PHYSICSMATHEMATICSANDASTRONOMYDIVISIONCALIFORNIAINSTITUTEOFTECHNOLOGYFreshmanPhysicsLaboratory(PH003)VadeMecumforDataAnalysisBeginners(September25,2003)Copyrightc⃝VirgíniodeOliveiraSannibale,June,20012AcknowledgmentsIstartedthisworkwiththeaimofimprovingthecourseofPhysicsLab-oratoryforCaltechfreshmenstudents,thesocalledph3course.ThankstoDonaldSkelton,ph3wasalreadyaverygoodcourse,welldesignedtosatisfytheneedsofnewsstudentseagertolearnthebasicsoflaboratorytechniquesanddataanalysis.Becauseoftheneedofintroducingnewexperiments,andnewtopicsinthedataanalysisnotes,Idecidedtorewritethedidacticalmaterialtryingtokeepintactthespiritofthecourse,i.eemphasisontechniquesandnotonthedetailsofthetheory.Anyway,Ibelieveandhopethatthisattempttoreorganizeoldexperi-mentsandintroducenewonesconstitutesanimprovementofthecourse.Iwouldliketothank,inparticular,EugeneW.Cowanforhisincom-mensurablehelphegavetomewithcritiques,suggestions,discussions,andcorrectionstothenotes.HisexperienceasprofessoratCaltechforseveralyearswerereallyvaluabletomakethecontentofthesenotessuit-ableforstudentsatthefirstyearoftheundergraduatecourse.Iwouldliketothankalsoalltheteachingassistantsthatmakethiscoursework,fortheirpatienceandvaluablecommentsthatIconstantlyreceivedduringtheacademicterms.ChristopheBassetdeservesapartic-ularmentionforhiseffortwhichwentbeyondhisassignments.Sincerely,VirgíniodeOliveiraSannibale34Contents1BasicsonErrorAnalysis91.1RandomVariablesandMeasurements.............91.2UncertaintiesonMeasurements.................121.2.1AccuracyandPrecision.................121.3StatisticsandMeasurements...................131.3.1MeasurementandProbabilityDistribution......131.3.1.1GaussianDistributionParameterEstimationforaSingleVariable..............151.3.1.2GaussianDistributionParameterEstimationfortheAverageVariable...........161.3.1.3GaussianDistributionParameterEstimationfortheWeightedAverage...........171.3.2Example(UnweightedAverage)............171.3.3Example(WeightedAverage)..............182ProbabilityDi...
