Chapter5Statisticalindexnumber.ppt

StatisticsinPractice,STAT,StatisticsinPracticeCoupleofyearsago,afilmcalledDontbothermeafterdivorcedbecamequitefamous,bothwiththetopicandacting.InJan.2003,therewasanewsonthesocialnewspageofanewspaper,whichtitledStillgettoyouafterdivorced.Thenewswasabouttherisingfeeofasingle-parentchildreninadivorcefamily.Inthenews,Mr.FuandMs.ZhangdivorcedinNov.1986.Afterthedivorce,thechildwastolivewiththemother.Thefatherwasjudgedtopayaalimonyof17Yuaneverymonth.Butafterwards,becauseoftheinflation,thelifeoftheplaintiffgetsharder.Hencethrough4suitsin1990,1994,1995and1996,thealimonywasrisento30,50,70and90Yuan.Fromastatisticalpointofview,whatmethoddidthejudgeusedwhenredeterminingthealimony?,StatisticsinPractice,STAT,Today,notonlyalimonyfordivorcedcouples,butalsopensionfortheretired;thedeterminationofcorruption;thestandardofsocialsecuritysubsidy;thestartingpointofpersonalincometaxandthepaymentofdebtsareusingthemethodsofindexation.Throughthelearningofthischapter,wecanunderstandthemeaningandthecalculationofstatisticalindices,andthewayofexplainingthequantitieschangesineconomicproblemswiththemethodofindexanalysis.,Chapter5Statisticalindex,STAT,Keypoints1.Theconceptsandtypesofindexnumbers（P723）;2.Thecompilingofindexnumbers;3.Theindexsystemsandfactoranalysis;4.Someindexnumbersinpractice。Difficulties1.Theprinciplesinthemakingqualitativeindex（质量指标指数）andquantitativeindex（数量指标指数）;2.Thedifferencebetweenaggregativeindexnumber（总指数）,meanindex（平均数指数）andindexnumbersofaverageindicator（平均指标指数）.,Chapter5Statisticalindex,STAT,Section1Theconceptsandtypesofindex1.Theconceptsofindexnumbers（P723）1)Theoriginofindexnumber:AstatisticalanalysismethodfirstdevelopedbyanEnglishmannamedRiceVoughanin1650.Example17091710Breadprice：1penny/piece1.21.2/1=120%2)Indexnumberinbroadsense（广义指数）:Therelativenumbersthatshowsthenumericchangesofphenomenon.(1)Initially“Dynamicchange”;(2)Afterwards“Spacechange”；ABPopulation(2005)10080100/80=125%,Chapter5Statisticalindex,STAT,3)Indexnumberinnarrowsense:Therelativenumbersthatshowsthenumericchangesofthepopulationofcomplexphenomenon.Salesofastore：Q0(2003)Q1(2004)TV(set)12000150001.5/1.2=125%Slipper(pair)50000400004/5=80%Robust(bottle)20000030000030/20=150%(1)QuantityIndicator(sales)(2)Changes:BaseperiodReportperiod;(3)RelativenumberDevelopmentspeed:Toreflectthedirectionanddegreeofthenumericchangesofphenomenon.,Chapter5Statisticalindex,STAT,2.Typesofindexnumbers1)Basedontherange(1)IndividualIndex（个体指数）,Chapter5Statisticalindex,STAT,(2)Totalindexnumber（总体指数总指数）,(3)Classindexnumber（类指数）Populationofatypeofphenomenon,Chapter5Statisticalindex,STAT,2)Basedonthetypeofindicator(1)Quantitativeindex（数量指标指数）q,(2)Qualitativeindex（质量指标指数）p,3)Basedonthedifferenttimeandstatus.(1)Dynamicindex（动态指数）Developmentspeed;(2)Staticindex（静态指数）PChina/PU.S=4Yuan/dollar=PPP.4)Basedonthecalculationmethod,TotalindexnumberAggregateindexnumber（综合指数）,meanindexnumber（平均数指数）.,Chapter5Statisticalindex,STAT,Section2Aggregateindexnumbers1.Definition:Firstaggregate,thencompareTotalindexnumber.2.Making(P723)1)Totalchangeindexnumber（总变动指数）;2)Quantitativeindex（数量指标指数）;3)Qualitativeindex（质量指标指数）;Example3kindofitemsinasupermarket.,Chapter5Statisticalindex,STAT,(1)Thetotaldegreeandthesumofchangeofsalesofthesethreegoods;AnalysisChangeofthesalesof1item:p0q0p1q1；Changeofthesalesof3items:p0q0p1q1；,Chapter5Statisticalindex,STAT,3.Totalchangeindexnumber（总变动指数）,Method:Firstaggregate,thencompareAggregativeindexnumber（compositeindex，综合指数）.,Chapter5Statisticalindex,STAT,(2)Calculatethedegreeofchangesofsalequantityforthe3goodsandthesuminfluencedbythosechanges.AnalysisSales(pq)=Salequantity