SpreadsheetActivities for aDataMaaagemeneUnit:
A Teachers 'Resource usingMicrosoft &eel
A proj ectsubmitted to theFaculty of Education in partial fulfillme ntof the require ments
forthedegree of Masters of Education, Teachingand Leaming
Ralph Percey MemorialUniversity ofNewfou ndland
2000
Acknowledgments
Iwould like to beginby tha nking Of".Jo hnGnluMcloughlinfo rhisrole as supervisor throughoutmy project.Fromassisting with thetopic selectio ntodirecting and editingthefinal copy.Dr.GrantMcLough linhasbeenthere.Feedbackwasalways prom pt.informative, and open for discu ssion.I alwa ysfelt incontrolof theproject with Dr.GrantMcloughlinthere toprovideguidingwordsofwisdom. Hisenthu siasm, readiness to meet011short noticeand overallapproach10 supervision made the final completionoftheprojecta welco me reality.(againoffer my manythanksto Dr.Grant McLough lin.
Iwould also like tothank my lovingwifeSusan.Tha nk youfor yourlo ve, support, help,patience.and understandingduringboth mygradua teand undergrad uatestudies.In mor ewaysthan you willeverknow, yo u havebeen the inspirationthatled me tothese degrees.Thankyou for ourtwobeautifulsonsDevin andDylanandthe sacrificesyou have madeand areyet tomake.I assure youthat nothin g youhave sacrificed hasgone unnoticed or unap preciated.Idedicat e thisprojectto YOU.Devin,andDylanasa symbol of my thanks and appreciation.
lwouldliketothankandpaytribute tomypare ntsJames and Catheri ne Perce y.
The lessonsyoutried sohard 10 teac hme did not all fallondeafears.Thank s for everything (except theproc rastina tiongene Dad).
In closing, Ioffer anoteof thanks toall those individual s(in-lawsincluded)that havehelpedme10 whereIam today.No smallpiec e ofadviceorwordsof wisdomare ever reckl esslydismi ssed.
Abstraet
Statisti csare allaroundus.Statistical reports fromareaslike business.weather, politics, andsports areencountered daily by studentsandadults.Yet,thestudyof statisti cs as a branch of mathematicshas primarilybeenanoptionalcourse offering in thehigh schoolcurriculumof Newfo und land.Ho wever,throug htheefforts of theAtlantic ProvincesEdu cationFoundation (AP EF),the study of statisticswill nowhave a compu lsory placeineachlevel of the regio nalhighschoolmathematics curriculum.This curriculumalsocallsfor the integrationof appropri atetechnologies likeco mputersoftware toexplorethe relevantobjectives.
The aimof thisprojectis tooffer teachersaresou rce that supportsthe inst ruction of statistics throughtheintegrati onof technology.Thisproject isdesigned toexplo re various curriculum topics in statisticsusingthecomputersoftware packageMicrosoft Excel.The highschool curriculumobjectivesfortheDataManagemen t unitas outlinedin CourseI, Le vel Y,Teacher'sPilotDraftGuidelines ofthe AtlanticCanadaMathematicsCurriculum
(1997)provides theframework fortheactivities
Theproject consistsof a series ofactivitiestha tuse Micro.roftExcelasatoo lto help studentsinvest igateseveralconceptsin statistics.TheNatio nal Council of Teachersof Mathematicshas longsupported:nvolvingstudentsin constructingand applying mathematicalideas.using a variety ofinstructional formatslike smal lcooperativegrou ps and individualexplorations.andusing computersas tool sforlearn ing and doing mathematics(NCTM.1989 .p.vi).This project integratestheseideas intoanorganized collectionof activities
iii
TableofCo ntents Acknowledgments..
Abstract..
Introductio n....
LiteratureReview..
The Need for TechnologyIntegration
. ii
. iii
••••••••••••1
. 3
...3
Why Use a SpreadsheettoStudy Statistics? . . 5
Coo perativeLearning and Refl ectivePractice..
Overview of Project.
Descriptio n .
Classroom Climale..
Note10 theTeacher....
Sequencingthe Act iv ities..
EvaluationPlan . .
Data Management:ASet of Activities in&eel..
Overviewof ActivityI. Activity 1..
Overview ofActivity2 . Aetiv ity2..
OverviewofActivity3...
Activity)..
Overview of Activity4. Acti vity 4..
iv
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. 12
..13
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. 15
. 17
..•..•..19
. 20
..21
. 27
...28
. J2
...33
. 38
....39
Overviewof Activity5 ...43
Aet ivityS.. . 44
Overviewof Activity6 .. . 49
Activity6.. . 50
References..
AppendixA:Backgro und toExcel..
Backgro und toExcel.. . Appendix8:StudentActivitySheets..
Student Activity 1. StudentActi\it y2..
StudentActivity3...
StudentActivity4..
StudentActivity 5. Student Activit y6...
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....7S
Introd ua ion
The Atlantic ProvincesEducationFound ation (APEF)is anorganization spo nsored and managed bythe governm ent s of thefourAtlanticProvinces.Inaddition to othersubject areas,theAPEF has been commissioned withthetask:ofdevelopinga common curriculumformathematics.Thepilot draft guidelines of the AtlanticCanada MathematicsCurriculum(199 7. p.i)stat ethatthe NationalCounci l ofTeachers of Mathematics(NCTM)Curriculumand EvaluationStandards/or Schoo l Mathematics (1989) hasgreatlyinfluenced thiscurriculum.This common curriculumnowincludes a singleunitdevotedto the study of statisticsin eachofLevels I,2,and 3 (grades10. II. and12).Theincreased emphasis onstatisti cs is a newfocusfortheNewfou ndland high schoolmathematicscurriculumthathas previouslyincludedonlyanoptionalcoursein statisticsat the highschoollevel. This is inconsistentwith alltheothergradelevels where statisticsremains a corepart ofthecurriculum.
Icurrently teachmathem atics inan urban seniorhighschoolsetting(Levels Ito 3).After nineyears ofteaching, I havecometotheconclusio n that the study ofstatistics hasnot been givenadequate anentionin high school.Mypresentschool offers onlyone sectionofthe optio nalStatist ics3 t04 course a year.This allowsonly 35 of725students to do thiscourse.My discussio nswith mathem atics teachersfromotherlocalurban schoolsconfirm similarcourse offerings.Isuspect that smaller schoo lswould be even less likely to offer such an electivecourse .Asstatistics becomesa corecompone nt of the curriculum,teacherswillbe teaching top ics with whichtheymayhaveminimal recent experience. Furthermore,theylikelyhavefewresourcesavailableto suppo rt them inthe implementationof the new curricul um.
lbe newdraftPrincip lesandStandardsDocument(NC'TM..1998)recommends that teachersnave abackgroundin mathematicswellbeyond thatwhichtheyarerequired toteach.However,Hoffer(1982. p.263)andHogg ( I992.p.6) claimthatmanyteachers do nothave anadequa tebackgr ound instatistics and thuslack theknowledgetoteach statisticaltopics.Theynotethatthisleadsto a lack ofabilityandexperienceinselecting and integratingmeanin gfulactivities. Noempiricalevidenceisoffered to supportthese claims, howeverevide nceofdeficiencies inteachers'backgrounds in statistics canbe foundamongstpresentteachers.In conversations withsevera l mathematics teaching colleagues,mostreported thattheynave onlycompletedtheone ortwostatistics courses required bythe degreeprogram. Thisraisessomeconcern overtheissue of teacher preparednesstodeliver thestatisti cs topics intheAPEF curricu lum.
TheAPEFmathematicscurriculum also calls fortheintegra tio n oftechnologyin meetingmany ofthe objectives oftheCOUI1le5.Inparticular,[refertothe unitentitled DataManagement fromCourseI.LevelV oftheTeacher'sPilo t DraftGuidelines:
AtlanticCanadaMathematicsCurriculum. TheKey StageCurricul um Outcomes2,3, and4callfortheintegra tionofappro priatetechnologies such as a statistics software package.Unfortunately,thisdocumentfails torecommendany approp riatesoftware or related activities.lnadditiontofinding and learningthesoftware, the teacher isnow facedwith the task of locating ordeveloping usableactivities.Ineithercase.itisa very time consuminganddauntingprocess.Many ofthesesame teachers[previouslyreferred to alsoreportedha vinglittleornoformaltrainingwithcomputers orspreads heet software.Regr ettabl y,thisalsorepr esentsmy personal backgroundandexperienc e.
