2023/1/4HarbinUniversityofCommerce1StatisticsWhatisStatistics?Statisticsisaboutgathering,communicating,analyzingandinterpretingdata.Statisticsisawaytogetinformationfromdata.Statisticsisatoolforcreatingnewunderstandingfromasetofnumbers.

2023/1/4HarbinUniversityofCommerce2DataInthischapterwebeginthestoryby:IntroducingvarioustypesofdataPresentingdataintheformbarcharts,piecharts,frequencylinediagrams,stem-and-leafdisplays,histograms,frequencydensitypolygonsandcurves.InformationandDataStatisticsisallaboutgathering,communicating,analyzingandinterpretinginformation.Theinformationisobtainedfromvarioussources,andinitsbasicformitiscalleddata.Theretwodistincttypesofdata,whicharequalitativeandquantitative.PayPlay2023/1/4HarbinUniversityofCommerce3Qualitativedata

Qualitativeinformation,asthetermsuggests,isdescriptiveinformation.Itmaybeexpressedasaproperty,orintermsofcategories,orasaqualityforexample:color,gender,nationality,style,…Wherethecategoriesarewelldefinedanddistinct,theinformationmaybedescribedasdiscrete.Forinstance,themakeofacalculatorfallsintoexactlyoneofthefollowingcategories:Canon,Casio,Sharp,Texas,HewlettPackard,other.ThereisnoinherentreasonwhyCasioshouldalwaysprecede–orindeedshouldneverfollow–Texas.Thereisnonaturalhierarchy,noinbuiltorderwithinthesecategories.

Play2023/1/4HarbinUniversityofCommerce4QuantitativedataI

Informationthathasanaturalhierarchy,suchasdatainnumericalmaybedescribedasquantitative.Suchnumericalinformationmaybeseparatedintocontinuousdataanddiscretedata.Whenmeasurementsaremade,thedatagatheredaregenerallycontinuoussinceallvalueswithinaparticularspanarepossible.Anexampleofthisisthelengthofaperson’sstride,whichmightbeanylengthbetween,say,0.3mand1.3m.

Play2023/1/4HarbinUniversityofCommerce5QuantitativedataII

Discretedataareusuallyobtainedbycounting.Forexample,thenumberoflettersdelivereddailytoahousemightbe0,1,2,3,4,5,…oranyotherintegerbutitcannotbeanyothersortofnumber.Discretedatamayalsoarisewhenthereisanorderintheinformation,suchasthesizesavailableinsomeclothes–large,mediumorsmall.

ManybrandsofT-shirtsareavailableinfivesizes:XL,L,M,SandXS;thesesizesarediscretedata.Britishshoesizesarenumberedas:……Asize8shoeisdesignedtofitafootoflengthLincheswhere.

Play2023/1/4HarbinUniversityofCommerce6TypesofdataCategoriesthefollowinginformationinto:Qualitativedata.Discretedata.Continuousnumericaldata.heightofstudentsareaofnoticeboardstypeoffootwearageofteacherscolorofflowersmakeofcarnumberofopenwindowsinaroomnumberofitemsofjewelleryworn2023/1/4HarbinUniversityofCommerce7LimitsAgeWhenaskedherage,astudentsaid,“I’m17yearsold.”Doseshemeanthatsheisprecisely17?Or,isshe17tothenearestwholeyears?Or,doseshemeansomethingelse?Thewayinwhichagesrecordedmeansthat,ifthisstudent’sageisx,then.Thestudentwillhavegivenherageas17fromthedayofher17thbirthday(i.e.thedayprecisely17completeyearssinceshewasborn)uptothedaybeforeher18thbirthday.Play2023/1/4HarbinUniversityofCommerce8

