AIOU Solved Assignments 1 & 2 Code 8614 Autumn & Spring 2024. Solved Assignments code 8614 Educational Statistics 2024. Allama iqbal open university old papers.
Code: 8614 Assignment No.1
Semester: Autumn & Spring 2024
Educational Statistics (8614)
Q.1Whatarelevelsofmeasurement?Explaineachlevelsothatreadercanunderstandthe descriptionoflevelanddifferentiateeachlevelfromotherlevels.Write down10examplesforeachlevelandfurtherexplainoneexamplefrom level.
NominalScaleExamples
Herearesomeoftheexamplesofnominalmeasurementthatwillhelpinunderstand thismeasurementscalebetter.
-Howwouldyoudescribeyourbehavioralpattern?
E-Extroverted I-Introverted.A-Ambivert
-Whatisyourgender?
M-Male F-Female
-Couldyoupleaseselectanoptionfrombelowtodescribeyourhaircolor.
1-Black2-Brown3-Burgundy.4-Auburn.5-Other
-Pleaseselectthedegreeofdiscomfortofthedisease:
1-Mild2-Moderate.3-Severe
Inthisparticularexample,1=Mild,2=Moderate,and3=Severe.Herenumbersaresimply usedastagsandhavenovalue.
OrdinalScaleExamples
“Howsatisfiedareyouwithourproducts?”
1-TotallySatisfied2-Satisfied3-Neutral4-Dissatisfied5-TotallyDissatisfied
“Howhappyareyouwiththecustomerservice?”
1-VeryUnhappy2-Unhappy3-Neutral4-Unhappy5-VeryUnhappy
RatioScaleExamples
Thefollowingarethemostcommonlyusedexamplesforratioscale:
1.Whatisyourheightinfeetandinches?
Lessthan5feet.5feet1inch–5feet5inches5feet6inches-6feetMorethan6feet
2.Whatisyourweightinkgs?
Lessthan50kgs51-70kgs71-90kgs91-110kgsMorethan110kgs
3.Howmuchtimedoyouspenddailywatchingtelevision?
Lessthan2hours3-4hours4-5hours5-6hoursMorethan6hours
AIOU Solved Assignment 1 & 2 Code 8614 Autumn & Spring 2024
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Q.2Whatisimportanceofpresentationofdata?Explaindifferentmethodsof effectivepresentationofdata.Listdifferenttypesofgraphsandwritenoteoneachtype.
Whatisdatapresentationandanalysis?
Datapresentationandanalysisformsanintegralpartofallacademicstudies,commercial,
industrialandmarketingactivitiesaswellasprofessionalpractices.Itisnecessarytomakeuse ofcollecteddatawhichisconsideredtoberawdatawhichmustbeprocessedtoputforany application.Dataanalysishelpsintheinterpretationofdataandtakeadecisionoranswerthe researchquestion.Dataanalysisstartswiththecollectionofdatafollowedbydataprocessing andsortingit.Processeddatahelpsinobtaininginformationfromitastherawdataisnon- comprehensiveinnature.Presentingthedataincludesthepictorialrepresentationofthedata byusinggraphs,charts,mapsandothermethods.Thesemethodshelpinaddingthevisual aspecttodatawhichmakesitmuchmorecomfortableandquickertounderstand
Datapresentationandanalysisplaysanessentialroleineveryfield.Anexcellentpresentation canbeadealmakerordealbreaker.Somepeoplemakeanincrediblyusefulpresentationwith thesamesetoffactsandfigureswhichareavailablewithothers.Attimespeoplewhodidall thehardworkbutfailedtopresentitpresentitproperlyhavelostessentialcontracts,thework whichtheydidisunabletoimpressthedecisionmakers.Sotogetthejobdoneespeciallywhile dealingwithclientsorhigherauthoritiespresentationmatters!Nooneiswillingtospendhours inunderstandingwhatyouhavetoshowandthisispreciselywhypresentationmatters!
AIOU Solved Assignment Code 8614 Autumn & Spring 2024
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Q.3 a) Explainthemeasuresofcentraltendencyandmeasuresofdispersion.How thesetwoconceptsarerelated?
Measuresofcentraltendency(alsoreferredasmeasuresofcenterofcentrallocation)allow ustosummarizedatawithasinglevalue.Itisatypicalscoreamongagroupofscores(the midpoint).Theygiveusaneasywaytodescribeasetofdatawithasinglenumber.Thissingle numberrepresentsavalueorscorethatgenerallyisinthemiddleofthedataset.
