ear 11 mathematics ias 1 - nulake 1.10 sample.pdf · • achievement standard ... which is for ncea...
TRANSCRIPT
• AchievementStandard . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2• TheStatisticalEnquiryCycle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3• TheComparativeStatisticalProblem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4• ThePlan . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7• TheData . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 – CensusAtSchool’sDataViewer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 – CleaningtheData . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11• TheAnalysis–Statistics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 – MeasuresoftheCentre . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 – Quartiles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 – MeasuresofSpread . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21• TheAnalysis–TheDataDisplay . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 – DotPlots . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 – StemandLeafPlots . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 – Histograms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 – BoxandWhiskerPlots . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27• DataDistribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35• CensusAtSchool’sData . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40• SamplesandthePopulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45 – MakinganInference . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46• PracticeInternalAssessment1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51• PracticeInternalAssessment2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55• Answers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59• OrderForm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
Year 11Mathematics
ContentsRobert Lakeland & Carl Nugent
Multivariate Data
uLake Ltdu a e tduLake LtdInnovative Publisher of Mathematics Texts
IAS 1.10
IAS 1.10 – Year 11 Mathematics and Statistics – Published by NuLake Ltd New Zealand © Robert Lakeland & Carl Nugent
2 IAS 1.10 – Multivariate Data
◆ Usingthestatisticalenquirycycleinvolvesusingeachcomponentofthestatisticalenquirycycletomakecomparisons .
◆ Usingthestatisticalenquirycyclewithjustificationinvolveslinkingaspectsofthestatisticalenquirycycletothecontextandthepopulationandmakingsupportingstatementswhichrefertoevidencesuchassummarystatistics,datavalues,trendsorfeaturesofvisualdisplays .
◆ Usingthestatisticalenquirycyclewithstatisticalinsightinvolvesintegratingstatisticalandcontextualknowledgethroughoutthestatisticalenquirycycle,andmayinvolvereflectingontheprocessorconsideringotherexplanationsforthefindings .
◆ Studentsneedtobefamiliarwiththestatisticalenquirycycletoinvestigateagivenmultivariatedataset,whichinvolves:
❖ investigatingdatathathasbeencollectedfromasurveysituation
❖ posinganappropriatecomparisonquestionusingagivenmultivariatedataset
❖ selectingandusingappropriatedisplay(s)
❖ givingsummarystatisticssuchasthefivesummaryvalues(minimum,maximum,median,quartiles)
❖ discussingfeaturesofdistributionscomparatively,suchasshape,middle50%,shift,overlap,spread,unusualorinterestingfeatures
❖ communicatingfindings,suchasinformalinferenceandsupportingevidence,inaconclusion .
NCEA 1 Internal Achievement Standard 1.10 – Multivariate DataThisachievementstandardinvolvesinvestigatingagivenmultivariatedatasetusingthestatisticalenquirycycle .
◆ ThisachievementstandardisderivedfromLevel6ofTheNewZealandCurriculum,Learning Media .Theachievementstandardisalignedtothefollowingachievementobjectivestakenfrom theStatisticalInvestigationthreadoftheMathematicsandStatisticslearningarea:
◆ Planandconductsurveysandexperimentsusingthestatisticalenquirycycle
❖ determiningappropriatevariables
❖ cleaningdata
❖ usingmultipledisplays,andre-categorisingdatatofindpatterns,variations,inmultivariatedatasets
❖ comparingsampledistributionsvisually,usingmeasuresofcentre,spread,andproportion
❖ presentingareportoffindings .
◆ Planandconductinvestigationsusingthestatisticalenquirycycle
❖ justifyingthevariablesused
❖ identifyingandcommunicatingfeaturesincontext(differenceswithinandbetweendistributions),usingmultipledisplays
❖ makinginformalinferencesaboutpopulationsfromsampledata
❖ justifyingfindings,usingdisplaysandmeasures .
Achievement Achievement with Merit Achievement with Excellence• Investigateagiven
multivariatedatasetusingthestatisticalenquirycycle .
• Investigateagivenmultivariatedatasetusingthestatisticalenquirycyclewithjustification .