NearestMeasurementsarefrequentlyrecorded‘tothenearestcm’,or‘tothenearestkg’,or‘tothenearestminute’.Thelengthofapencilthatisactually12.6cmlongwouldberecordedas13cmtothenearestcm,andoneofactuallength12.49cmwouldberecordedas12cmtothenearestcm.Pencilsforwhichthelengthsarerecordedas12cmcouldhavealength,pcm,where.Frequency(1)Whencollectinginformation,forinstancethecolorofcarsinacarpark,therewillberepeatedexamplesofparticularcolors.Theremaybefouryellowcars,13redcars,eightbluecarsand20carsofothercolors.Theinformationisqualitative.Thenumberofcarsofeachcoloristhefrequencyofobservationofthatitemofinformation.PlayPlay2023/1/4HarbinUniversityofCommerce9Frequency(2)Inevitableingatheringanyinformationtherewillbeacollectionoffrequenciesassociatedwithitemsofdata.Thefrequenciesarenotonlythedata,theytellussomethingaboutthedistributionofthedata.Presentationofdata(1)Qualitativedatamaybepresentedinafrequencytablesuchastheonebelow.ColorofcarNumberofcarsobservedyellow413820redblueothersPlay2023/1/4HarbinUniversityofCommerce10Presentationofdata(2)Apictorialpresentationmaymakethedatainterpret.Ablockgraph,orbarchartisshownontheleft.Theheightofacolumnisproportionaltothefrequencyofseparatequalityitrepresents.YYellowRRedBBlueOOthercolorOOthercolorRRedBBlueYYellowEachcolumnshouldhavethesamewidth,theaxesshouldbelabeledbutthereisnoneedtopresentthedataintheordergiven.Itwouldbeequallyacceptabletopresentthesedataasshownontheleft,here.2023/1/4HarbinUniversityofCommerce11Presentationofdata(3)Apiechartisanothereffectivewayofdisplayingdataofthisnature.Acircleisdividedintosectors,theanglesofwhichareproportionaltothefrequencyofthequalityrepresented.Inthiscasetheanglesareasshownontheright.YYellowRRedBBlueOOthercolorNotethatsomeonelookingatthepiechartislikelytothinkthattheareaofthesectorrepresentsthefrequencyofobservationofthequalityconcerned,ratherthantheangle.Isthisafairrepresentation?Why?2023/1/4HarbinUniversityofCommerce12Presentationofdata(4)Discretedatamayalsobedisplayedinafrequencylinediagram.Considerthefollowingdatawherethenumberofpeopleinahouseholdwasrecorderforallthe93housesinanestate.NumberofhouseholdFrequency12345678183321154101Thefrequencylinediagramforthesedataisshownonthetop.Isthisanappropriatedisplayfordiscretedata?2023/1/4HarbinUniversityofCommerce13Presentationofdata(5)Itissometimesnecessarytogroupdiscretedata,orperhaps,thedatamayalreadybeavailableinagroupedfrequencytable.Dataconcerningthenumberofbedroomsavailableinguesthousesandhotelsinaseasideresortcanbeshowninthegroupedfrequencytable

below.NumberofbedroomsFrequency1-56-1011-1516-2021-2526-3031-3536-40>404221128431102023/1/4HarbinUniversityofCommerce14Vocabulary(1)interpretvt.解釋?zhuān)焕斫?；體現(xiàn)；口譯;vi.作解釋?zhuān)蛔骺谧g.[in’t?:prit]distinctadj.不同(different)，明顯.[dis’ti?kt]qualitativeadj.定性.[‘kw?lit?tiv]quantitativeadj.定量.[‘kw?ntit?tiv]discreteadj.離散.[dis’kri:t]inherentadj.固有，內(nèi)在；天生.[in’hi?r?nt]hierarchyn.分層，層次；等級(jí)制度；統(tǒng)治集團(tuán).[‘hai?rɑ:ki]inevitableadj.不可避免,必然發(fā)生.[in’evit?bl]observev.觀(guān)察，研究；遵守.[?b’z?:v]pictorialadj.繪畫(huà)的；有圖片的；圖畫(huà)似的；形象化的n.畫(huà)報(bào)；畫(huà)刊；畫(huà)頁(yè).[p?k’t?:ri:?l]proportionaladj.比例的，成比例的；相稱(chēng)的，均衡的n.[數(shù)]比例項(xiàng)，比例量.[pr?’p?:??n?l]tabulationn.作表，表格；表列結(jié)果；列表；造表[,t?bju’le??n]questionnaire

n.調(diào)查表,調(diào)查問(wèn)卷.[,kwesti?’n??]characteristic

adj.特有,獨(dú)特;n.特性,特征,特色[,k?rikt?’ristik]illustratev.表明,說(shuō)明.[‘il?streit]

censusn.調(diào)查,統(tǒng)計(jì),人口普查.[‘sens?s]