There is a shiftinmathematicseducationawayfromdrillandpracticeteacher- directed instruction.The teacher' srole is now to helpdirect andfocus student activityso those studentscan construct and build theirO\Vl1meaningandunderstanding.lncreased emphasisis beingplacedupon:
activelyinvo lving studentsinconstruct ingand applyingmathematicalideas;
usingproblemsolving as ameansas well as agoalof instruction;
usingavariety of instructionalformats:smallcooperativegroups, individual explorations.wholeclassinstruction. andprojects ;
usingcalculatorsandcomputersastoo ls forlearni ng and doi ngmathematics (NCTM.1992,p.VI).
The previouslyide ntifieditems and thisnew shift.in mathematicseducationhasled meto developaseriesofactivitiesinMicrosoftExcet.Theintent isto provideasetof curriculumspecificinvestigat iveactivitiesthatincorporate theuse of spreadsheet technology intotheexplora tion of selectstatistical topicspertinent10 thecurricu lum.
Lite ratureReview TheNeedfor Technology Im e m 1jo n
The NCTM states that"theuseoftec hnologyininstructionshou ldfurther alter boththe teachingand learning ofmathematics"(l989.p.128).Forteachers,thiswould invo lve usingcomputersoftware for class demonstrations.Forstudents,itwouldinvolve independe ntlyexploring additionalexamples,performing inde pendentinvest igations, and genera tingandsummarizing data as part ofaproject(NCTM,1989. p.128).Also, beca usetech no logyis changingmathematics and itsuses,the NCTMbelievesthat:
• appropriate calculato rsshouldbeavailabletoall students atalltimes;
a compu tershouldbeavailablein everyclassro omfor demon strationpurpo ses;
every studentshouldhave access to a computer for individualand groupwork; students should learn to usethe computeras a toolfor processinginformationand performing calculations to investigate and solve pro blems (NC'TM.. 1989,p. 8).
The NCTM continuestoemphasize the roleoftechn ol ogy in educationin thenew draft Princ iplesand StandardsDoer/me,,'."Mathematicsinstructi onal programs shoulduse technology tohelpstudentsunderstandmathematicsandshouldprepare themtouse mathematicsin an increasingly technologica l wo rld" (NCTM, 1998).
The computerisnot intended toreplacetheteacher.Itisatool that can guidea student throug h.the developm entof a mathematicstopicusing activitiesthat h.ave been carefully workedinto theschoolcurriculum (Posamentier andStepelman, 1999,p.144).
PosamentierandStepelman (1999,p.144)referto such activitiesas computerassisted instru ction andofferthatit "should supplement. not supplant, theregu larinstru ction."
The NCTM(1998)also statesthattechnological too ls"s hould not be used as replacements for basic understa ndingsand intuitions;rather,theycan and should be used to foster those understandings andintu itions."Inthe area ofstatistics, "co mputers can be used effect ivelythroughoutstudents'studyof data analysis,statistics,andprobability to illustrate concepts, perform calculations,createrepresentations,andprovide datafrom simulations"(NCTM,1998).
Therearetwo relevantareasthat providedirecti o n totheproject.The first examinestheroleof spreadsheetuse inthe studyofstatist ics .The otherconside rsissues pertinenttothelearningenvironment:coopera tivelear ning, construct ivism, andreflective practice .
Why Usea Spreadsh eet(QSDJdyStatiSliCl?
Spreads heet software was initia llycreated for thebusiness world.However, Arganbright (1992 ,p.226)claims thatan electronic spreads heetis apowerfuland creati ve too l forthe stu dy of statistics.He argues that itprovides a natural med ium throughwhichto examine statistical ideas interactively, implement algorithms ,and genera teinsightfulgraphic displays.Otherbenefitshe fee ls thatcanbeachie vedinclude increased studentinterestandthe preparat ionofstudents fur manycareers.Hall(1995, p.5)claims thatusing aspreadsheetpackagenotonlyaidsthelearningproc ess but also adds toastudent'sprofessionalcompetence.The long-termbenefitsof spreads heet knowledge to stude ntsfor statisticalanalysis are extended by Nash and Quon(1996)
Spreadsheettechnology canalso serve as a toolto enhancetheexplorationof statisticalconcepts.Thistechnologyhas thecapabilit yofhandlinglarge samplesof datainperformingcomplexcalculations andproducingprofessionalcharts.Inmy previous instru ctionofthe high schoolstatisticscourse,students often repon edthat workingwithlarge sets ofdatawastimeconsuming,monoton ou s, andevendifficult.
Forte(1995, p. 208) offers thatspreadsheetsoftware enablesstudentsto organ ize, analyze,and compute statisticsfrom data withoutperforming complexmanual computations.Forte (1995,p.208) clai msthiswillallowstudentsto spend more time ana.lyzingandinterpreting thegenerateddataandlesstime learni ng complex statistical fonnulas.
Dreyfus,Feinstein,and Talmon(1998, p. 68)alsoacknowledge thatspreadsheet use provides freedom fromcomplexand tedious calculationswhen theyintegrated spreadshee tsinto a biologycurriculum.They furtherconcludedthatstudents became
"acti velyand personally involvedintheconstruction of scientificconcepts andconcep ts related totheempiricalandquantitative statisticalcharact erof biological sciences"
(Dreyfus eral,1998,p.68).They alsofelt thatlearning touse a spreadsheetplaced no extra cognitiveload on students,In fact,"inthe eyes of anoverwhelming majorityof the teachers,thetechnicalaspectsof the use of thespreadsheetwasnotregardedas a source of difficulty"(DreyfuseraL,1998, p.78).Inadd itiontothe relativeease withwhich students can leamto use a spreadsheet .aspreadsheetoffersother features thatcanhelp studentsinvestigate concepts.
Mitchell(1997,p.203) developed a problern-cri ented approach tostatistics education usingacomputer-basedspreadsheet.In support of his choice to use spreadshee ts.he offersfivereasons.First. aspread sheetcan be used tocreatemultiple representatio nsof statisticalmeasures.Mitchell (1997, p.203), felt that"fro m an instructionalviewpoi ntitisquiteusefultopresent both an analytic(or algebraic) and a
visual (orgeometric)representationsimultaneo usly,"Thro ughthe use ofwell chosen
graphs,students can buildmodelswhich displaythe analytic andvisualreprese ntations dynamically.This featureismade possib le bythe fact thatvisual representations and calculationsareupdatedautomatically as a piece ofdata changes(Mitchell.199 7.
p.203).Student simmediately seethe effect sof editingexistingdataor enteringnew data,Thisallowsthemto actively investigateand"reinforce theconceptual underpinningsofastatistical concept"(Mitchell.1997.p. 204).
A second relatedite m Mitchell(1997,p.204)describes is "numbe r playgrounds."
Here. theuser inputs raw dataforalimitednumberof subjectsandthespreadsheet automaticallycalculatesrelevant statistical measures.Studentsthenchangeorplaywith
data toexperimentwithstatisticalconcepts.Thisfocusesonstudents'"concep tual understanding"(Mitchell,1997,p.204).
Two other reasonsto use a spreadsheetare offeredby Mitchell(1997,p.204) under theheadings of"storylines" and"creativity."Togethe r,he isreferringto the capabilitiesofthespreadsheet, which allow for the additionoftext,sound, color,and graphics.Thesefeaturesallow the student to create descriptive products that havehigh visualappeal.
Finally,Mitchell(1997,p.204)discusses"thepower ofopenended softwar e programs ."HeSlates that "t he potentialuses for asprea ds heetprogramace limitedonly by theskillandpatienceof the user"(Mitchell,1997,p.20S). Mitchell arguesthat together,"these fiveelementsprovidea powerful cognitivefoundation forbuilding instructional activitiesaimedatdeve loping adee perunde rstandi ng of statiSlica l concepts"(1997,p.20S).