• Investigateagivenmultivariatedatasetusingthestatisticalenquirycyclewithstatisticalinsight .
IAS 1.10 – Year 11 Mathematics and Statistics – Published by NuLake Ltd New Zealand © Robert Lakeland & Carl Nugent
4 IAS 1.10 – Multivariate Data
The Comparative Statistical Problem
Asking the QuestionWhatisitthatyouwouldlikemoreinformationon?Ifyouhadthecapacitytocollectanydatafromallthestudentsinyourclassyoumaydecidetolookinto,forexample:
◆ thestrengthofstudents◆ differentreactiontimes◆ howmanytextmessagesweresentor
receivedetc .Allthisdataiscalledquantitativeornumericdata,itistheresultofmeasuringorcounting .Itisthemeasureofaquantityhencethetermquantitative .Theinformationbecomesinterestingifyouareabletoshowonegroupwithinyourpopulationisdifferentfromanothergroupinsomeway .Groupsthatwelooktocomparewithinthepopulationarecalledqualitativegroups .Theyaredifferentdependinguponsomequalitythatdefinesthem .Possibleexamplesofqualitativegroups(orsubgroups)are:
◆ gender–maleorfemale◆ transport–bike,walk,carorbus◆ yearlevel–Year9,10,11,12or13◆ phone–nil,basicorsmart .
Possiblythegroupofstudentsthatbiketoschoolisdifferentfromthegroupthatwalkbysomecharacteristicthatyoucanmeasure .If,whenlookingatthequalitativegroupsyouaskyourself‘I wonder if ...’thencompletingthequestionoftenidentifiesthevariableyouwillusetocompareandthequestionyouwillinvestigate .Remembertofitthecriteriaforaninvestigationofmultivariatedata,youmustidentify
◆ twoormoresubgroupsofthepopulation .◆ variablesthatcanbemeasuredwhichare
likelytoshowdifferences .Ifweweregivenasamplefromthe‘SuperRugby’ofNewZealandandSouthAfricanplayers .Welookatthequalitativegroups(countryorposition)andstarttowonderif,forexample,thereisadifferencebetweentherugbyplayersofthetwocountries .Ourquestioncouldbe:DoSouthAfricanrugbyplayersinSuperRugbytendtobeheavierthantheNewZealandSuperRugbyplayersfromthepopulationofSuperRugbyplayersplayinginthecurrentyear?
Statistical LiteracyThepopulationisthegroupyouwishtoinvestigate .
Asampleispartofthepopulationthatyouwillusetoseeifyoucanconcludethatdifferencesexistinthepopulation .
Aquantitativevariableistheresultofmeasuringorcounting .Itisameasureofhowmuch(quantity)wehave .
Aqualitativevariableisacategorythatdiffersbysomequality .Forexample,genderoryearlevelarequalitativevariables .
Weusequalitativevariablestoidentifysubgroupsofthepopulationtocompareandquantitativevariablestoseeiftherearedifferencesinthesequalitativegroups .
Aquestionmustidentify◆ thepopulationthesamplewastakenfrom .◆ thequalitativegroupstobecompared◆ thequantitativevariablewhichwillbeused
tocomparethetwogroups◆ thedirectionofanydifference .
Cntry. Ht. Wt. PositionNZ 197 112 Forward
NZ 192 104 ForwardSA 178 109 ForwardSA 190 94 BackNZ 185 98 BackSA 199 114 ForwardNZ 180 90 BackNZ 188 100 ForwardSA 183 114 ForwardSA 183 83 BackSA 188 96 ForwardNZ 192 109 ForwardNZ 187 101 BackSA 191 110 BackNZ 180 103 ForwardNZ 174 92 BackSA 183 91 BackSA 180 88 BackNZ 183 91 BackSA 192 120 ForwardNZ 184 91 Back
Asampleof‘SuperRugby’players’statistics .
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9IAS 1.10 – Multivariate Data
IAS 1.10 – Year 11 Mathematics and Statistics – Published by NuLake Ltd New Zealand © Robert Lakeland & Carl Nugent
Census At School’s Data Viewer
TherearetwoapproacheswithCensusatSchooltogettingyoursample .Wewillexplainbothbutrecommendthesecondapproachofdownloadingthedatasoyoucan‘clean’thedatapriortoanalysingit .