Thegoalofthemeasureofcentraltendencyis:
i)Tocondensedatainasinglevalue.
ii)Tofacilitatecomparisonbetweendata.
Goodmeasureofcentraltendencyshouldbe:
i)Bestrictlydefined.
ii)Besimpletounderstandandeasytocalculate.
iii)Becapableoffurthermathematicaltreatment.
iv)Bebasedonallvaluesofgivendata.
v)Havesamplingstability.
vi)Notbeundulyaffectedbyextremevalues.
Commonlyusedmeasuresofcentraltendencyarethemean,themedianandthemode.
Eachoftheseindicesisusedwithadifferentscaleofmeasurement.
IntroductiontoMeasuresofDispersion
Measuresofcentraltendencyfocusonwhatisanaverageorinthemiddleofthedistributionof scores.Oftentheinformationprovidedbythesemeasuresdoesnotgiveusclearpictureofthe dataandweneedsomethingmore.Itmeansthatknowingthemean,median,andmodeofa distributiondoesallowustodifferentiatebetweentwoormorethantwodistributions;andwe needadditionalinformationaboutthedistribution.Thisadditionalinformationisprovidedbya seriesofmeasureswhicharecommonlyknownasmeasuresofdispersion.Thereisdispersion whenthereisdissimilarityamongthedatavalues.Thegreaterthedissimilarity,thegreaterthe degreeofdispersionwillbe.
Measuresofdispersionareneededforfourbasicpurposes.
i)Todeterminethereliabilityofanaverage.
ii)Toserveasabasisforthecontrolofthevariability.
iii)Tocomparetwoormoreserieswithregardtotheirvariability.
iv)Tofacilitatetheuseifotherstatisticalmeasures.
Measureofdispersionenablesustocomparetwoormoreserieswithregardstotheirvariability. Itisalsolookedasameansofdetermininguniformityorconsistency.Ahighdegreewould meanlittleconsistencyoruniformitywhereaslowdegreeofvariationwouldmeangreater uniformityorconsistencyamongthedataset.Commonlyusedmeasuresofdispersionare range,quartiledeviation,meandeviation,variance,andstandarddeviation.
HowTheseTwoConceptsareRelated?
Explanation:
Measuresofcentraltendencyaremean,modeandmedian.Evenwehavethreetypesofmean, suchasarithmaticmean,geometricmeanandharmonicmean.
Theytellusthecentralvaluearoundwhichthedataisdistributed.Forexampleconsiderthe dataset#6,8,2,4,12,5,8,10,3,4#.Inthissumofnumbersis#62#andastheyaretenin number,meanis#62/10=6.2#
Notethatsmallestnumberis#2#andlargestnumberis#12#.Now,evenifwehadsetof numbersas#5,6,7,5,8#andassumofnumbersis#31#andtheyarefive,meanisstill #31/5=6.2#.But#5,6,7,5,8#arefarmorenarrowlyspreadandhencenatureofdataisnotvery
wellbroughtoutbyjustmean.
Similarly,wecanhavetwodatasetswithsamemedianormode,buttheirspreadmaybe different,asmodeisjustthemorefrequentamongdatapointsandmedianisthevalueof centraldatapoint,whenthesammeisarrangedinincreasingordecreasingorder.
Measuresofdispersiontellusbetteraboutthekindofspread.Inaway,meandeviationor standarddeviationtellusmoreaboutthewaydataisspread.
Forexample,dataset#30,40,50,60,70#anddataset#10,30,50,70,90#havesamemean,mode andmedianbutwhilemeandeviationoffirstdatasetis#12#,thatofseconddatasetis#25#, indicatingthatseconddatasetistoowidespread.
Whatabouttwodatasets#30,40,50,60,70#and#130,140,150,160,170#?Theirmeandeviation issamei.e.#12#,butaretheynotwidelydifferentasmeanoffirstdatasetis#50#,whilethat ofseconddatasetis#150#.
Itisobviousthatmeasuresofcentraltendencyandmeasuresofdispersionarebothimportant andcomplementary.
b) Howthesetwoconceptsarerelated?Suggestonemeasureofdispersionfor eachmeasureofcentraltendencywithlogicalreasons.
HowTheseTwoConceptsareRelated?
Explanation:
Measuresofcentraltendencyaremean,modeandmedian.Evenwehavethreetypesofmean, suchasarithmaticmean,geometricmeanandharmonicmean.