Theneedfor knowledgeandskillwithusingspread s heet technolo gy is also being documentedin theworkplace.Perry(1998) conducteda study of employerswho advertised forcomputer relatedvacanciesin five metropo litan newspapersinthe southeasternUnitedStatesduring a monthin1996.Employerswereaskedtoexamine a listofspreadsheetcompetencies todetenn inethe degree towhich they were needed for their workplace.They ratedeachspreadshee t competen cyas'Essential to Very Essential' for theirbusiness(perry,1998,p.37).TheNCTM(1998)Slatesthat"ifschoolsdo have a levelof technology equivalenttothelevel foundoutside of schools,andif theydo not preparestudents appropriatelywithit,then theyareplacingstudentsat a serious disadvantage." More and more schoolstoday arebeing outfittedwith compute rlabsand
thelatest insoftwareinclu ding spreadsheetsoftware.Incorpo rating this software into classroo m instruction is arespo nsiblefirststepinpreparin g stu dentsto enter the workfo rce
Coope ratjve Learning andRefl ecti vePractjg;
Slavin (as citedin McManusandGettinger.1996.p.13) definescooperative learni ng as a process by which students work.togeth er in groups to masterthe material presentedbythe teacher.Studiesby both SlavinandJohnso nandJohnson(as cited in Brush, 1997,p.52) statethatforcooperativelearninggroups to be effective,they must receive inst ruct ionanddirectionin areasthey call positive interdepende nce, individ ual accountability.grouprewards,andgroup instruction.
Acco rdingtoJohnson,Jo hnson,andSmith(as citedinGarfield,1993), cooperativelearning isnot havingthefirstpeoplein a class to finish.theirwork helpthe slowe r stud ent s.It isnotagroup projectthatonepersondoes andeveryo neputshis or h.ernames onas contributors.It isnot havingstudents sit side-by-s ideat the sametable and talkto eachotheras theydo individualwork orassignments There mustbe small groups engagedin help ing each other gainunder standi ng as theyattemptto solvea problemorcomp letesome task.Developingth.iscooperative environmen t has been foun d to haveseveral ad vantages.
Cooperativelearni ng structureshave been linked toincrease sin academic performance.Dees (as citedinKeelerand Steinhorst,199 5) reportedtha t theuse of learn ingpartners andpeer mo nitors resultedinincreased perform a nceinproblem solving,quizz es, andtests.StudiesbyKeeler and Steinhorst(1994,(995)found that stude nts alsoachieved higher academicscoreswhilebecom ingmoreengaged in the
coursematerial.Giraud(1997)also reponedhigh er test scores forstudentsworkingin randomlyassignedcooperative groupsbutfeltthis forma twasespeciallybeneficialto
"thoseleast preparedforstatistics."Benefits ofthisapproacharenotlimitedto only academics.
JohnsonandJohnson(ascitedin Giraud,1997)advocate cooperative learning for
"its effects on achieveme ntand onother attributes that accompanythe acquisition of
know ledge.including motivation, classroomsocializat ion. the student'sconfide nce in learning,andattitudetoward thesubjectbeinglearned."AccordingtoLegere(L99(,p.
170),the smallgroups' exchangeofideas "increased the interestof theparticipantsin additiontopromoting criticalthinking."Whicker.Be l, and Nunnery (1997,p.47) report that moststudentsenjoyed the social aspect ofworkingwithandreceiving help from other students. Some justification forthisis offered byForte(199 5,p.211)when he claimsthatstudentsin agroup setting arefreefromthe surveillanceof theinstructor They are nowfree to"take risksinwaysthatminimize anxiety andembarrassment"
(Forte, 1995,p.211).Brush (1997,p. 51)noted improvedstudents'attitudes toward math and computermath activitiesfor stu dentswho used anIntegrated Learning System with cooperative lear ningpairs:compared10 thosewhousedonlyanIntegratedLearning Syste m.
Work ing in cooperative groups,studentscan avail ofgroupinteraction and dynamics to construct their own mean ings ofconceptsdiscussed.As students investigate aconcept,"it is Impo rta ntthat provisions bemadefor studentsto sharetheir experiences.
clarifytheir thinking, generalizetheirdiscoveries.and provideconvincingexplanations"
(NCTM.1992,p.vi).The questions and observations that resultfrom groupefforts can
to
andshouldbesharedwiththe wholeclass.This may open uptopicsforfurther investigati on.
Reflection is ofte n associatedwiththe"looking back"stepinPolya'splan for solving problems:read. plan,solve.andlook back (Krulik andRudnick,1994).Asa facilitat or cf'understandiugand knowledgeacquisition,manywouldarguethat reflection isthe step inthe processthathold s themostpotential.Wheatl ey (1992) claimsthat
"reflect ion playsa criticallyimportantroleinmathematicslearning" andoffers evidence that"reflect ionresultsin greatermathematicsachievement"(p.529).What isinvolved in reflectio n?
Krulik and Rudnick (1994)claim thatfor manyteachers.looking back is simply
to"determine ifthemathematics iscorrect,seeifitmakessense. andcheckhowwellit
answers thequestion" (p.334).Thisisnot the truereflectionthatleads to indivi du al insights.For Sigel(as citedin Wheatley.1992). reflect ionformathematicslearn ing"is charact erized bydistancingoneself fromthe action of doing mathematics"(p.535).It involves the deliberate investigationof"one's own action"in solvingthe problem.
Wheatle y (1992)summarizesthe powe r of reflectionwhenhe statesthat"perso ns who reflect have greater control over theirthinking and candecide which of severalpathsto take,rather thansimply beingintheaction"(p. 535).
Inaddingsome extrasubstance tophilosophical approaches to reflection. Krulik and Rudnick (1994 ) identifyfive elementsofeffective reflectio n. Theseinclude:
1)test the reasonablenessand practicalityof the answer,
2)writeasummary paragraphabo utthe problem andits solutionincluding thoughtprocesses andfalsestarts.
11
3)findothersolut ions.
4)change thecondit ionsaCthe problem,
5) extendthe problem10 a mathematical fbrmula, concept, orgeneralization (p.334).
Krulik and Rud nick (1994) claim that "engaginginthis process not only improved students critical thinking. but found thatstudentsare motivated by.and enjoy the challe ngeof findingalternate solutions,asking whatif.and findin g a mathematica l express ionorco nceptthatdescri be sthesituation" (p. 338).Inthinki ngabo ut one's thinking, students clarifytheir thoug ht processes and focus their directi onfo rfuture pro blems.Itawakens thest udenttodiversitythat existswithina probl emand the attemptswithwhichit maybe solved. Whenreflectionisdoneinsma ll groupsor in whol e class sett ings, stu dents ben efitfromotherstudent 'sinsightsandappro ac hes.Such discussions canalso be enlightening toteachers andhelpshape their future instructional activities. Cobb. Bou fl,McCla in.and White nack (1997) speculate thatthereis a relationshi pbetween"reflecti ve discourse and conceptual development inmathemencs"
(p.265).Fo r theteacher, "analysis ofreflecti vediscou rse clarifies how teachers might pro actively suppo ntheir studentsmathe mat ical development"(Cobb et
at.
199 7,p.274) Teach ers andstudentshave a role topla y ineffecti ...e reflection.TheCurriculumand EvaluationStandards/orSchool Mathematics (NCTM.
1989) encouragestudents "to exploremathematics. to gatherevIde nceandmake conjec tures, and toreason andcommunic ate mathematically aslhey discuss and write ideasthat usethe language of mathemati cs"(p.vii).Theseacrivlries cha nge theroleof the teac he r from thatofan informationdispe nserto thatofa facili tat or.The emphasis isnot
on showi ngthe students the correctway,but onhelpingthem to formulatean acceptable, usable and validwayto managedata-The teacherwill needto pay careful attentionto stu de nts'smallgroupand wholeclass prese ntations.Throughreflectionon theseevents, theteacher win determinethedegree towhichstudentshave formed appropriat e interpre tations of therequiredconcepts.
