensitivetoextremevaluesinasamplethantherange.Forthetwosamples(1,3,5,8,9and1,5,5,5,9),theirinter-quartilerangesare5and0respectively.BeltonConfidential:Fortrainingonly17MeasureofShape-SkewnessSkewnessThedegreeofassymmetryofadistributionarounditsmeanisreferredtoasitsskewness.BeltonConfidential:Fortrainingonly18MeasureofShape-KurtosisKurtosisKurtosischaracterizestherelativepeakednessorflatnessofadistributioncomparedtoanormal(mesokurtic)distribution.BeltonConfidential:Fortrainingonly19MiniTab’sDescriptiveStatisticsStatBasicStatisticsDisplayDescriptiveStatisticsproducesstatisticsforeachcolumnofdata(orsubsetswithinacolumn)anddisplaysthemintheSessionWindowandoptionallyinagraphtheuserhasnocontroloverwhichstatisticsarecomputed/displayedStatBasicStatisticsStoreDescriptiveStatisticsdescriptivestatisticsforeachcolumn(orsubsetswithinacolumn)aredisplayedinadjacentcolumnswithintheWorksheettheusercanselectwhichstatisticsaretobecomputed/displayed,buthasnocontrolovertheorderinwhichtheyaredisplayedInstructorwillshowyouthemethodofusingMinitab.BeltonConfidential:Fortrainingonly20GraphicalPresentationVisualinterpretationthethedataset.Com