Theytellusthecentralvaluearoundwhichthedataisdistributed.Forexampleconsiderthe dataset#6,8,2,4,12,5,8,10,3,4#.Inthissumofnumbersis#62#andastheyaretenin number,meanis#62/10=6.2#
Notethatsmallestnumberis#2#andlargestnumberis#12#.Now,evenifwehadsetof numbersas#5,6,7,5,8#andassumofnumbersis#31#andtheyarefive,meanisstill #31/5=6.2#.But#5,6,7,5,8#arefarmorenarrowlyspreadandhencenatureofdataisnotvery wellbroughtoutbyjustmean.
Similarly,wecanhavetwodatasetswithsamemedianormode,buttheirspreadmaybe different,asmodeisjustthemorefrequentamongdatapointsandmedianisthevalueof centraldatapoint,whenthesammeisarrangedinincreasingordecreasingorder.
Measuresofdispersiontellusbetteraboutthekindofspread.Inaway,meandeviationor standarddeviationtellusmoreaboutthewaydataisspread.
Forexample,dataset#30,40,50,60,70#anddataset#10,30,50,70,90#havesamemean,mode andmedianbutwhilemeandeviationoffirstdatasetis#12#,thatofseconddatasetis#25#, indicatingthatseconddatasetistoowidespread.
Whatabouttwodatasets#30,40,50,60,70#and#130,140,150,160,170#?Theirmeandeviation issamei.e.#12#,butaretheynotwidelydifferentasmeanoffirstdatasetis#50#,whilethat ofseconddatasetis#150#.
Itisobviousthatmeasuresofcentraltendencyandmeasuresofdispersionarebothimportant andcomplementary..
(2partanswernotavailable)
AIOU Solved Assignment 1 & 2 Autumn & Spring 2024 Code 8614
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Q.4Whatisnormaldistribution?Explaintheroleofnormaldistributionindecisionmakingfor dataanalysis.Writeanoteonskewenessandkurtosisandexplainitscauses.
Anormaldistribution,sometimescalledthebellcurve,isadistributionthatoccursnaturallyin manysituations.Forexample,thebellcurveisseenintestsliketheSATandGRE.Thebulkof studentswillscoretheaverage(C),whilesmallernumbersofstudentswillscoreaBorD.An evensmallerpercentageofstudentsscoreanForanA.Thiscreatesadistributionthat resemblesabell(hencethenickname).Thebellcurveissymmetrical.Halfofthedatawillfallto theleftofthemean;halfwillfalltotheright.
Manygroupsfollowthistypeofpattern.That’swhyit’swidelyusedinbusiness,statisticsandin governmentbodiesliketheFDA:
Heightsofpeople.
Measurementerrors.
Bloodpressure.
Pointsonatest.
IQscores.
Salaries
1) Ithasoneoftheimportantpropertiescalledcentraltheorem.Centraltheoremmeans relationshipbetweenshapeofpopulationdistributionandshapeofsamplingdistributionof mean.Thismeansthatsamplingdistributionofmeanapproachesnormalassamplesize increase.
2) Incasethesamplesizeislargethenormaldistributionservesasgoodapproximation.
3) Duetoitsmathematicalpropertiesitismorepopularandeasytocalculate.
4) Itisusedinstatisticalqualitycontrolinsettingupofcontrollimits.
5) Thewholetheoryofsampletestst,fandchi-squaretestisbasedonthenormal distribution.
Thesearetheimportanceorusesorbenefitsofnormaldistribution.
a)Skewness
Skewnesstellsusabouttheamountanddirectionofthevariationofthedataset.Itisa measureofsymmetry.Adistributionordatasetissymmetricifitlooksthesametotheleftand rightofthecentralpoint.Ifbulkofdataisatthelefti.e.thepeakistowardsleftandtherighttail islonger,wesaythatthedistributionisskewedrightorpositivelyskewed.Ontheotherhandif thebulkofdataistowardsrightor,inotherwords,thepeakistowardsrightandthelefttailis longer,wesaythatthedistributionisskewedleftornegativelyskewed.Iftheskewnessisequal tozero,thedataareperfectlysymmetrical.Butitisquietunlikelyinrealworld.
