95672458 state9 project work statistics pdf may 24 2012-5-25 pm 1 8 meg evozi

7/31/2019 95672458 State9 Project Work Statistics PDF May 24 2012-5-25 Pm 1 8 Meg Evozi

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FORM52012Name:I/CNo.:FormPanel::

CurriculumDevelopmentCentreMinistryOfEducation


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No1

ContentsPART1ImportanceofdataanalysisindailylifeThetypesofMeasureofCentralTendencyandofMeasureofDispersionPART2RawdataFrequencyDistributionTableMeasureofcentraltendencyi)Meanii)Modeiii)MedianPART3MeasureofDispersion-Interquartilerange-StandarddeviationPART4ProblemsolvingREFLECTIONREFERENCES

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PART1ImportanceofdataanalysisindailylifeDataanalysisisaprocessusedtotransform,remodelandrevisecertaininformation(data)withaviewtoreachtoacertainconclusionforagivensituationorproblem.Dataanalysiscanbedonebydifferentmethodsasaccordingtotheneedsandrequirements.Forexampleifaschoolprincipalwantstoknowwhetherthereisarelationshipbetweenstudentsperformanceonthedistrictwritingassessmentandtheirsocioeconomiclevels.Inotherwords,dostudentswhocomefromlowersocioeconomicbackgroundsperformlower,asweareledtobelieve?Orarethereothervariablesresponsibleforthevarianceinwritingperformance?Again,asimplecorrelationanalysiswillhelpdescribethestudentsperformanceandhelpexplaintherelationshipbetweentheissuesofperformanceandsocioeconomiclevel.Analysisdoesnothavetoinvolvecomplexstatistics.Dataanalysisinschoolsinvolvescollectingdataandusingthatdatatoimproveteachingandlearning.Interestingly,principalsandteachershaveitprettyeasy.Inmostcases,thecollectionofdatahasalreadybeendone.Schoolsregularlycollectattendancedata,transcriptrecords,disciplinereferrals,quarterlyorsemestergrades,norm-andcriterion-referencedtestscores,andavarietyofotherusefuldata.Ratherthancomplexstatisticalformulasandtests,itisgenerallysimplecounts,averages,percents,andratesthateducatorsareinterestedin.Therearemanybenefitsofdataanalysishowever;themostimportantonesareasfollows:-dataanalysishelpsinstructuringthefindingsfromdifferentsourcesofdatacollectionlikesurveyresearch.Itisagainveryhelpfulinbreakingamacroproblemintomicroparts.Dataanalysisactslikeafilterwhenitcomestoacquiringmeaningfulinsightsoutofhugedata-set.Everyresearcherhassortouthugepileofdatathathe/shehasco

llected,beforereachingtoaconclusionoftheresearchquestion.Meredatacollectionisofnousetotheresearcher.Dataanalysisprovestobecrucialinthisprocess.Itprovidesameaningfulbasetocriticaldecisions.Ithelpstocreateacompletedissertationproposal.Oneofthemostimportantusesofdataanalysisisthatithelpsinkeepinghumanbiasawayfromresearchconclusionwiththehelpofproperstatisticaltreatment.Withthehelpofdataanalysisaresearchercanfilterbothqualitativeandquantitativedataforanassignmentwritingprojects.Thus,itcanbesaidthatdataanalysisisofutmostimportanceforboththeresearchandtheresearcher.Ortoputitinanotherwordsdataanalysisisasimportanttoaresearcherasitisimportantforadoctortodiagnosetheproblemofthepatientbeforegivinghimanytreatment


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ThetypesofMeasureofCentralTendencyandofMeasureofDispersion.Centraltendencygetsatthetypicalscoreonthevariable,whiledispersiongetsathowmuchvarietythereisinthescores.Whendescribingthescoresonasinglevariable,itiscustomarytoreportonboththecentraltendencyandthedispersion.Notallmeasuresofcentraltendencyandnotallmeasuresofdispersioncanbeusedtodescribethevaluesofcasesoneveryvariable.Whatchoicesyouhavedependonthevariableslevelofmeasurement.MeanThemeaniswhatineverydayconversationiscalledtheaverage.Itiscalculatedbysimplyaddingthevaluesofallthevalidcasestogetheranddividingbythenumberofvalidcases.xfxxorxNfThemeanisaninterval/ratiomeasureofcentraltendency.ItscalculationrequiresthattheattributesofthevariablerepresentanumericscaleModeThemodeistheattributeofavariablethatoccursmostofteninthedataset.