Thedataviewerisdesignedtotakeasampleanddisplaythisasadotplotoverlaidontopofaboxplot .
Select‘Usethedataviewer’ .
Thenextpageistoconfirmthatyouagreewiththeconditionswhichmeansyoumustusethedataforeducationandneedpermissiontousethedataforanythingelse .
Agreetotheconditionsandyouwillbeaskedsomequestionsaboutwhatdatayouwanttoanalyse .Itisdesignedtohelpyouconsideryourstatisticalquestionbutassumingyouhavealreadycompletedthis,selectyourpopulationandsamplesize .
InthisexamplethepopulationistheCensusAtSchool2013dataandoursamplesizeis100 .Donotselect‘Iamayear12student’asitwilladdaninformalconfidenceintervaltoyourdisplay,whichisforNCEA2AchievementStandardIAS2 .9 .
Nowselect‘GetData’ .Yoursamplewillbedrawnandyouwillbeaskedfortwovariablestoanalyse .
Fromyourstatisticalquestionyouselectyourqualitativevariable(forthisexamplewehaveselectedgender)andyourquantitativevariable(inthisexampletheresultsofthememoryexercisestudentscompletedaspartofthequestionnaire) .
Nowselect‘Addsummaries’and‘DoAnalysis’ .Thedotplotandboxplotwillbedrawnforthetwocomponentsofyourqualitativevariable(inthiscasegender) .Youwillbeabletocomparetheresultsforyourquantitativevariable .
Notethatalthoughweselected100inthesampleforthisexampleonlytheresultsfor98ofoursamplearedisplayed .Twostudentsfromthesampleleftoneofthetwovariablesblankandthesewere‘cleaned’fromtheanalysis .
TheadvantageoftheDataViewerisitisquicktouseandgivesyouagooddisplay .Youcancontrolorrightclickontheimagetosaveorcopytheoutput .
Adisadvantageistheremaybeotherdatavaluesyoushouldremove(seeCleaningtheDataonPage11) .
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19IAS 1.10 – Multivariate Data
IAS 1.10 – Year 11 Mathematics and Statistics – Published by NuLake Ltd New Zealand © Robert Lakeland & Carl Nugent
39. Acleaningcompanyislookingatthetotaltimerequiredtocleantwoschoolsofsimilarsizeandarea .Thetotalcleaningtime(inhoursperday)afterfiveweeksare:
School1: 36,39,42,29,45,29,35,42,38,29,42,34,42,37,36,96,78,32,28,34,41,42,30,38and42 .
School2: 28,35,43,52,27,67,61,42,28,64,31,29,63,59,28,29,57,32,61,29,48,73,36,56and62 .
40. Apharmaceuticalcompanyiscomparingthetimeforpatientstorecoverfromillnessusingtheirdrug‘A’andacompetitor’sdrug‘B’ .Timesareindaysandtheshortertimesarebetter .
DrugA:3,4,5,11,13,7,6,na,8,13,6,5,8,11,3,6,9,12,6,6,9,46,5,8,8,11,18,5,7,5and9days .
DrugB:7,8,9,8,5,10,11,12,7,8,6,7,9,21,8,7,12,11,6,14,9,8,21,9,22,15,8,18,9,8and31days .
Merit/Excellence–Investigateeachtwinsetofdatabycalculatingrelevantstatistics(averages,quartiles,minimumandmaximum)foreachsampleandthenusethesestatisticstodescribeanysimilaritiesanddifferences .
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21IAS 1.10 – Multivariate Data
IAS 1.10 – Year 11 Mathematics and Statistics – Published by NuLake Ltd New Zealand © Robert Lakeland & Carl Nugent
Dot plot of the half-days absent from school
0 1 52 3 4 6 7
10
8
6
4
2
8 9 121110
16
14
12
Half-days absent
Freq
uenc
y
The standard deviation is a numeric measure of
spread. In this case 2.2 half-days.