Herearesomerulesofthumb:
i)Iftheskewnessislessthan–1orgreaterthan+1,thedistributionishighlyskewed.
ii)Iftheskewnessisbetween-1and-orbetween+and+1,thedistributionismoderately skewed.
iii)Iftheskewnessisbetween-and+,thedistributionisapproximatelyskewed.
b)Kurtosis
Kurtosisisaparameterthatdescribestheshapeofvariation.Itisameasurementthattellsus howthegraphofthesetofdataispeakedandhowhighthegraphisaroundthemean.Inother wordswecansaythatkurtosismeasurestheshapeofthedistribution,.i.e.thefatnessofthe tails,itfocusesonhowreturnsarearrangedaroundthemean.Apositivevaluemeansthattoo littledataisinthetailandpositivevaluemeansthattoomuchdataisinthetail.Thisheaviness orthelightnessinthetailmeansthatdatalooksmorepeakedoflesspeaked.Kurtosisis
measuredagainstthestandardnormaldistribution.Astandardnormaldistributionhasa kurtosisof3.Kurtosishasthreetypes,mesokurtic,platykurtic,andleptokurtic.Ifthedistribution haskurtosisofzero,thenthegraphisnearlynormal.Thisnearlynormaldistributioniscalled mesokurtic.Ifthedistributionhasnegativekurtosis,itiscalledplatykurtic.Anexampleof platykurticdistributionisauniformdistribution,whichhasasmuchdataineachtailasitdoes inthepeak.Ifthedistributionhaspositivekurtosis,itiscalledleptokurtic.Suchdistributionhas bulkofdatainthepeak.
AIOU Solved Assignment 1 & 2 Code 8614 Autumn & Spring 2024
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Q.5Explainthefollowingtermswithexamples
a) ContinuousVariable
Avariableisaquantitythathasachangingvalue;thevaluecanvaryfromoneexampletothe next.Acontinuousvariableisavariablethathasaninfinitenumberofpossiblevalues.Inother words,anyvalueispossibleforthevariable.
Acontinuousvariableistheoppositeofadiscretevariable,whichcanonlytakeonacertain numberofvalues.
Acontinuousvariabledoesn’thavetohaveeverypossiblenumber(like-infinityto+infinity),it canalsobecontinuousbetweentwonumbers,like1and2.Forexample,discretevariables couldbe1,2whilethecontinuousvariablescouldbe1,2andeverythinginbetween:1.00,1.01, 1.001,1.0001…
Afewexamplesofcontinuousvariables/data:
Timeittakesacomputertocompleteatask.Youmightthinkyoucancountit,buttimeisoften roundeduptoconvenientintervals,likesecondsormilliseconds.Timeisactuallyacontinuum: itcouldtake1.3secondsoritcouldtake1.333333333333333…seconds.
Aperson’sweight.Someonecouldweigh180pounds,theycouldweigh180.10poundsorthey couldweigh180.1110pounds.Thenumberofpossibilitiesforweightarelimitless.
Income.Youmightthinkthatincomeiscountable(becauseit’sindollars)butwhoistosay someonecan’thaveanincomeofabilliondollarsayear?Twobillion?Fiftyninetrillion?Andso on…Age.So,you’re25years-old.Areyousure?Howabout25years,19daysandamillisecondor two?Liketime,agecantakeonaninfinitenumberofpossibilitiesandsoit’sacontinuous variable.
Thepriceofgas.Sure,itmightbe$4agallon.Butonetimeinrecenthistoryitwas99cents. Andgiveinflationafewyearsitwillbe$99.nottomentionthegasstationsalwaysliketouse fractions(i.e.gasisrarely$4.47agallon,you’llseeinthesmallprintit’sactually$4.479/10ths
b) CategoricalVariable
Asthenamesuggests,categoricalvariablesarethosevariablesthatfallintoaparticular category.Haircolor,gender,collegemajor,collegeattended,politicalaffiliation,disability,or sexualorientationareallcategoriesthatcouldhavelistsofcategoricalvariables.Usually,the variablestakeononeofanumberoffixedvariablesinaset.
Forexample:
Thecategory“haircolor”couldcontainthecategoricalvariables“black,”“brown,”“blonde,”and “red.”
Thecategory“gender”couldcontainthecategoricalvariables“Male”,“Female”,or“Other.”
Notethat“haircolor”and“gender”arethecategoriesandarenotcategoricalvariables themselves.Acategoricalvariableisavaluethatvariablesinastudytake;thevaluevariesfrom persontoperson.Let’ssayyousurveypeopleandaskthemtotellyoutheirhaircolor.They wouldrespondwithacategoricalvariableofblack,brown,blond,orred.Theywouldn’trespond “haircolor.”
Isthereanordertocategoricalvariables?
