STATISTICS FOR
V
SCIENTISTS AN
V V
D ENGINEERS
V
,STATISTICS FOR V V
SCIENTISTS AND V V
ENGINEERS
RAMALINGAMVSHANMUGAMVR
AJANVCHATTAMVELLI
,CopyrightV©V2015VbyVJohnVWileyV&VSons,VInc.VAllVrightsVreserved
PublishedVbyVJohnVWileyV&VSons,VInc.,VHoboken,VNewVJers
eyV PublishedVsimultaneouslyVinVCanada
NoVpartVofVthisVpublicationVmayVbeVreproduced,VstoredVinVaVretrievalVsystem,VorVtransmittedVinVanyVf
ormVorV byVanyVmeans,Velectronic,Vmechanical,Vphotocopying,Vrecording,Vscanning,VorVotherwise,Vex
ceptVasV permittedVunderVSectionV107VorV108VofVtheV1976VUnitedVStatesVCopyrightVAct,VwithoutVeit
herVtheVpriorV writtenVpermissionVofVtheVPublisher,VorVauthorizationVthroughVpaymentVofVtheVappropr
iateVper-
copyVfeeVtoV theVCopyrightVClearanceVCenter,VInc.,V222VRosewoodVDrive,VDanvers,VMAV01923,V(97
8)V750-8400,VfaxV (978)V750-
4470,VorVonVtheVwebVatVwww.copyright.com.VRequestsVtoVtheVPublisherVforVpermissionVshouldV beV
addressedVtoVtheVPermissionsVDepartment,VJohnVWileyV&VSons,VInc.,V111VRiverVStreet,VHoboken,V
NJV 07030,V(201)V748-6011,VfaxV(201)V748-6008,VorVonlineVatVhttp://www.wiley.com/go/permission.
LimitVofVLiability/DisclaimerVofVWarranty:VWhileVtheVpublisherVandVauthorVhaveVusedVtheirVbestVeff
ortsVinV preparingVthisVbook,VtheyVmakeVnoVrepresentationsVorVwarrantiesVwithVrespectVtoVtheVaccura
cyVorV completenessVofVtheVcontentsVofVthisVbookVandVspecificallyVdisclaimVanyVimpliedVwarrantiesV
ofV merchantabilityVorVfitnessVforVaVparticularVpurpose.VNoVwarrantyVmayVbeVcreatedVorVextendedVb
yVsalesV representativesVorVwrittenVsalesVmaterials.VTheVadviceVandVstrategiesVcontainedVhereinVmayV
notVbeVsuitableV forVyourVsituation.VYouVshouldVconsultVwithVaVprofessionalVwhereVappropriate.VNeit
herVtheVpublisherVnorV authorVshallVbeVliableVforVanyVlossVofVprofitVorVanyVotherVcommercialVdamage
s,VincludingVbutVnotVlimitedVtoV special,Vincidental,Vconsequential,VorVotherVdamages.
ForVgeneralVinformationVonVourVotherVproductsVandVservicesVorVforVtechnicalVsupport,VpleaseVcontactVou
rV CustomerVCareVDepartmentVwithinVtheVUnitedVStatesVatV(800)V762-
2974,VoutsideVtheVUnitedVStatesVat
(317)V572-3993VorVfaxV(317)V572-4002.
WileyValsoVpublishesVitsVbooksVinVaVvarietyVofVelectronicVformats.VSomeVcontentVthatVappearsVinVpri
ntVmayV notVbeVavailableVinVelectronicVformats.VForVmoreVinformationVaboutVWileyVproducts,VvisitVo
urVwebVsiteVatV www.wiley.com.
LibraryVofVCongressVCataloging-in-PublicationVData:
Shanmugam,VRamalingam.
StatisticsVforVscientistsVandVengineersV/VRamalingamVShanmugam,VRajanVChattamv
elli.V pagesVcm
IncludesVbibliographicalVreferencesVandVindex.V I
SBNV978-1-118-22896-8V(cloth)
1. MathematicalVstatistics.V I.VChattamvelli,VRajan.VII.VTit
le.V QA276.S456V2015
519.5–dc23
2015004898
PrintedVinVtheVUnitedVStatesVofVAmericaV 1 0 9 8 7 6
54321V
1V V 2015
, CONTENTS
Preface xv
AboutVTheVCompanionVWebsite xxi
1 DescriptiveV Statistics 1
1.1 Introduction,V 1
1.2 StatisticsVasVAVScientificVDiscipline,V 3
1.2.1 ScalesVofVMeasurement,V 4
1.3 TheVNOIRVScale,V 6
1.3.1 TheVNominalVScale,V 6
1.3.2 TheVOrdinalVScale,V 6
1.3.3 TheVIntervalVScale,V 7
1.3.4 TheVRatioVScale,V 7
1.4 PopulationVVersusVSample,V 8
1.4.1 ParameterVVersusVStatistic,V 9
1.5 CombinationVNotation,V 11
1.6 SummationVNotation,V 11
1.6.1 NestedVSums,V 12
1.6.2 IncrementVStepVSizes,V 14
1.7 ProductVNotation,V 19
1.7.1 EvaluatingVLargeVPowers,V 20
1.8 RisingVandVFallingVFactorials,V 22
1.9 MomentsVandVCumulants,V 22
1.10 DataVTransformations,V 23