2.22.2
We can use a graphics calculator to find the range, inter-quartile range and the standard deviation.
Measures of SpreadOftenwewantafigurethatdescribeshowspreadoutourdatais .
The RangeTheRangeisthedifferencebetweenthemaximumandminimumvalues .Therangeisveryeasytocalculateandiseasilyunderstood,butifthereisanextremedatavalue,thenthemaximumminustheminimumdoesnotreflecthowspreadoutthemajorityofthedatavaluesare .
The Inter-quartile RangeTheInter-quartile Rangeisthedifferencebetweentheupperquartileandthelowerquartileandgivesustherangeofthemiddle50%ofthedata .Becauseextremevaluesaregoingtobeoutsidethemiddle50%ofthedata,theinter-quartilerangegivesaclearindicationofthespread .
The Standard DeviationAcalculatororcomputerwillalsocalculatetheStandard Deviation .Thisisanumericalmeasureofspreadwhichisnotaseasytointerpretbutyoucansafelyconcludethatasetofdatawithalargerstandarddeviationismorespreadoutthanasetofdatawithasmallerstandarddeviation .Forthedotplotabovethestandarddeviationisabout2 .2halfdays .
Withasymmetrical‘bellshaped’distributionofdata,onestandarddeviationisthedistancefromthemeantoapproximatelywherethecurvestopsgettingsteeperandstartstolevelouttothepeakofthemean .Therearetwostandarddeviationstothecorrespondingpointontheothersideofthecurve .Ifwegoonestandarddeviationeithersideofthemeanitincludesapproximatelytwothirdsofthedatavalues .
To calculate the range we find the maximum and minimum and subtract them. Similarly with the inter-quartile range, we will subtract the lower quartile from the upper quartile.
The symbol for standard deviation is usually σx.Dot plot of the half-days absent from school
0 1 52 3 4 6 7
10
8
642
8 9
The inter-quartile range measures the spread of the middle 50%. In this case the inter-quartile range is 3.
121110
16
14
12
Half-days absent
The range measures the spread of all the data, that is the maximum minus the minimum. In this case the range is 12.
Freq
uenc
y
If we go one standard deviation either side of the mean it approximately includes two thirds of the data values.
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36 IAS 1.10 – Multivariate Data
Dstandsfordatadistribution .Itistoremindyoutolookatyoursampletoseehowthedataisdistributed .Lookattwotypesofgraphs .
i includingthefollowing
SShift .Lookatstatisticsandgraphsofyourcategories .Hastherebeenashiftindatafromonetotheother?Areresultstendingtoincreaseordecrease?
CCentre .Lookatthemediansasthebestmeasureofthecentre .Whatdotheytellyouaboutyouabouttypicalresults?
Uunusualfeatures .Arethereanyextremevalues?Isthegraphskewedtowardsoneend?Group2hereisskewedleft(directionofitstail)andhasan
extremevalueat2 .5 .
SShape .Weoftenexpecta‘bellshaped’distributionasperGroup2 .Howwouldyoudescribetheshapeofyourdistribution?Doyouhaveabimodaldistribution?
S Spreadofyourresults .Howdoestheinter-quartilerangecompareforyourtwocategories?
Ifthedistributionisnotsymmetricalbutispredominantlyatoneendthenwedescribethedistributionasskewed .Itcouldbeskewedtotheleftortotheright .Aleftskewedresulthasthetailontheviewer’sleft .Arightskewedresulthasthetailontheright .Themedianwillstillhavehalfthedataoneithersideofitbutthemeanwillbeonthetailsideofthemedian .
Askewedresultonaboxandwhiskerplotisshownbelow .Againitisleftskewedasthelongtailisontheviewer’sleft .
Ifourdistributionhastwodistinctpeakswedescribethedistributionasbimodal(morethanonemode) .
Intheexampleaboveofabimodaldistribution,wecanseetheshapeofthedistributionwiththehistogrambutthisinformationislostintheboxandwhiskerplotofthesamedata .Itshowstheimportanceofpresentingahistogram(oradotplot)inadditiontotheboxandwhiskerplot .