Forungroupdata,wecanfindmodebyfindingthemodalclassanddrawthemodalclassandtwoclassesadjacenttothemodalclass.Twolinesfromtheadjacentwecrossedtofindtheintersection.Theintersectionvalueisknownasthemode.MedianThemedianisameasureofcentraltendency.Itidentifiesthevalueofthemiddlecasewhenthecaseshavebeenplacedinorderorinlinefromlowtohigh.Themiddleofthelineisasfarfrombeingextremeasyoucanget.NF2CmLfm


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Thereareasmanycasesinlineinfrontofthemiddlecaseasbehindthemiddlecase.Themedianistheattributeusedbythatmiddlecase.Whenyouknowthevalueofthemedian,youknowthatatleasthalfthecaseshadthatvalueorahighervalue,whileatleasthalfthecaseshadthatvalueoralowervalue.RangeThedistancebetweentheminimumandthemaximumiscalledtherange.Thelargerthevalueoftherange,themoredispersedthecasesareonthevariable;thesmallerthevalueoftherange,thelessdispersed(themoreconcentrated)thecasesareonthevariableRange=maximumvalueminimumvalueInterquartilerange(IQR)isthedistancebetweenthe75thpercentileandthe25thpercentile.TheIQRisessentiallytherangeofthemiddle50%ofthedata.Becauseitusesthemiddle50%,theIQRisnotaffectedbyoutliersorextremevalues.1NFCQ1L4fmIQR=Q3-Q13NFCQ3L

StandardDeviationThestandarddeviationtellsyoutheapproximateaveragedistanceofcasesfromthemean.Thisiseasiertocomprehendthanthesquareddistanceofcasesfromthemean.Thestandarddeviationisdirectlyrelatedtothevariance.Ifyouknowthevalueofthevariance,youcaneasilyfigureoutthevalueofthestandarddeviation.Thereverseisalsotrue.Ifyouknowthevalueofthestandarddeviation,youcaneasilycalculatethevalueofthevariance.Thestandarddeviationisthesquarerootofthevariancefx22xf


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PART2

1.MarchAdditionalMathematicstestscoresfor30students.Students123456789101112131415161718192021222324252627282930Marks556063657374757576777880818283848486868687888889909090919395


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2.Frequencydistributionstable:Marks55-5960-6465-6970-7475-7980-8485-8990-9495-99Tally||||||||||||||||||||||||||Frequency121256751

a)I)MeanThemeanmarkof30studentscanbefoundbyusingtheformula:

fxfFrequencyf121256751f=30fx571246714438549260946097fx=2435

Marks55-5960-6465-6970-7475-7980-8485-8990-9495-99

Midpoint,x576267727782879297

Fromthetablef=30fx=2435Therefore,mean,

243530=81.1667


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II)ModeThemodalclassis85-89,i.e.,themajorityofthestudentsgotthatmarks.Tofindthemodeweight,wedrawthemodalclassandtwoclassesadjacenttothemodalclass.

Fromthehistogram,themodemarkis86.5

III)MedianMethod1ByusingformulaMedianisthevalueofthecentreofasetofdataMedianweightfor50studentscanbeobtainedbyusingtheformula:NMedian,mL2fmWhereL=lowerboundaryofmedianclass,N=totalF=cumulativefrequencybeforethemedianclass,fm=frequencyofmedianclass,C=classintervalsize.


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Marks55-5960-6465-6970-7475-7980-8485-8990-9495-99

LowerBoundary54.559.564.569.574.579.584.589.594.5

Upperboundary59.564.569.574.579.584.589.594.599.5

Frequencyf121256751f=30

CumulativeFrequency13461117242930

Fromthetable,Medianclass=302=15thvalue=80-84L=79.5F=11fm=6C=69.5-64.5=5TotalfrequencyN=30

30115m79.526m82.8333Method2bydrawinganogiveOgiveOgiveisagraphconstructedbyplottingthecumulativefrequencyofasetofdataagainstthecorrespondingupperboundaryofeachclass.Notonlythat,ogiveisalsothemethodofcalculation,themedian,andtheinterquartilerangeofasetofdatacanalsobeestimatedfromitsogive.


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b)Mean,x=81.2kg

Median,m=82.8333(or82.75)

Mode=86.5

Fromtheabovemeasureofcentraltendency,meanissuitablemeasureofcentraltendencybecausetheminimumvalueofrawdataisnotextremewherethedataseemstobeclustered,whereasmodeandmediandoesnottakeallthevaluesinthedataintoaccountwhichdecreasetheaccuracyofcentraltendency.