2023/1/4HarbinUniversityofCommerce15Vocabulary(2)surveyn.,v.調(diào)查,測(cè)量.[‘s?r,ve?]quantitativeadj.定量.[‘kw?ntit?tiv]discreteadj.離散.[dis’kri:t]inherentadj.固有，內(nèi)在；天生.[in’hi?r?nt]hierarchyn.分層，層次；等級(jí)制度；統(tǒng)治集團(tuán).[‘hai?rɑ:ki]inevitableadj.不可避免,必然發(fā)生.[in’evit?bl]observev.觀(guān)察，研究；遵守.[?b’z?:v]pictorialadj.繪畫(huà)的；有圖片的；圖畫(huà)似的；形象化的n.畫(huà)報(bào)；畫(huà)刊；畫(huà)頁(yè).[p?k’t?:ri:?l]proportionaladj.比例的，成比例的；相稱(chēng)的，均衡的n.[數(shù)]比例項(xiàng)，比例量.[pr?’p?:??n?l]tabulationn.作表，表格；表列結(jié)果；列表；造表[,t?bju’le??n]

2023/1/4HarbinUniversityofCommerce16Vocabulary(3)asthetermsuggests:顧名思義presentingdata:表達(dá)數(shù)據(jù)barcharts:條形圖;piecharts:餅圖;frequencylinediagrams:頻數(shù)線(xiàn)型圖;stem-and-leafdisplays:莖葉圖;Histograms:直方圖;frequencydensitypolygonsandcurves:頻率密度多邊形和曲線(xiàn);Canon,Casio,Sharp,Texas,HewlettPackard：佳能,卡西歐,夏普,得克薩斯州,惠普i.e.

即；也就是[=idest]centimeter[‘senti,mi:t?]CMKilogram[‘k?l?ɡr?m]KG2023/1/4HarbinUniversityofCommerce17Exercise(1)1.Ahotelmanagerusedaquestionnairetoaskdinershowtheyratetheatmosphere,service,foodquantity,foodqualityandpricesinthehotel’srestaurant.Eachcharacteristicisratedonthescale:Outstanding(O),Verygood(V),Average(A),Poor(P).Thefollowingaretheratingsforfoodqualityawardedbyrandomsampleof60diners.GOVVOVOVGGVOPOPVVOGGVAGOVOGOOOGAVVAVVGVGVGAAGAPAAGAOVVGGAVVSummariesthesedatainanappropriatetable.Whatconclusionscanyoudrawabouttheapparentqualityofthefoodintherestaurant?Illustratethedataindiagram.2023/1/4HarbinUniversityofCommerce18Exercise(2)2.Acensusofthehouseholdsinavillageresultsinthefollowingfamilysizesbeingrecorded.34534224343653445213214431213241354345621563425121314453421343144543223424221343561423232112352Constructanappropriatetabulationofthesedataanddescribewhattheyreveal.Illustratethedataindiagram.3.Inasurveyintoviewinghabits,50TVownerswereaskedtonamethechannelwhichtheyhadwatchedforthemajorityoftimeonthepreviousevening.Theresultareshowninthistable.(seenextslides)2023/1/4HarbinUniversityofCommerce19Exercise(3)ChannelFrequencyBBC1BBC2ITVChannel4Satellite1761935Drawadiagramtoillustratethisinformationintheupperleft.Thissurveyhadalsobeendonepreviouslywiththesame50viewerstwoyearsago,whentheresultswereasshownintheupperrighttable.b)Drawadiagramtorepresentthisdata.Compareandcontrastthetwosetofresults.ChannelFrequencyBBC1BBC2ITVChannel4Satellit1/4HarbinUniversityofCommerce20Exercise(4)4.Statewhetherthefollowingdataarediscreteorcontinuous.thedailyrainfallataparticularlocationthemonthlynumbersoftelephonecallsthenumbersofdefectivefusesproducedthedurationoflong-distancetelephonecallstheagesofstudentsinaclass5.Classifythefollowingasqualitativeorquantitative,anddiscreteorcontinuous.gender(M/F)b)height(cm)examinationmarkinstatistics(%)GCSE(GeneralCertificateofSecondaryEducation)gradesinstatistics(AtoG)blousesize(8to18)f)carowner(0=no,1=yes)weeklyself-studytime(%of30hournorm)2023/1/4HarbinUniversityofCommerce21Exercise(5)Mandywasaskedbyhermathteachertodoastatisticsproject.Sherepresentedherschoolathockey,soshedecidedtorecordthenumberofgoalsscoredpermatchbyherteamoveraseasonof35matches.Sherecordedherresultinthistable.Numberofgoals01234Numberofmatches1213721Displaythedatainanappropriatediagram.DosethistellyouanythingabouthowsuccessfulMandy’steamwas?2023/1/4HarbinUniversityofCommerce22Stem-and-LeafDisplaysAmethodofpresentingdata,usingtheitemsofdatathemselves,whichprovidesaswiftandconvenientwayofcollecting,storinganddisplayingnumericaldataisknowsasstem-andleafdisplay.Supposetheitemsofdataare:274,286,345,402,193,237,318Eachitemhasamostsignificantpartandanextmostsignificantpart.Forinstance,themostsignificantpartof274maybethe2sinceitrepresents200,thenthenextmostsignificantpartis7.Thestemofthestem-andleafdisplaysconstructedfromthesesignificantparts.Thestemactsasaverticalscale,sofortheabovedata,thestemwouldbeshownlikethis(seenext).2023/1/4HarbinUniversityofCommerce231234stemThennextmostsignificantpartoftheitemofdataesaleafalonganappropriatebranchofthedisplay.12347alongthebranchdefinedbythe2inthestem.Thecollectionofsevenitemsofdatacouldberepresentedbythestem-and-leafdisplay.leaffromtheitem274123497408132023/1/4HarbinUniversityofCommerce24Onlythemostsignificantandnext-most-significantpastsofdataarestoredinthedisplay.Noattemptismadetoroundthedata,thepresentationisdonebytruncatingtheitems,the4of274islost.Thus,the2-branchwouldcontainanyitemintherange200to299.Truncationisfeatureofthismethodofpresentingdata.UnitAtthisstage,thereisnoindicationofthemagnitudeofdisplayeddata.Toremedythisitisnecessarytoindicatetheunitofdisplay.Unitis1012349740813Inthiscase,theunitis10becauseafactorof10isneededtoscaleadisplayeditemsuchas27toitsturnmagnitude.GroupedfrequencytablesAstem-and-displaycanbeusedtobuildupafrequencytable.Thenumberofleavesonanybranchrepresentsthefrequencyofoccurrenceoftheitemsofdata.2023/1/4HarbinUniversityofCommerce25Developingthestem-and-leafdisplaySupposetheitemsofdataare:

894,947,904,933,906,920,916,941,899,925,935,924,947,937,916,909Thedataoftheaboveexplorationmaybedisplayedusingaunitof10,likethis（Unitis10）．899940302142324310However,itisalsopossibletoconsiderthemostsignificantpartofthedataitem894to89,thentheleafpartwouldbe4.Doingthistoallthedataleadstothefollowingdisplay.Unitis18990919293944460379665519477Thiscreateasomewhatdifferentimpressionofthedistributionofthedata.Whichisthemoreappropriate?2023/1/4HarbinUniversityofCommerce26Two-partstemConsiderthedatashowninthefollowingstem-and-leafdisplay(unitis1).0437067310823733111518322Thedataspantherange0to20andchoosingadifferent‘mostsignificantpart’isnotrealistic.However,itispossibletospliteachstemintotwoequalparts–lowerandupper–denotedby‘-’and‘+’respectively.Thenthetwo-partstemdisplayofthedatalookslikethis.0-430310233310+767871-1131+582-2Notethatthelowerpartcontainthe0,1,2,3,4leavesandupperpartcontainsthe5,6,7,8,9leaves.Thesamedecayisstillseeninthedistributionofthedata.Usingatwo-partstemisratherliketakingamagnifyingglasstothedata.2023/1/4HarbinUniversityofCommerce27Five-partstem0.9,1.7,2.7,3.1,3.4,4,2,4.8,5.7,5.6,6.3,6.2,6.9,7.4,7.3,8.4,8.7,9.8,10.9,11.5,13,2,15.4Hereisonepossiblestem-and-leafdisplay.Unitis0.10917273144285766329743847981091151213214154Onoccasionwemaywanttotightenupthewidthvaluesofthedataasshownbyasimplestem-and-leafdisplay.Considerthefollowingdata.Itisrathersparse,perhapshintingatadegreeofsymmetryinthedataorperhapssuggestingthatthedataareevenlydistributed.Telescopingthedisplaymayhelpingaininganappropriateviewofdata.Thisisachievedbycombiningpairsofstem