As partoftheteacher'spreparation,teachersmustrecognizethat"th e only thing thatispred ictablein teac hing is that class roo m activitieswill not go aspredicted"
(Simon, 1995,p.133).Carefulattentionneeds to be givento thebackgroundof thegroup andthelearningexperienc esthey haveenco untered.Listening to studentswill be a key componentof assessingtheirunderstanding(Simon,1995, p.141).Whenthe stu dentsare learni ng the mathematics,the teacher shouldbe learningaboutmathematics,learni ng, teaching, andthemathematical thinkingofhis or herstudents(Simon,1995,p. 14 1).
Throughsuch attention and reflection, theteacher preparesto directdiscussions that help direct stu dents toappropriateconstructions.
Overview ofProject
Stude nts todaylivein anever-changingtechnologicalsociety.It isno longer sufficientfor them toleave schoolsimplybeing ableto read,write,and do arithmetic.
The NCTM (1998) claimthat a legit imat eneed has beenidentified forthe respo nsible use oftechno logywith the aim of enriching studentlearning.Traditionaldidactic method s and chalkand talklectu rescanno longerstandas the onlyorevenprimarymedi umsof instruction.Studentsneedtobefreeto explore andconstructtheirownmeanings from thelearning environment.This enviro nment needs to includecurriculumspecific
activitiesand dieappropriatetechnologiestoallowthemto investigateandmeetthe prescri bed course objectives.
Amongthe objectivesof theDataManageme nt unitofCou rse I.levelY, Teacher'sPilot Draft Guideli nes:Atlamic Canada Mathemati cs Curricul /lm.students are requ iredto:
I. Calculateldetenninemanu allyandwithtechnol ogythe mean, median , mode, range.
andstandarddeviationof aset of data.
2. Use the mean,median. mode,range.andstandarddeviationtodescribeaset of data 3. Produce/createmanually andwith techn ologytables" scatterplot s,stem-and-leaf
plots. and histograms for thepresentationandinvestigationof data.
4. Use interpolat ion.extrapolation.andthe equationto predictandsolveproblems . 5 Use theregressionanalysiscapabilities oftechnologyto determinetheline of bestfit.
6. Developan intuitiveunderstandingofcorrelationandthe correlationcoefficie nt.
Through a series ofsix:activities.thisprojectprovides students withopportunities to learnandinvestigate thepreviouslymentioned conceptsof statisticsasthey learn various featureso fMierosojt Excel97.Stude ntswilluse Excel as atool to free them fro m time consumingandtedious calculations.This willenable themto havemoretimeto exploreand conjecturebasedontheir observa tions.Excetwill allow themtoproduce profess iona llooking charts andtables sothat they can illustrate andsupportor disprove their conject ures.
ClamQQffiClimate
Theactivitiesarecreatedwiththe assu mptionthatstudents will haveaccesstoa labcontainingappropriatetechn ology.The natureoftheteaching/ learning environment
mayvarydependingupo n laboratory constrai nts.Itis suggestedthatstude ntsengage in each activitythrougha cooperati velearning atmospheredevelopedby theteac her.Fo r example,in myteaching envi ron me nt, each computer lab isequipped with 20 computers andthereare 30to35students ina typicalclass. Acomput er wouldbe assigned to each gro upof 2or3 student s with extracomputersavailable inthecase of breakd o wn s.Each groupmemberwould alternateturnsenteri ng data and commandsintothe computer . Studentswould discussthe relevantquestionsat the endofeach activityin anattemptto arrive atsolutions agreeableto both memb ers.Atthe conclusio nofeach activity,each group wouldthenbe invitedto share/present theirfindings and insightswiththewhole group fo rfurther discus sio n andanalysis.
Theseacti vitiesace notintendedto entire lyreplaceregul ar classroominstructio n.
Priortothe laborato ryexperience.sometraditiona linstructionrela tingto the relevant statisticsconcepts mayberequired.Instead, the laboratoryactivitiesare intended10 be usedmorelike sciencelabs. Theyprovide amedium forstudents tolearn, explore, reinforce, and apply statisticsconce pts.
Note to theTeacher
The activities thatfollow are intend edto provide hig h schoolteacherswitheasily accessible materi als that willmake theintegrationof technology less threaten ing.This resourcefeaturessixactivitiesthatappear inteacherandstudentvers ions.Both copies maybereproduced forclassroom useprovidedthat acknowledgementis giventothe author.
The firstsetof activit iesencounteredis theteacher ' s versio ns.Each activit yis precededbyan overviewoftbe activit yandtheobjectivesitintendsto address.The
actualactivities that followthis include additionaldetailsthat are inte ndedto help troubleshoot someofthe tec hnical problemsthatmay arise.Obviously,it is impossibleto predictallsuchproblems .
Anaccompanying set ofstude nt activity sheetsisincludedin Appe ndixB.The studentsheetsadd ressall the sameideasastheteacher sheetsbutsome ofthe extra explanationis omitted.Asbothsetsof activitiesprogress,some previo usly add ressed Excelcommandsand procedure saretreated as assum edknowledgeIf the userdecidesto skipanactivity,theyshouldbecarefulto ensurethattheflowof the activitywouldnotbe interruptedby a lac kofprerequ isiteExcelknowledge.
SequencingtheActiviti es
Tea chersandstude nts shouldread through theBac:kgnJund10Excet(see AppendixA) befor e comme ncing theact ivities.Thebackgr ound readingis best donein thelab wheretheusercanopenExceland viewtheitems discussed.Theteachermay chooseto guidethe studentsthroughtheintroductorymaterial.
Theactivitiesthatmakeupthisprojectaredesignedtoaddressthe conceptsinthe orderthatthey occur in thecourseobjective s.Many ofthe activities arebased on the data collectedinthe first activity withpreviouslyintroduced £:ccelcommandstreatedas assumedIc.nowledgeinlatt eractivities.Itis notnecessarytodo all 6activitiesnor do themin order.Thefoll owing is a summaryofrelationshipsbetwee ntheactivities-
ActivityIisa prerequisiteto alloftheotheractivities.
Activity 2 usestheChart Wizard andisa prerequ isiteto activities5and6whichare independent of one another.
16
Act ivitiesI,2,and3presentlyuse the samesetofdatafor alloperationswithactivity 6 revisiting thatdata for funheranalysis.
Activities3 and4are independent activities
The following flow chan summarizes the suggested sequenceofthe activities bynumber:
Thedegree to which these activitieswill meettheneeds of a teacher willvary based on hislherown strengths andthose ofthestudents.lndividualteachers mayfeel thatother teach ing methodologiesare required to meet the object ivesof the curriculum.
For this reason, theinstruct ions are intendedonly to help focus student direction.
AJthough not specifically addressed in the activitiesthat follow,homeworkcomplements classwor kandshould be aregu larpartof this unit.The prescribed textbook can be used aloneorinconjunction withExcel to reinforcetheobjectivescoveredin thisunit.
Noactivityshouldrequiremorethan two hours oflab sessions,however the qualityofcompute r hardware mayinfluencethistiming .The activities ofth isprojectare devel opedusingExcel91 in Windows 95.Inadditiontoensuringthe appropriate software
is available,theteachershouldchecktheToolsmenuofExcel to ensureSta tis tica l Ana lysisis installedasan option. Thisparticular functionis optionaland oftenleftout whenMicrosoftOffice is installed.Check withyourlocaltechnology expert, especially if thecomputers areon a network.
Evaluati onPlan
At the endof every unit,thestudentswillneed to undergo some sumrnat ive evaluation.At this point, a knowledge ofExcelis notlistedas aperformance objectiveof the DataManagementunit.However. sincestudentsare required to integrate technology intotheanalysisofdata, some items thattest such knowledgemay belegitimate.
Thissetofactivitiesisintendedtobe aresou rceto teachers. Ifit is to be accep ted as appropriate, itshould be subjectto someformof formativeevaluation.Through reflectionontheuse of theseactivities, theuserwill beable to shapethese activitiesinto a better resou rce orjustifyatotal rejectionofthem. Some questionsthat may help direct this reflectiveevaluation process are offered here:
Weretheobjectives/activitiesprese ntedto studentsina suitablesequence?
Werethecourse objectivesmet?
Was studentperformanceontestingimproved,decreased,or thesame?
Was the instructionsuitedto the leve l ofthestudents?
Howwere individ ualdifferencesaccommodated?