(q)saleprice(p)Thechangeofsalequantityforthe3goods:q0q1;,Chapter5Statisticalindex,STAT,4.QuantitativeIndex(P736),Unifyingfactor（同度量因素）:Themediumfactorthattransferthedifferentmeasurementunitsintoasamemeasurementunit.,Chapter5Statisticalindex,STAT,Indexationfactor:Thechangingfactor,Unifyingfactor:Theconstantfactor,Chapter5Statisticalindex,STAT,Question:Inthetwoindices,whichonecanbetter(morepurely)reflectthechangeofsalequantity?,Theprincipleofmakingquantitativeindex:UseLaspeyresindex（“数拉基”）.,Chapter5Statisticalindex,STAT,(3)Calculatethedegreeofchangesofsalepricesforthe3goodsandthesuminfluencedbythosechanges.AnalysisThechangeofthepriceofanitem:p0p1；Theoverallchangeofpricesof3items:p0p1；,Chapter5Statisticalindex,STAT,5.QualitativeIndex(P725),Chapter5Statisticalindex,STAT,Price:Therealeconomicmeaningiswhatpeopleareconcernedwith.1Thisyear,0Lastyear.Ifcov（p，q）0，LP.Theprincipleofmakingqualitativeindex:UsePaascheindex.,Chapter5Statisticalindex,STAT,6.Aggregativeindexnumbersystem1)Indexnumbersystem:Thesystemthatwasconsistedof3ormoreindices,whichareeconomicallyandnumericallyrelated.(1)EconomicallyrelatedSales=Salequantitysaleprice(pq)Industrialproduct=OutputPrice(qp)Cropyield=YieldperareaPlantingarea(2)Numericallyrelated,Chapter5Statisticalindex,STAT,2)Factoranalysis,(1)Thesalequantityof3goodshaverisen15.88%inthereportperiodcomparingtothebaseperiod.Thiscausedthesalestorise27.75thousandyuan.Salequantityfactoranalysis;(2)Thesalepricesof3goodshavedropped16.05%.Thiscausedthesalestodrop32.5thousandyuan.Salepricefactoranalysis;(3)Astheresultofthetwofactorscombined,thesalesdropped2.72%,whichtranslatesto4.75thousandyuan.Totalchangeanalysis.,Chapter5Statisticalindex,STAT,3)Usageofindexnumbersystem(1)Factoranalysis;(2)Determinetheperiodforunifyingfactor（数拉基，质派报）;,Chapter5Statisticalindex,STAT,(3)EstimationofunknownindexnumbersExampleInafactory,comparingtothebaseperiod,thenumberofemployeesincreased2%inthereportperiod,andthetotalproductincreased20%.Howdidtheproductivitychanged?Solution:FindoutrelationsbetweenindicatorsIndustrialproduct=NumberofemployeesProductivitySymbolize:pq=qp,Chapter5Statisticalindex,STAT,Section3Meanindexnumber1.Theproblemsofaggregativeindexnumber,1)Obtainingthedata:p1q1;p0q0;p0q1.2)Theeffortneededtocalculateandobtainthedataismassive.2.Theconceptsofmeanindexnumber（平均数指数）1)Definition:UsingthemethodofmeanTotalindex2)Types(1)Meanindexnumbersthatwastransformedfromaggregativeindexnumber（综合指数变形的平均数指数）(2)Independent(fixedweights)meanindexnumbers,Chapter5Statisticalindex,STAT,3.Meanindexthatwastransformedfromaggregativeindexnumber,1)Totalindexofsales(Indexnumberoftotalchanges),Chapter5Statisticalindex,STAT,2)Totalindexofsalequantity(Quantitativeindex),Weightedarithmeticmeanindexnumbers（加权算术平均数指数）thatwastransformedfromaggregativeindexnumber,Chapter5Statisticalindex,STAT,3)Totalindexofsaleprice(Qualitativeindex),Weightedharmonicmeanindexnumbers（加权调和平均数指数）thatwastransformedfromaggregativeindexnumber,Chapter5Statisticalindex,STAT,4)Systemofmeanindexthatwastransformedfromaggregativeindex,Chapter5Statisticalindex,STAT,Section4Indexofmeanindicator1.Definition:Therelativenumbercalculatedbycomparingtheweightedarithmeticmeanoftwoperiods.,Chapter5Statisticalindex,STAT,2.Typesofindexofmeanindicator（平均指标指数）1)Indexofvariableconstruction（可变构成指数，Totalchangeindex）,Chapter5Statisticalindex,STAT,AnalysisBecauseofthechangesinbothaveragemonthlysalaryandemployeestructure,thetotalaveragesalaryhasdropped1.72%,means10Yuanperpersononaverage.,Chapter5Statisticalindex,STAT,2)Fixedstructureindex（固定构成指数，Qualitativeindex）,Chapter5Statisticalindex,STAT,AnalysisIfweruleoutthechangeintheemployeestructure,thenthechangeofaveragemonthlysalarycausedthetotalaveragesalarytorise9.62%,means50Yuanperpersononaverage,andthesalarycoststhefactory50,000Yuanmore.,Chapter5Statisticalindex,STAT,3)Indexofstructureinfluence（结构影响指数，Quantitativeindex）,Chapter5Statisticalindex,STAT,AnalysisIfweruleoutthechangeintheaveragemonthlysalary,thenthechangeofemployeestructurecausedthetotalaveragesalarytodrop10.34%,means60Yuanlessperpersononaverage,andthesalarycoststhefactory60,000Yuanless.,Chapter5Statisticalindex,STAT,4)Thesystemofindexnumbersofmeanindicator,Chapter5Statisticalindex,STAT,AnalysisIfweruleoutthechangeintheaveragemonthlysalary,thenthechangeofemployeestructurecausedthetotalaveragesalarytodrop10.34%,means60yuanlessperpersononaverage.Thecombinedeffectoftwofactorcausedthetotalaveragesalarytodrop1.72%,means10yuanlessperpersononaverage.,Chapter5Statisticalindex,STAT,Section5Multi-factorindexnumbersystem1.ConceptTax=SalesTaxrate=SalequantitySalepriceTaxrateqmp=qmp2.Principles1)Quantitativeindicatorsfirst,qualityindicatorssecond;2)Theproductionoftwoneighboringindicatorsmusthaverealeconomicalmeaning;3)Whenanalyzingtheinfluenceofafactor,keepthefactorsonthebackatthebaseperiod,whilekeepthefactorsonthefrontatthereportperiod（前报后基）.,Chapter5Statisticalindex,STAT,ExampleTax=SalequantitySalepriceTaxrateqmp=qmp,Chapter5Statisticalindex,STAT,Section6Someeconomicalindexinpractice1.Thequestions1)AggregateindexandmeanindexbasedonAggregateindex,requirethoroughdatatomake,whichisquitedifficultinpractice.,2)Thoughtsonimprovement,Chapter5Statisticalindex,STAT,2.RetailPriceIndex（零售价格指数，P729）1)ClassifyingthemerchandisesandpickingtherepresentativesAllmerchandises：Bigclass,Mediumclass,Smallclass,GroupofmerchandisesPickingtherepresentatives。(1)14bigclassesFood;Beverage,tobaccoandalcohol;Clothing;Textiles;Medicine;Cosmetics;Publications;Stationergoods,etc.(2)Food10mediumclassincluding:Grain;Grease;Meatandeggs;Aquaticproducts;Freshvegetable;Driedvegetable;Freshfruits;Driedfruits;Otherfood;Restaurantfood.(3)Grain2smallclass:refinedgrainandcoarsegrain.(4)Refinedgrain4groupsofmerchandises:Flour,rice,stickyrice,finedriednoodles（挂面）.(5)FlourStandardflourrepresentative（标准粉）.,Chapter5Statisticalindex,STAT,2)Acquiringthepricedataandcalculatingtheaverageprice(1)Investigationpoints:35pointsinmajorcities;12pointsinsmallcities;(2)Calculatingthechronologicalaverageoftheprices.3)Theformulasandthesourcesofweights.,Chapter5Statisticalindex,STAT,4)CalculationSteps:IndexoftherepresentativesIndexofGroupsofmerchandisesIndexofthesmallclassesMediumclassesBigclassesTotalindex.,Chapter5Statisticalindex,STAT,(1)Indexnumberofmerchandisegroup,Chapter5Statisticalindex,STAT,(2)Indexnumberofsmallclass(Refinedgrain),Chapter5Statisticalindex,STAT,Exercise1.Theproductofafactoryhasincreased5%fromthebaseperiodtothereportperiod,whilecostforeveryproductreduced5%.Sothetotalcostofthefactoryremainsthesame.()Answer:Wrong.0.25%2.Thedataofamarketisasfollowing(unit:Yuan).Trytofindtheinfluenceofsalequantityandsalepriceonthechangeofsales(salesisroundedtointegers).,Chapter5Statisticalindex,STAT,2.,Chapter5Statisticalindex,STAT,3.Afterthepricesdropped,thesameamountofRMBcanbuy15%moreproducts.Whatsthepriceindex?4.Iftheretailsalesofacityinbaseperiodis86millionYuan.Itincreasedto128.9millionYuaninthereportperiod.Thepriceindexraised15%.Makeafactoranalysisbasedontherenumbers.5.Thetotalcostofaproductis129,000Yuaninthereportperiod,whichis9000Yuanmorethanitcostsinthebaseperiod.Andthecostperunitdecreased3%inthereportperiod.Trytofactoranalyzethefact.,Chapter5Statisticalindex,STAT,4.Iftheretailsalesofacityinbaseperiodis86millio