20 m 40 m 60 m
Box and Whisker plot of Distances Thrown
0 m
01020304050607080
20 m 40 m 60 m
Histogram of Distances Thrown
A left skewed graph has the tail on the left side.
Distribution Terms cont...Use the Mnemonic DiSCUSS
Acknowledgment: This mnemonic was suggested to us by Claire Laverty of Bayfield High School.
010203040
20 m 40 m 60 m
Distances Thrown
A bimodal graph has two peaks
f
020 m 40 m 60 m
0 208 16124
Grp. 1
Grp 2
0 208 16124Grp. 1
Grp 2
0 208 16124
Grp. 1
Grp 2
0 208 16124Grp. 1
Grp 2
0 208 16124
Grp. 1
Grp 2
0 208 16124Grp. 1
Grp 2
0 208 16124
Grp. 1
Grp 2
0 208 16124Grp. 1
Grp 2
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IAS 1.10 – Year 11 Mathematics and Statistics – Published by NuLake Ltd New Zealand © Robert Lakeland & Carl Nugent
46 IAS 1.10 – Multivariate Data
Making an InferenceAboxandwhiskerplothastheadvantagethatyoucaneasilyseetheminimum,quartiles,medianandmaximum .Wewillconcentrateonthisformofgraphbutotherforms(dotplots,histogramsetc .)shouldalsobeused .InIAS1 .10youshoulddisplayyourdatausingatleasttwodifferenttypesofgraphs .Inexplaininghowtodecideifthedifferencesyouseeinapairofboxandwhiskerplotsarelikelytobesimilarinthepopulationwewillconcentrateonthespreadbetweenthetwoquartileswhichwewillcallthesample’s‘middlespread’ .Thespreadofthesamplemiddle50%ofresults .
Wehavetodecidewhenadifferencebetweensamplesislikelytoindicatethatadifferencealsoexistsinthepopulation .Thefirsttwogeneralisationsareforsamplesofsize20to40 .1. Nooverlapbetweenthetwosamples‘middle
spreads’ .Wecanconcludethereisadifferenceinthepopulation .Withnooverlapofthe‘middlespreads’thenthewholeboxor‘middlespread’ofonesubgroup(females)isbelowthewholeboxoftheothersubgroup(males)orviceversa .
2. Thesample‘middlespread’ofonesubgroupisabovethemedianofthesecondsubgroup .
10 20 30 40 50 60
Throwing competition
Male
(m)
75% is below 50%
Female
10 20 30 40 50 60
Throwing competition
(m)
From lower quartile to upper quartile = ‘middle spread’
10 20 30 40 50 60
Throwing competition
Male
(m)
75% is below 75%
Female
Wecanagainconcludethatthereislikelytobeadifferenceinthepopulation .Withthemedianofonegroupbeingabovetheupperquartilethen75%ofthatsamplemustbeabove50%oftheothersample .
Wherethereisanoverlapbetweenthetwosamples‘middlespreads’wecanstillidentifywhetheradifferenceislikelytoexistinthepopulationifwehaveasufficientlylargesample .
3. Withasamplesizeofatleast30,lookatthedifferencesinthetwomedians .Visuallymultiplythisbythree .Inthiscasethedifferenceis7times3=21 .
Wecanconcludethatthereislikelytobeadifferenceinthepopulationifthis‘threetimesspread’isgreaterthanthedifferencefromthehighestupperquartiletothelowestlowerquartile .Wecallthisthe‘Spread of the middle spreads’ .
Thesethreecaseswillaccountformostoftheexampleswherewecanconcludethereisadifferenceinthepopulation .Ifthereisalargersamplesizethenthemultiplierofthedifferencebetweenthemeansincreases .
4. Wherethereisasamplesizeofatleast100lookatthedifferencesinthetwomedians .Visuallymultiplythisbyfive .
Wecanagainconcludethatthereislikelytobeadifferenceinthepopulationifthis‘timesfivespread’isgreaterthanthedifferencefromthehighestupperquartiletothelowestlowerquartile,the‘Spread of the middle spreads’ .