Thereisnoordertocategoricalvariables;inotherwords,theyaren’trankedfromhighestto lowestorlowesttohighest.Forexample,thereisnointrinsicordertothecategoriesofmale andfemale.Ifthereissomekindoforder,thenthosevariableswouldbeordinalvariablesand notcategoricalvariables.Forexample,youcouldcategorizehousepricesbycheap,moderate andexpensive.Althoughthesearecategories,thereisaclearorder(withcheaponthebottom andexpensiveontop).
Examplesofcategoricalvariables:
Brandoftoothpaste(Colgate,Aquafresh…)
Collegemajor(English,Math…)
Telephonecompany(BellSouth,AT&T…)
Checkingaccountlocation(Jacksonville,NewYorkCity…)
Schoolattended(LeeHigh,WescottHigh…)
Examplesofquantitativevariables:
Numberoftoothpastetubesusedperyear.
G.P.A.forcollegemajor.
Bytesofdatauploadedonyourphone.
Checkingaccountbalance.
Averagenumberofstudentsinaclass
c) IndependentVariable
IndependentVariableDefinition.
Independentvariablesarevariablesthatstandontheirownandaren’taffectedbyanythingthat you,asaresearcher,do.Youhavecompletecontroloverwhichindependentvariablesyou choose.Duringanexperiment,youusuallychooseindependentvariablesthatyouthinkwill affectdependentvariables.Thosearevariablesthatcanbechangedbyoutsidefactors.Ifa variableisclassifiedasacontrolvariable,itmaybethoughttoaltereithertheindependent variableordependentvariablebutitisn’tthefocusoftheexperiment.
Example:youwanttoknowhowcalorieintakeaffectsweight.Calorieintakeisyour independentvariableandweightisyourdependentvariable.Youcanchoosethecaloriesgiven toparticipants,andyouseehowthatindependentvariableaffectstheweights.Youmaydecide toincludeacontrolvariableofageinyourstudytoseeifitaffectstheoutcome.
Theabovegraphshowstheindependentvariableofmaleorfemaleplottedonthex=axis. “Male”or“Female”isunchangeablebyyou,theresearcher,oranythingyoucanperforminyour experiment.Ontheotherhand,thedependentvariableof“meanvocabularyscores”is potentiallychangedbywhichindependentvariableisassigned.Inotherwords,themean
vocabularyscoresdependontheindependentvariable:whethertheparticipantismaleor female.
Anotherwayoflookingatindependentvariablesisthattheycausesomething(orarethoughtto causesomething).Intheaboveexample,theindependentvariableiscalorieconsumption. That’sthoughttocauseweightgain(orloss).
d) DependentVariable
DependentVariable:
Adependentvariableiswhatyoumeasureintheexperimentandwhatisaffectedduringthe experiment.Thedependentvariablerespondstotheindependentvariable.Itiscalleddependent becauseit”depends”ontheindependentvariable.Inascientificexperiment,youcannothavea dependentvariablewithoutanindependentvariable.
Example:Youareinterestedinhowstressaffectsheartrateinhumans.Yourindependent variablewouldbethestressandthedependentvariablewouldbetheheartrate.Youcan directlymanipulatestresslevelsinyourhumansubjectsandmeasurehowthosestresslevels changeheartrate.
.Covarianceis ameasureofhowmuch tworandom variablesvarytogether. It’ssimilarto variance,butwhere variancetells youhowasinglevariable varies,co variancetellsyouhow twovariables varytogether.
TheCovarianceFormula
Theformulais:
Cov(X,Y)=?E((X-?)E(Y-?))/n-1where:
Xisarandomvariable
E(X)=?istheexpectedvalue(themean)oftherandomvariableXand
E(Y)=?istheexpectedvalue(themean)oftherandomvariableY
n=thenumberofitemsinthedataset
Example
Calculatecovarianceforthefollowingdataset:
x:2.1,2.5,3.6,4.0(mean=3.1)
y:8,10,12,14(mean=11)
Substitutethevaluesintotheformulaandsolve:
Cov(X,Y)=?E((X-?)(Y-?))/n-1
=(2.1-3.1)(8-11)+(2.5-3.1)(10-11)+(3.6-3.1)(12-11)+(4.0-3.1)(14-11)/(4-1)
=(-1)(-3)+(-0.6)(-1)+(.5)(1)+(0.9)(3)/3
=3+0.6+.5+2.7/3
=6.8/3
=2.267
Theresultispositive,meaningthatthevariablesarepositivelyrelated.
AIOU Solved Assignment 1 & 2 Autumn & Spring 2024 Code 8614
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