Couldthecourse objectivesbemoreapp ropriatel y metthroug hother techn ologies?
Was theresufficientcomputers to conduct each activity?
Was a reasonableamountoftimeallocate dforcompletingthe unit?
Wasthereampleclass timeto complete each activity?
Should some activitiesbe omitted?
Which activities bestmettheeduca tionalobjectivesofthecourse?
Was the method oftesting students appropriate?
These and many morequestionsshould be carefullyaskedandansweredin the searchfor an approp riatemethod tointegrat etechnologythatenhances st udents learn ing and developme nt.
Da ta Man agemen t: A Set of Activities in Excel
OverviewofActivityI
Inthis activity, stude ntswilluse a surveytogather data on studentage, grade level,hoursa weekstudying math,mathaverage.height,andability toshoot freethrows inbasketball.Thisactivitywillintroducestudents to entering datainto a spreadsheetand explore someof itscalculation capabilities astheyapplytothe study ofstatistics. This datawillbe used forfutureactivitiesandwillneed tobesaved.
~ Statistica ltopics
Studentswill collectandorganize data. They will analyze thedata using meas ures of central tendency (mean, median, mode),maximum/minimumvalues,and range.
Mathernatica lthinking
StudentswilluseExcelto analyzedata and arrive at definitionsfor eachofthe mathematicsterms aboveandoutlinehow each is found.They will also be encour age dtomakeinferencesandconjecturesbasedon thesecalculat ions
Students willlearnhow toentertextanddata intocells,save, andprinttheresults.
UsingExcel.theywillperformbasic calculationsand functions suchas MAXIMUM,MlNlMUM ,RANGE,AVERAGE (mean),MEDIAN,and
MODE.Thecopy andfilloptions will be usedto apply fonn ulas and functionsto adjac entcells. Theso rtfunct ion willalso beemployedtoarrange data toassist analysis
Activity1 Part \.Prepa ringtocol!ectandsavedata
Prese nt students withthe followingsituation:
Your consulting firm has beenasked togatherthe followingclass data for futureanalysis:name, age, gradelevel,hours spentstudyin gmath (wee k),mat h average ,height (cm) ,andbasketball free throw ability.Answerall questions hone stlyandtakestepsto ensureaccuratemeasurements .Eachstude ntattempts ten basketsand you recordthe numberof successes
Distribut eaclas s list of student names andopenExcelfrom the startmenu as befo re.Fo r consiste ncy,move tocellBIand typethe titleSTUD EN T PROFlLE.Notice thatthewordsalsoappearinthebloc k tothe rightof the Na me Box.Thisbox: iscalled theFormulaBar.Pressing ~or one ofthe arrow keyswill nowassignthese words to the cell81.To edit thiscellyoucan move to it, retype the entry andpress ~.This replaces thelastentry.If the mistakeisminor, the ndoub leclickon thecell. No w youcan edit thetyping and press~tohavethe change acceptedExcel,likeword processo rs, alsohas a spellchecker for tidying mostof thisup at theend.
***ActivityI is an adapt ationof anactiv ity fromanarticleen titled"Ex ploring Mean ,Medi an , and Mode with a spreadsheet "byWilsonand Kr apel (1995).
Now let 'sname thecolumns.Ince llA4typeName. Someheadin g s maybe two wordsso you may like to enterthe words in two rowsas be lowinBJand84orCJand C4for example.
NAME JohnDoe
A '
Present Hrs. Stud Math He iht Baskets
Grade Math wk) Avera e cm) (110)
Kee p theheadingsshort but descriptiv e. lfnames are toolo ng for the formattedcell,do not worry. To fix this.beg inbymo v ing the pointerto the verticallineat the right of the columnletter. Whenthe plus signchang esto apair of vertical parallel Jines, double click it.The columnis now formatte d to thewidthof the lo ngest entry.Proce ed to enter the othercolumnnames. Enter the student names under NAMEin cellsAS,A6, etc.
When you have completed thisexercise, save the work forfuture reference. To help organize your work, you shouldcreatea folderto store all relat ed files.Click the disk in the upper left corner and you will get a'Sa veas' message.Click thethird folder to therightto create anew folder to store yourExcel files.In theNewFolderscreenthat appears typeExcelFiles inthe~box and clic k OK.A new folder wil lappear. Click thefolderso it appearsin the~box.Name yournew workbook by typing Student Profilein the !File namel boxat the bottomand clickSave. The workbook is now savedin yourExcel Files folder asSeude ntProfile. You should save your workregular ly.
Nowtosee what your file will looklike,go toFileand selectPrintPreview.
Notice that thereare no lines to work with.andyoumay be missing a colu m n.Select ,!;;;Iose.To get a grid, selectthe range inwhich. you want thelines beginningwithAJ
SelectFormat, Cells,and Border.Click Outline,Insid e,and selectOK.Preview your document andobserve thechanges. Wereyou missingacolumn? Selectblase.
[fyouwere missing a columnon thissheetit meansthatitwouldbeprintedon the next:page.Thiscansometimes be avoidedbyorienting the paper sideways usingthe landscapefeature .SelectFile,PageSetup,Page,clickLandscape,andOK.This turns thepaper on its side sothat morecolumnscan be displayed .Preview yo ur doc umentand observe the changes again.
SelectPrintand noteyou roptionto printthe entire documentor just selectpages Fornow, selectOKandyou willhaveasheet withwhichto collectdata.Re memberto save before youexit.Toexittheworkbook,selectFile,Close,andusuallyhitYesif you madechange sthatyou wanttosave.Thenclick the @inthe upper right corner ofthe screentocloseExcel.
Congratulations, youhavejustopened,formatted,saved,and printed a potential worksheet.Forthebegin ner,thisisnosmalltask.Inthe nextphaseof theactivity, stu dentswillgather data and beg inthe analysis of it
Part2·Collectingandenteringdata and formul as
Dividethe classinto groups of threeandhave themcollectandrecord the data in the table they created.Ateam leaderwill needto beselectedornominatedto direct the activitie s ofeac hgroup.Whenthis processis complete,direct studentstoopentheir Excelworkboo k and begi nenteringtheir data.For consistency, allstudentswill needthe sameclass information so they will needtosharetheir datasheets untiltheyeachhave therequireddata.
Next.skipa row andenterthe staristjcalterms to be investiga tedincolumn Aas below:
"
B C EC30 Maximum
31 Minimum
32 Range
33 M Av
3. Median
35 Mod.
36
lnthe celladjacentto thewordMaximumenter-ma xa(BS:B20)and press
~Thisassumes that8.5isthefirstelementintherange andB20is thelast.The equalssign,"=",tellsExcelthataformulaorpredefinedtasklikemaxawillfollow.After thetask, openbracketsto enterthe range of ce llsthatcontainthenumericaldata separatedbyacolonandclosethebrackets .Whenyou openthe bracketsyoucanquickly definetherangebyhighlig hting it withthemo useandclosingthe bracketatthe end.
In thecelladj ace nttoMini m umenter=m ina(B.5:B20)and press~Inthe celladjacenttoRangeenter "83D-83 1andpress ~Inthe cell adjacenttoMean enter -a nra gc(BS:B20 )and press~Inthecelladj ace nt toMed ian ente r
"'median(BS:B20)andpress~Inthe celladjace nt toModeenter=modc( B5:B20) andpress~Carefully study thenumbersthat appear.
Youwillalso wanttocalculatethesevalues for theothercolumnsof data.Wecan takeadvanta geofExcefscopycommandtosavesome typinghere.First,highlight the rangeofcellsthat wejustenteredformulasinto.Next,clickthecopy iconarthe topof the page nexttothescissors and a dashedbordersurro undstherange ofcells. Highlight
the entire rang e of ce lls that wili ltoidthe informat io n andclickthe pasteicon(nextto copy).£reefperform sthe samecalcula tionsoneachofthe othercolumns.
Add so mecusroreiz ano n to your worksheet bydou ble clickingtheSheet1tabat the botto mofthesheet. The wordShee t1 willbehighlig hted.Simplytypea new titlefor thepage likeIn itia lDa taandhit~Sheet I is now ca lled Initia lDa ta. Savethistile replacin g the previo uswo rksheet.Printthe sheetand submitit with yoursolutionsto the questions in pan 3 of this activity.