10 20 30 40 50 60
Throwing competition (n ≥ 30)
Male
(m)
Female
Median differenceTimes three
10 20 30 40 50 60
Throwing competition
Male
(m)
Female
Median differenceTimes five
(n ≥ 100)
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60 IAS 1.10 – Multivariate Data
Page 15 cont...32. Bestmeasureismedianweight
of3 .5kgashalftheclasshavebagslessthanorgreaterthanthisfigure .Ifmostofthebagsabovethemedianarecloseto3 .5kgandmostofthebagsunderthemedianarecloseto0kgthenthemeanwillbelowerthanthemedian .
Page 1833.
Theaveragetimespentonhomeworkis75minutesandhalfthestudentsspendbetween30and100minutesonhomework .
34.
ThespendingonChristmaspresentsaveraged$72 .50(mean$82 .30)withhalfthestudentsspendingbetween$35and$100 .Themaximumspentwas$275 .
35.
Onequarterofthestudentsreceivedatleast450textslastmonth .Themediannumberoftextsreceivedwas260andhalfthestudentsreceivedbetween125and450texts .
Page 12 cont...
19. • SexneedssameunitssochangeboytoMandgirltoF .
• Facebook .StudentAisfine .StudentBat5lookswrongandcouldbeminutes,check .
• Facebook .StudentFat0maynothaveaFacebookpageinwhichcasenaisbetter .
• UnitsneedtobethesamesochangeallofFacebooktominutes .StudentGlookslike1hour20minutessocheck .
•Texts .CheckStudentB .•Timetogethome .StudentCeitherhasajoborthereissomethingsuspiciousinthetime .Itisanoutlier .StudentFlivesverycloseortheunitsarehours,check .
20. • Ageneeds<18or≥18socorrectShopperCandShopperG .
• TimeinMallmaybesuspicious .Iftakenwhentheyleavecouldbefinebutiftakeninsidetheymayhavejustarrived .
• NumberofparcelslooksapoorchoiceofvariableparticularlyasChas0buthasspent$25whileGhas11butonlyspent$30 .
• Amountspentshouldbelimitedtotypesofpurchase .CheckifFintendstoshopandifnecessaryreplacewithna .
Page 14
21. Mean=14 .75Median=15Mode=8,15and21
22. Mean=28 .3Median=19Mode=0
Statistics TimeMinimum 0min .LowerQ . 30min .Mean 79min .Median 75min .UpperQ . 100min .Maximum 250min .
Statistics DollarsMinimum $15LowerQ . $35Mean $82 .30Median $72 .50UpperQ . $100Maximum $275
Statistics TextsMinimum 32LowerQ . 125Mean 351Median 260UpperQ . 450Maximum 1250
Page 14 cont...
23.
Year11appeartypicallytosendtwiceasmanytextsonaSaturdaycomparedtoaMonday .
24.
Year13appeartypicallytosendovertwiceasmanytextsonaSaturdaycomparedtoaMonday .
25.
Year11andYear13typicallyappeartosendasimilarnumberoftextsonaMonday .
26.
Year13typicallyappeartosendapproximately20%moretextsthanYear11onaSaturday .
Page 1527. a) Totalofclass=1100
Newmean=57%(0dp) b) Newstudent=10%28. a) Totalofclass=850 b) Classmean=56 .7%
Therearemoregirlsandtheirmeanmarkishigher .
29. a) Mean=1 .35hours Median=1 .5hours
b) Mean=81minutes Median=90minutes
30. a) Mean=37minutes Median=30minutes
b) Mean=397minutes Median=390minutes
31. Bestmeasureismediandistanceof2 .3kmashalftheclasstraveleachsideofthisfigure .Afewstudentsabovethemediantravellingalongwaywillraisethemeanbutnotaffectthemedian .
Y11Texts Mon . Sat .Mean 14 .7 29 .2Median 11 28 .5
Y13Texts Mon . Sat .Mean 15 .2 34 .9Median 15 35
Monday Y11 Y13Mean 14 .7 15 .2Median 11 15
Saturday Y11 Y13Mean 29 .2 34 .9Median 28 .5 35
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