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PART3MeasureofDispersionisameasurementtodeterminehowfarthevaluesofdatainasetofdataarespreadoutfromitsaveragevalue.a)I)TheinterquartilerangeMethodIByusingformula1NFCQ1L4fmQ1e=75-59L=74.5fm=5F=6C=5130645Q174.5530

3NFCQ3L4fmQ3class=30x=22.5thvalue=8589L=84.5F=17fm=7C=5N=30

3301745Q384.57Q388.4286

ThereforetheInterquartilerange,Q3Q1=88.428676.0=12.4286


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MethodIIByusingogive

FromtheogiveInterquartilerange=88.576.25=12.25


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II)TheStandarddeviationMethodIMarks55-5960-6465-6970-7475-7980-8485-8990-9495-99Midpoint,x576267727782879297Frequencyf121256751f=30fx571246714438549260946097fx=2435fx232497688448910368296454034452938423209409fx2=200450

243530=81.1667

v

200450281.1667309.6764

MethodIIMarksMidpointx55-595760-646265-696770-747275-797780-848285-898790-949295-9997

Frequencyf121256751f=30

xx-24.1667-19.1667-14.1667-9.1667-4.16670.83335.833310.833315.8333

xx2

584.0294367.3624200.695484.028417.36140.694434.0274117.3604250.6934

fxx

2

584.0294734.7248200.6954168.056886.80694.1663238.1917586.8019250.69342fxx

2854.1666


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fxxf

2

2854.1666309.7539

b)Thestandarddeviationgivesameasureofdispersionofthedataaboutthemean.Adirectanalogywouldbethatoftheinterquartilerange,whichgivesameasureofdispersionaboutthemedian.However,thestandarddeviationisgenerallymoreusefulthantheinterquartilerangeasitincludesalldatainitscalculation.Theinterquartilerangeistotallydependentonjusttwovaluesandignoresalltheotherobservationsinthedata.Thisreducestheaccuracyitextremevalueispresentinthedata.Sincethemarksdoesnotcontainanyextremevalue,standarddeviationgiveabettermeasurescomparedtointerquartilerange.


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PART4a)Iftheteacheradds3marksforeachstudentinclassfortheircommitmentanddisciplineshown,Thenewmarksfor30studentsStudents123456789101112131415161718192021222324252627282930Marks586366687677787879808183848586878789898990919192939393949698


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NewFrequencydistributionstable:fx232493844897802964526896529836771218818fx2=381495

Marks55-5960-6465-6970-7475-7980-8485-8990-9495-99

LowerBoundary54.559.564.569.574.579.584.589.594.5

Midpoint,x576267727782879297

Frequency,f112054782f=30

C.Frequency1244913202830

fx57621340385328609736194fx=2505

2505Newmean,30x83.5xNewmode,Modalclass=9094

NewMode=90.75


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NewMedianMedianclass=80843095m79.524m87.0Classinterval=5NewinterquartilerangeQ1class=30x=7.5thvalue=7579130445Q174.55Q178.0Q2class=30x91.2857ThereforetheInterquartilerange,Q3Q1=91.285778.0=13.2857

3814952Newstandarddeviation,83.53075.7908


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b)Marks55-5960-6465-6970-7475-7980-8485-8990-9495-99LowerBoundary54.559.564.569.574.579.584.589.594.5Midpoint,x576267727782879297Frequency,f112054783f=31C.Frequency1244913202831fx57621340385328609736291fx=2602fx2324938448978029645268965298367712282272fx=390904

2602Newmean,31x83.9355x3909042Newstandarddeviation,83.93553174.5965Mode,median,andinterquartilerangearenotaffectedbytheaddingfornewmarks.


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REFLECTION


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REFERENCESwww.worldteacherspress.comwww.heartscan.com.mywww.tips.com.my/article.phphttp://nutriweb.org.myhttp://geminigeek.com/blog/archives/2004/08/addmath-project-tips-1http://www.sagepub.com/upm-data/43350_4.pdfBlogAForm4SasbadibyPuaKimTeckPrestonAdditionalMathematicsForm4&5referencebookbyTanLiLanFokusUnguMatematikTambahanForm4&5byWongTeckSingAdditionalMathematicsForm4TextBook.MathematicsForm4TextBook.


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ADDITIONALMATHEMATICSPROJECTWORKFORFORM52012

Vision2020aimstoproduceabalancedhumancapitalintermsofphysical,emotional,spiritualandintellectualinaccordancewiththeNationalEducationPhilosophy.Inordertoexpandtheintellectualaspect,everyindividualshouldhavetheabilitytoanalyzedata.Thepictureaboveshowsstudentsinasecondaryschoolhavingtheirfinalyearexamination.TheSchoolExaminationsecretarywillcollectthemarksforeachsubjectstodeterminetheaveragegradeofthesubjects,theaveragegradeschoolandwhichwillgivethepictureoftheperformanceoftheschool.Datarepresentationreflectsthegeneralcharacteristicsofdatathatallowsustocompareandthuspredictandplanforthefuture.PART1:1.Listtheimportanceofdataanalysisindailylife.2.SpecifythetypesofMeasureofCentralTendencyandofMeasureofDispersion.


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PART2:1.GettheMarchAdditionalMathematicstestscoresforyourclass.Attachthescoressheet.2.ConstructafrequencytableasinTable1whichcontainsatleastfiveclassintervals.Chooseasuitableclasssize.