Next,makea copy ofthe originaldata.Hig hlig ht all thecells usedin theInitial Dat asheet andclick thecopy icon .
y-
ou can also select co pyby clicking the right mouse buttonandselecting it from themenuthat appears.Selectthe She et 2tabat thebottom of thepageandclickpaste.Allthedata is nowtransferred toSheet 2.Renamethis sheetas 'Wo rking Data'.fee lfreetoalterthisdata as you answer the questionsin pan3At times,itmay be easierto analyzethedata byso rtingit usingsome criteria High light theentire range of data below the column headers(donot includethe calculat ionsyoumade orthe headers).SelectDa taandSort.In the So rtdialoguebox clickthedownarrow inthefirstSort bysectio n.Each afthecolumn header s will be there.Se lectAgeandOKSon again and as oftenas you pleasebut rememberto highlig ht the entire range sothatthe overall arrangement of datais preserved.
Pan3·Analyzingthe data and mak ingconclusions
Basedon thedata, write a definitionformaximum,minim um,and range 2. What relationship existsbetween maximum, minimum,andmea n(avg.)in each
ofthe columns?
Whatwillhappen10the maximum,minimum, and mean(avg.)ifoneofrhe entriesis changed10 zero?Wha t happens ifone valueismade extremelybig?
Lookatthe sorteddata values inrelationtothe valuethatrepresentsthe mode.
Writea definitionformode.
S. Lookatthe sorted datavaluesin relat iontothevaluethat represents the median.
Write a definitionformedian
6. Chang e a datavalue to zero or toan extremelylarge number.Whateffect does th.is have onthe mode andthe media n? Isthisconsistentwithyour definitio n?
7. Experiment and changesome datacle ments. Explain howthe media n issimilarto but differentfrom themean .
Which. single descript ivestatis tic - maximum,minimum,range ,mean,median,or rnode .bestdescribeseac hof thecategories?
9. If studentshad beenasked to namethe ir favorit e span,couldeither of mean, median, or modebeusedto describe the resultingdata? Why?
•••••Re me mber-to submit a copyofyo ur Initial Data sheetwithyour work.
21
Overvi ew ofAct ivity2
This activityuses datagatheredintheprevious activity.Itwillintroduce students tothe graphingcapabilit iesof a spreads heet.Theywilluse these graphs to explore relationshipsamong:pairs of items .
StatiSIiCj!!topies
Studentswill createlinegra phs,ba r graphs.andsealter plou. They willuse thesegraphsand the statisti calcalcul ationsdonein thepreviousactivityto discuss andmakeco njectu res onpossiblerelationship s amo ngdata.Samplesizeand populationwillalsobediscussed.
Mathematical thinking
Thestudents will analyzethe graphs andthestatisticalcalculatio ns.Theywill makeinferencesandconjectureson potential relationshipsor trendsbetween pairs ofitems .
Students willlearn howto createlinegnaphs.bargraphs.andscatt erplou usingtheChanWIZard.Theywill add titles, fo rma ttitles ,define axis,change scales onaxis,andpositi onand sizechartsintheworksheet.Students willalso copythechartinto a brieffonnletterinMicrO_foilWont.
Activity2 PaaI Crea ting andeditinga chart
Presentstud entswith the following situation:
Is therearelat ion s hip between study time andmat hgrades?Disp laythese relations hipsinasepara tebar graph,line graph,and XY scatter graph.Yo ur companywouldlikeyoutosummari ze yourobservationsandincludethemwith thecharts ina brief writtenreport.
OpenExcetand open the fileStudent Profile. Now copythe original data to Sheet 3. Click theInitialDatasheettab and select entirerange of data. Selectcopy;
clicktheShee t3 tab at the bottom of thepage and clickpast e.
Create thechan.
UsetheChar t Wiza r dto createthegraphs.This function leadsthe user through a simplyfour-ste pprocedure. Beg inby highlighting the range ofcellsto be includedin the chan.To graphHou rs of StudyversusMarh Average,highlight theentire range of data includ ingthe column titles incolumns DandE.Whenthe ranges are not adjacent.
highlightonera nge,press andhold the controlkey~andhighlightthe other range With the rangeselected,click theCha rt Wizardicon.If the Office Assistant offers help, clickNO.TheCh a r t Wizarddialogueboxindicates thatthis is 'stepI of 4- chart typ e'.ClickColum nfro mthe list thatappears and the types of columnchartswill appeartotherigh t.Selectthecharttype'clustered column,compares values across catego ries' andthen ~.
In step2, you are asked for the chansource data. The range you selected is alreadyinthe blankopposite!!at arang e. EnsurethatColumns is selectedinthe'S eries in'sectio nandclick~.
Step3 allowsfor some customizing of the chart. SelecttheTilles tab from the above list. For thetitle enter'Math Avg. versusHours Study (wk)'.Similarly,labelthe x- axis 'HoursStudy(wk)', the y-axis 'MathAvg.',andclick ~.
Thefinalstepsimplyasks if you desireto havethe chancreated on its own page orplaced inthe presentsheet.Select'As objectin'and~.The chan willappear on top ofthe datain your worksheet.Clickandholdthe mouse button on a whitepan of the chart.Whenthe poin ter changes to a four-direct ion a larrow,you can dragthe chan to anotherpart of the worksheet. Place it directlybelowthedata by dragging the border.
~
To edit the chart, clickthe white area of the chartwindowand the chanEdit window is activated.You may then click on any objectin[he chan to activateit.When activated, the objectwill have handles(sma llblack boxes) around it This allows the user to makeany desiredchanges.
Click on the upperright handleof thechartand drag theborder so that it rests in the upperright cell one row below the data. Next, clickon the lowerleft handle and drag the border to make the chart six rows and six columns larger.
We can also changefonts and movetextinthe chart. Activate the Editwindow and click thetitle(aframe will surroundit ). SelectFontSizefrom the menu above and choos e14.Next clickon the frame andmo ve it to thecenter.This canalso be done with the labelsontheaxis
The scale that appeared on the axis can alsobe modified.Clickon thevertical axis andthehandlesappearagain.Next.clickthe rightmousebutto nand selectFormat axisSelect the Scaletab.Tum offthecheckmarkinMajorunitandtype10 inthe blank.Turn off thecheck mark inMinor unitandtype 5in theblank.SelectOK.
You mayalso want to highlightthe axis and add gridlinesto help the reader interprettheresults.Activatethe verticalaxisline and click the rightmousebutton.
SelectFor ma tand thePalternstab.ClickAxis,Cust om.selectWeight,click the thick line.andOK.Repeat this process for thehorizontal axis.To get gridlines.click the white area of the chart window to activate it.Clickthe rightmouse button andselect Chart Options.Selectthe Gridlines tab.The horizontal axisisCategory (X)axis.Selectonly theMinorgri dlineshereand in theValue0')axis. Select OKand dosethe Edit windowby clicki ngoutside the chart. Saveand printyour work.
Changesomedatavalues.Notice thatthe chartis automaticallyupdatedtoshow the change.When you exit,answerNOwhen askedifyouwant to save changesto the worksheet.This will preservethe originaldatafor thenext activity.
Part 2:Creatingline graohsand scatte rplots
Follow thesetof instructionsfrom PartIto createa Line chart ofthetype 'Line with markersat each datavalue' andplaceit underthe previousone.Similarly.createa XV(Scatter )chart of the type'Scatter,comparespairsof values'. Use onlythe formattingyoufeelis necessarytoclearlydisplaythedata
Copy your charts toanew page inthe workbook. Arrange the charts so thatthey can allbe printedonthe same page (fit them in betwe en the dashedlines).Youwill have to fit thecharts into thisspace.Save andprintyour work.
1I
Part3:Intem ret ing and presentin gyourfindi ngs
The followingquestionswillbeansweredin paragraphform and thesolutions typedinMicrosoft Word.This is a wordprocessingprogr am thatworks muc hlikeExcel forformatting,saving, andprintingadocument .Aspart of yourresponseto ques tion number three, youwillbe askedto copyand paste a chanintoyourwork.