V
SCIENTISTS AN
V V
D ENGINEERS
V
,STATISTICS FOR V V
SCIENTISTS AND V V
ENGINEERS
RAMALINGAMVSHANMUGAMVR
AJANVCHATTAMVELLI
,CopyrightV©V2015VbyVJohnVWileyV&VSons,VInc.VAllVrightsVreserved
PublishedVbyVJohnVWileyV&VSons,VInc.,VHoboken,VNewVJers
eyV PublishedVsimultaneouslyVinVCanada
NoVpartVofVthisVpublicationVmayVbeVreproduced,VstoredVinVaVretrievalVsystem,VorVtransmittedVinVanyVf
ormVorV byVanyVmeans,Velectronic,Vmechanical,Vphotocopying,Vrecording,Vscanning,VorVotherwise,Vex
ceptVasV permittedVunderVSectionV107VorV108VofVtheV1976VUnitedVStatesVCopyrightVAct,VwithoutVeit
herVtheVpriorV writtenVpermissionVofVtheVPublisher,VorVauthorizationVthroughVpaymentVofVtheVappropr
iateVper-
copyVfeeVtoV theVCopyrightVClearanceVCenter,VInc.,V222VRosewoodVDrive,VDanvers,VMAV01923,V(97
8)V750-8400,VfaxV (978)V750-
4470,VorVonVtheVwebVatVwww.copyright.com.VRequestsVtoVtheVPublisherVforVpermissionVshouldV beV
addressedVtoVtheVPermissionsVDepartment,VJohnVWileyV&VSons,VInc.,V111VRiverVStreet,VHoboken,V
NJV 07030,V(201)V748-6011,VfaxV(201)V748-6008,VorVonlineVatVhttp://www.wiley.com/go/permission.
LimitVofVLiability/DisclaimerVofVWarranty:VWhileVtheVpublisherVandVauthorVhaveVusedVtheirVbestVeff
ortsVinV preparingVthisVbook,VtheyVmakeVnoVrepresentationsVorVwarrantiesVwithVrespectVtoVtheVaccura
cyVorV completenessVofVtheVcontentsVofVthisVbookVandVspecificallyVdisclaimVanyVimpliedVwarrantiesV
ofV merchantabilityVorVfitnessVforVaVparticularVpurpose.VNoVwarrantyVmayVbeVcreatedVorVextendedVb
yVsalesV representativesVorVwrittenVsalesVmaterials.VTheVadviceVandVstrategiesVcontainedVhereinVmayV
notVbeVsuitableV forVyourVsituation.VYouVshouldVconsultVwithVaVprofessionalVwhereVappropriate.VNeit
herVtheVpublisherVnorV authorVshallVbeVliableVforVanyVlossVofVprofitVorVanyVotherVcommercialVdamage
s,VincludingVbutVnotVlimitedVtoV special,Vincidental,Vconsequential,VorVotherVdamages.
ForVgeneralVinformationVonVourVotherVproductsVandVservicesVorVforVtechnicalVsupport,VpleaseVcontactVou
rV CustomerVCareVDepartmentVwithinVtheVUnitedVStatesVatV(800)V762-
2974,VoutsideVtheVUnitedVStatesVat
(317)V572-3993VorVfaxV(317)V572-4002.
WileyValsoVpublishesVitsVbooksVinVaVvarietyVofVelectronicVformats.VSomeVcontentVthatVappearsVinVpri
ntVmayV notVbeVavailableVinVelectronicVformats.VForVmoreVinformationVaboutVWileyVproducts,VvisitVo
urVwebVsiteVatV www.wiley.com.
LibraryVofVCongressVCataloging-in-PublicationVData:
Shanmugam,VRamalingam.
StatisticsVforVscientistsVandVengineersV/VRamalingamVShanmugam,VRajanVChattamv
elli.V pagesVcm
IncludesVbibliographicalVreferencesVandVindex.V I
SBNV978-1-118-22896-8V(cloth)
1. MathematicalVstatistics.V I.VChattamvelli,VRajan.VII.VTit
le.V QA276.S456V2015
519.5–dc23
2015004898
PrintedVinVtheVUnitedVStatesVofVAmericaV 1 0 9 8 7 6
54321V
1V V 2015
, CONTENTS
Preface xv
AboutVTheVCompanionVWebsite xxi
1 DescriptiveV Statistics 1
1.1 Introduction,V 1
1.2 StatisticsVasVAVScientificVDiscipline,V 3
1.2.1 ScalesVofVMeasurement,V 4
1.3 TheVNOIRVScale,V 6
1.3.1 TheVNominalVScale,V 6
1.3.2 TheVOrdinalVScale,V 6
1.3.3 TheVIntervalVScale,V 7
1.3.4 TheVRatioVScale,V 7
1.4 PopulationVVersusVSample,V 8
1.4.1 ParameterVVersusVStatistic,V 9
1.5 CombinationVNotation,V 11
1.6 SummationVNotation,V 11
1.6.1 NestedVSums,V 12
1.6.2 IncrementVStepVSizes,V 14
1.7 ProductVNotation,V 19
1.7.1 EvaluatingVLargeVPowers,V 20
1.8 RisingVandVFallingVFactorials,V 22
1.9 MomentsVandVCumulants,V 22
1.10 DataVTransformations,V 23