Marks

Tally

Frequency

Table1.a)FromTable1,find(i)(ii)(iii)themean,themode,themedianusingtwomethods.

b)Basedonyourfindingsfrom(a)above,statetheappropriatemeasureofcentraltendencytoreflecttheperformanceofyourclassinAdditionalMathematics.Explainwhy.PART3:MeasureofDispersionisameasurementtodeterminehowfarthevaluesofdatainasetofdataisspreadoutfromitsaveragevalue.BasedonthedatafromTable1,a)usingtwomethods,find(i)theinterquartilerange(ii)thestandarddeviationb)Explaintheadvantagesofusingstandarddeviationcomparedtointerquartilerangetodescribethedata.


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PART4:a.Ifyourteacherwantstomakeadjustmentsbyadding3marksforeachstudentinyourclassfortheircommitmentanddisciplineshown,findthenewvalueofmean,mode,median,classinterval,interquartilerangeandstandarddeviation.Checkyouranswerswithothermethods.b.InApril2012,anewstudenthasenrolledinyourclass.Thestudenthasscored97%intheAdditionalMathematicsMarchTestinhis/herformerschool.IfthestudentscoresweretakenintoaccountintheanalysisofyourschoolMarchTest,statetheeffectofthepresenceofthisstudenttothemean,mode,median,interquartilerangeandstandarddeviation.REFLECTIONWhatmoralvaluesdidyouputintopracticewhenconductingthisproject?PrepareacardaccordingtoyourcreativitystatingyoureffortstoincreaseormaintaintheexcellentresultforAdditionalMathematicsinSPM2012.


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GuidelinesfortheImplementationofAdditionalMathematicsProjectWorkForm4andForm52007(Students Edition)1.EverystudenttakingAdditionalMathematicsisrequiredtocarryouttwoprojectworks,oneinForm4andanotheroneinForm5.2.Theaimsofcarryingoutprojectworkare:i.toapplyandadaptavarietyofproblem-solvingstrategiestosolveproblems;ii.toimprovethinkingskills;iii.topromoteeffectivemathematicalcommunication;iv.todevelopmathematicalknowledgethroughproblemsolvingjnawaythatincreasesstudents interestandconfidence;v.tousethelanguageofmathematicstoexpressmathematicalideasprecisely;vi.toprovidelearningenvironmentthatstimulatesandenhanceseffectivelearning;vii.todeveloppositiveattitudetowardsmathematics.3.Projectworkcanbedoneingroupsorindividuallybuteachstudentisexpectedtosubmitanindividuallywrittenreportwhichincludesthefollowings:ReportPresentation:-GeneralAspect-IntroductionTaskSpecification-SpecifythetaskProblemSolving-ProcedureFindings-ExplorationConclusion/Generalisation:

4.Studentsaregiventhreeweekstocarryouteachprojectwork.Thewrittenre

portmustbesubmittedbytheendofthethirdweek.


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RubricforAdditionalMathematicsProjectWork2012Name:..Form4/5RangeofmarksMarkAwardedSubtotal

AppropriatetitleA1.GeneralContentspageAspect(6%)SystematicpresentationCreativityComprehensiveintroduction-mayincludeA2.Introductionhistory/moral/valuesandotherinformationrelevanttothetask.(7%)Satisfactoryintroduction.Relatinggiventasktoreal-lifesituation.B.TaskSpecificationIdentifyandstateallgiveninformationandrequiredresultsinpropermathematicalstatements.B1.SpecifictheIdentifyandstateallgiveninformationandTask(10%)requiredresultsonly.Identifyandstategiveninformationandrequiredresultsincompletely.C.ProblemSolvingChooseatleasttwosuitableproblem-solvingmethods.C1.Procedure(47%)Chooseonesuitableproblem-solvingmethod.Applyatleasttwoofthechosenproblem-solvingmethodcorrectly.Applyanyoneofthechosenproblem-solvingmethodcorrectly.Applyanyoneofthechosenproblem-solvingmethodincorrectly/incompletely.Conciseandefficientcommunicationusingsymbols/graph/table/diagramswhennecessary.Notconciseandinefficientcommunication.Answerallquestionscorrectly.C2.FindingsDonotanswerallquestionscorrectly.(10%)Detaileddiscussionoffindings.Satisfactorydiscussiononfindings.C3.ExplorationExplorethetaskefficiently.(12%)Explorethetask.D.Conclusion/GeneralisationD1.Conclusion/Checkanswersusinganalternativemethod.GeneralisationDrawconclusion/generalisation.

111-21-2

4-51-31-28-104-71-3

4-51-320-3010-191-98-121-751-44-51-38-121-72-42-4


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(8%)

Totalscore(A1+A2+B1+C1+C2+C3+D1)


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95672458 state9 project work statistics pdf may 24 2012-5-25 pm 1 8 meg evozi

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