To copythechart,minimizeMicrosoftWordby clicki ngthefirst of three box e sin the upperright comerwithaflat barinit.Open yourExcelfileas usua landclickthe wh itepan of the chartyou want.SelectCopyanda border appearsaround the chan.
CloseExcel andreactivate yourMicrosoft Word documentby clickingonitinthe sta tus barby thestartmenu atthebottom of the screen.Move to the location that you want the chart andselect paste.Do not worry about the appearanceor formattingof yourworkin Microsoft Word.Finishtyping youranswers, thensaveand printyourwork.The questions areas follows:
Describe any relationshipsyou feelmayexistbetweensuccessin mathema tics andhours of study,Do thiswithout looking at the datayoucollected 2. Inlookingatthe raw dataalone(notthe charts),describewhatyouobserved that
supported or wentagainst yourideas of a relationship?
3. Of the three types ofchartsexplored,whichdoyou feel bestdisplaysand supports yourideas? Why?
4. The sampleofdatacame from yourclass. Couldit be used todescribe all the students in theschool,theprovince,orCanada? Supportyour views in each case withsome logicalargu ment .
Overviewof Activity3
In this activity.studentswillusedatagathered on student math averages to create a stem-and- Ieaf plot.Theywillalsocreate histogram s ofthe respectivedata sets for comparison to stem-and-Ieafplots.Chartswill alsobe discussed inrelationto calculationsinvolvingmean andstandard deviation.
~ Statistica ltopics
Studentswilluse a stem-and-lea fplotto organizedataand create a histogram Theywill analyz ethe data withmeasuresof centraltendency(mean,median,and mode).
Mathematica lthinking
Studen tswillcreatea stem-and-leafplot to organizedata in bins (groups) by order of size. They will investigatehow this plotcan be used to arrive at numerical valuesformedi anand mode.Students will comparethis chanto ahistogram
Studentswill lea rn howto Insertnewpages into a workbook., changecellwidths on a sheet,and formatarange of cells . They willuse the cut. paste,andsort functionstoorganize the stem-and-leafplotforco mparison to a histogram.The Data Analysistool bar will be used tocreateahistogr a m
Jl
Activi ty 3 PartI'Creating theSte m-and-Leaf Plot
OpenyourExcel workbook.Toenteranewsheet. selectInsertandWo r ksheet Adda coup leof sheets while youarehere. Click theSheet4 tab tobeginworkingon a new sheet.Change thenameto Stem-and -Leafplot.
A stem-and-leafplotallowsfororganizingdata intoclasses for analysiswhile pre servin gtheoriginal data values.Inthisact ivity, wewilluse the math average data collectedfor Act ivity I.Thedataare marks outof100so thesterner fixed itemsinthe dataare the tens digitsTypeLeavesincell AIOandtypeStemsinAILIncolumnsBII, ClI,011,...•Lll,enterO. 1,2,... •toas below.
Leaves
Stems 0 1 2 3 4 5 6 7 8 9 10
Theste mlabe ls representthe intervalslike a to 9, 10to19.and 20to29respec tively.To separateLea vesandStemsas above,select the rangeAIItoLII forformatting.Select For ma t,Cells,Bor de r,and doubleline inLineStyle.Clickonlythetopborder andOK.
To record a data value,we now enter theonesdigit abovetheappropriate te ns digit.Forexa m ple.if 34 werethe firstdat a value,enter4above thestem 3.For 30, you placea
°
above the 4in the 3stem.An85 wou ldresult ina5 overthe 8.Continueto enter thedatainthis manner.Part 2· Formattingthestem-and-Ieafplot
Startingin rows10andII shouldallowyouto do most stem-and-lea f plots witha smalldataset.If youneed more rows, simplygo[Qrow I orany placeabovethe highest entryandselectInsertandRows.
To close upthe spacebetween thecolumns, move themouse pointer to thelineto the left of each columnletter.Whenthepointerchanges to a setof vertical parallel lines, clickit.Thecolumnisnow formattedto thewidthofthe longestentry in the column.
It is often easier to readthe chartwhenaverticallineseparateseachcolumn.
Higblightthe range of cells fromBi ltoLItandupto highestrowused.SelectFormat, Cells,Bord er, anda solidsinglelinein Line Style.IntheBorder section ofthis dialoguebox, selecteach of thevertical lineoptions andOK.
Select File and Print Preview to viewthe results.Close.In cell AI,enterthetitle
"Stem-and -IeafChan forMath Averages".Selectany cellin theupper right corner of the page and enter yourgroup number and thenames ofthose in yourgroupinthe cells below.
Part 3:Drawin g aHistogram
Excelwill automatically sortdata into severalpredefined ranges to createa histogram.To controlthe bin widths for the sorting of data,youmust planahead.For now, sort thedatavalues in the intervals (bins) of 0 to 9,10 to 19,20to 29, ... ,80 to 89, and90 to 100.Returnto yourInitial Data sheet. Go to columnHand enter the heading Bin Widthin cellHI.To get thedesired class widths,enter9, 19,29,39,49,59,69,79, 89 belowin the respective column Hcells.
The histogram is not containedintheChart Wizard.Instead, you must select Tool s,DataAnalysis,Histogr am, andOK. IntheHistogramdialogue box, click in the line forInput Ra nge.Hig hlig ht the set of data valuesin the Math Averagecolumn and the range appears in theInp ut Rang e.You can typethis in manuallyif you prefer. Next, clickintheBinRangeline and highlightcellscontainingthe range values.Before movingto the outputoptions, ensure the Labels box: is not activatedwith. acheckmark.
Excelwill generate appropriate labelsin the output table.IntheOut p ut option s, select NewWorksheetPlyandensureonly Chart Out putis activatedbya checkmark. The histogram and output tablewit!be created on a new sheet in the workbook.Rename this sheet as Histogram I.
Pa rt 4:Fo rmattingtheHistogra m
The histogram can be customizedin much the same way as charts createdwiththe Chart Wizard. Click th.e white area of the chartwindow to activatethe chartEditwindow.
Drag the(ower righthandle to expand the histogramover2 more columnsand 6 rows.
Note the spaces betweenthe bars.What chart does it look like? To removethese spaces, rightclick on any vertical bar.SelectFormat Dat a Serie s,Opt io ns, set theGa p Widthto zero,and click OK.Itnowloo ks like a true histogram.
Fo r some finaltouches,recall some work from the previous activityto personalize thehistogram.Changethe titleof the chart from"Histogram"to "Histogram for Math Averages."Changethelabelon theh.o rizo nta l axis to somethinglike"UpperBin Boundary."Make the horizontaland vertical axis a heavier line.Then,move the legend.
Rightclick onFreque ncy, selectFor m atLegend,Placeme nt,clickBott o m, andclick OK.Now left click andholdto drag itto thelower left comer.
Part 5·Com paring and analyzi n gthe charts
Copy thestem-and -leafplot to thesame page asthehist og ram for compar ison.Go tothe page calledStem-an d-Leaf plot. Highlightthe requiredrangeandselectcopy.
Return to the Histogra mIsheet and select a cell below thehistogram.Selectpaste.Print this sheet.
Answereach oft befollowingquestions:
I.(a) Explain now a ste m-an d-leafplotfacilitatesfinding themod e ofa setof data.
(b) Explain now astem-and-leafplot facilitates findingthemedianofa set ofdata (c) Explai nnowa stem-an d-le afplotcanbe used to quickly add the datafor finding
the mean.
Of mean,med ian, and mode, which bestrepresentsthis set of data? Explainwhy 3. What doesa stem-and-leafplotshowabo ut the data that measures of central
tendency donot?
4. Compar ethestem-and-leafplotyoucreatedto the histogram.What similaritiesdo younoticeand whatinformationis lost inthehistogram?
5.( a) What is thetotal areaunde rthe individu albars that make upthe histogram?
(b) Whatis the areaunder the individual bar fortherange70to 79?
(c) Whatpercent of the totalareais containedinthisinterval?
(d) Ofthe total nu mbe rof values,what percent fall in the range70 to79?
(e) For any interval contain ingvalues,find thearea and repeat(c)and (d). (f) Istherea relationship betw eenthe area of a region inthe histogram andthe
frequency of valuesintheco rre spo nding range? Explain youranswer.
6.(a) What interva ls wouldyouneed tohavefiveequalwidthbins ?
(b) Goback totheInitialData sheetand adju st (edit) theBinWidthcolumnto obtain thesebins.Create anewhistogram onanew sheet as before.Namethesheet Histogram2and printit.
(c) Describehow thiscompares tothe previous histogram.Whichoffers a better pictureof thedata?Why?
(d) Predict whatwouldhappenif youusedabinwidth of'five.
Overview of Activity 4
Inthisactivity,studentswill enter a set of data and use it to investigatehow standar ddeviationis calculated.Theywillthen explore how standardthedeviation measures thespreadof a set of data.
Objectives Statjsticaltopics.
Students willlearnthe stepsinvolvedincalculatingthe standarddeviat ion.They explorethe relationshipmean and standard deviation.They willdiscuss outlier-sa andthe spreadof thedata.
Math emat ical th jnkjng.
Students will follow the process involvedin the calculatio nof the standard deviat ion.They willintroduceoutliersandmanipulatethe datatoinvestigate relationship s between mean and standarddeviation.Studentswill developan understanding of how standarddeviationmeasuresthe degreeto whichdata valuesclusteraround the mean.
~
Students will entertext anddata intocells. They willname a rangeand useit in calculations involvingformulas.Preprogramrned functions forMea nand Standa nl Deviationwill also beused.
Aetivity4 Part \.Pre pari ng to investigate standard deviation Presentstudents withthe followingsituation:
Open a new workbook inExcel and setup a spreadsheetto matc hthe format below:
SuaredDe viation X-Mean
Variance Standard De viatio n
The bestknown methodof findingthe standarddeviatio n beginsbycalcula ting the mean.
Befo re we can find the mean(average),weneed to find the sum ofthe fivedata element s To find the sum,begin by activatingcellBIO.Next,selectInser t,Functi on,and select Stati stical.SelectSUM from theFunctionname list anddickOK.IntheNumberI box, entertherangeB5:B 9manuallyor by highlightingitwith the mouse.Ifthe resulting
...Activity 4is anad ap ta t io nof anactivityenti tled"Discove ring Im po rta nt Statistica lConceptsusing Spreads he ets"byHunt andTyr rell, 1995at http://wwwmiscoventry.ac.uklresearchfdiscusldiscus.homeht ml
dialogue box coversyourdata.clickand hold on agraypartofthebox and mo veitas requiredRepeat this proces stofindthe mean and stand arddeviatio n inadjacentcells 811and812.Theseare found in Sta tistica lfunctionsasAVERAGEand ST DEVP respectively.Chec k that the valuefor themean concurs wit h.your definition ofaverage
You nowkno w thevaluefor standarddeviation witho utany reallabor.Continue the processinits calculatio ninhopesof receivingenlightenmenttowardswhatit measu res. Defining a celLorrangeof ce llswithaname is often helpfulforcalculations The namecan thenbeusedin aformula andthiselim inates alwayshavingto enterthe range.
TonamethecellBllas"mea n", click thecell(orrange).Select thedown arro w in the namebox andtype "mea n"and press~
CaLculatethe deviationsfromthe mean.Click cellC5andtype~B5- m eanand
~Notethevalue. Co py this formulatoC6:C9.Some of thevalues will be positive and somewillbenegati ve. Copythe formulas forSumandMean to theiradjace ntcells and notethevalues.They shouldalwaysbe zero.If'yougetavaluelike7.IIE - ISin this ce ll, itis givingyou7.11X10-15or0.000 000 000 000 007II.Thevalue existsbecauseof roundingby thecomputerforvaluesthatdo notdivideevenly.True.the value isno tzero However, it is close enough tozerothatstudentswill likely acce pttheproperty thatthe sumof the deviatio nsfrom themeanis alwayszero.Thishelpswith the justificationof the nextstep.
Explain to students thatto getaround a sumofzeroso that ausable mean canbe found,we square the deviatio ns.Click cellD5andtype"'{85- mea n)"2and~.Note thevalue. Cop y this formu latoD6:D9 and copytheformu lasforSumandMeanto their
adjacentcellsinDI0andOil.The mean ofthe squared deviationsis calledvari a nce.
Standarddeviationisthe squareroot ofvarianceor squareroot ofthe meanof the squareddeviations .Explain that thiskind ofreverses theprevious squaring.Name celt DII"var' forvarianceasbefore.In cellD11type =(var )" O.5. The valueshouldbe the same as in812.Youare nowreadyto changevalues andinvestiga te howthesechanges affectmeanandstandard deviation.
Part 2:Investigating standarddeviatjon
Changethedata values asrequiredtocomplete eachoft he followingquesti ons : I.(a) What effect does substantially decreasing a valuehaveon the mean andthe
standarddeviation?
(b) Whateffectdoes substantiallyincreasing a valuehaveonthemean and the standard deviation?
2.(a) Isthesum ofthe deviationsfromthe mean alwayszero?
(b) Can allthe deviatio nsfrom the meanbe positive ?Why?
(c) Canallbut one ofthe deviationsbepositive?Giveanexample.
(d) Descr ibe what happensifallthe originalintegersare negative 3.(a) Finda set of fivevaluessothat themean islarger than the standarddeviat ion .
(b) Findasetof fivevaluessothatthestandard deviationislarger thanthemean.
4. For a setof five numbersrecord the mean and standard deviation.Add tento each number.Whathappenstothe mean and thestandarddeviation ?Tryanother number.Is therea generalruleto describethe meanand thestandarddeviationfor addition of aconstant toeach.data element?
5. Recor d the meanand stan dard deviation foranotherset oftive numb ers.Multiply each numb er byte n.Whathappens to themean andthe standarddeviation?Try anothe rnumber.Is ther ea generalruletodescribethemea nandthe standard deviationwheneac hdataelementismultiplied by a constant?
6. Open theinitia ldat a sheetfromactivity1.Co py the data to Sheet3 and name the sheetStandardDeviat io n. Belowthe names incolum nA,label ro ws forMean and Sta n dar d Devi ation.Intheadjacentcells,usetheprede fin edExcel functions to calcu latethesevaluesfor each column.Use tberawdata, mean, and thevalue fo r stan dard deviati on to describe how the data aredispe rsedin relationto the mea n for eachcolu mn.
Overview of Activity5
In thisactivi ty,studentswill enterand analyze data gathered from an accelerated mot ionexperim ent.Stude ntswill drawchartsandperformcalculationsto findthe equation ofthe line of bertfit.They willalsointerpolate and extrapolate information fromthe graphand data in thechan
~ Statistical topics.
Studentswillsquaredatavalues and use thedata to investigate an equation for the graph.Theywill determinethe parameters (slopeand intercept)for the equation ofaline.Interp olatio n andextrapolatio nof information willalsobe investigated. Mathe mat ical thinking.
Studentswill program formulas and perform calculationson data to find the equationfor the line of best fit.Thegraph,line of bestfit, and data willbe used to interpolate and extrapolate information.Studentswillalso manipulate the equation of thefunction.
Studentsenter dataand text into cells,save, and print theresults.They willenter formulasand copy themto other cells.They will applythe statistical functionsof slopeandinter cept.The ChanWizard will beused to createa chart.Charts will be editedand modified.The lineof bestfit willbe inserted.
Activity5 PanJ'Enterthedata and createachan
Presentstudents with the followingsituarlon :
A cart was rolleddown aninclinedplanefor a Merion-Timeexperiment The databelow wascollected.Enterthe datainto a spreadsheet.Use thegiven stepsto findtheline of bestfit forthedata,the equationof the lineofbestfit, and the equationof the actualfunction.Usetheseitemstoextrapolateandinterpolate the informationindicated.
ACCELERATEDMOTIONEXPERlMENT Distancevers usTime Data
DISTANCE(cm) TIME(s)
o
02.1 I
8 2
16 .2 3
35 4
42.4 5
78.3 6
94.6 7
Ferconsisten cywiththese instructions, begin entering theabovedatastartingin cellA I with "ACCELERATED MOTIONEXPERTh1ENT".Do notskip any rows.Your final dataentries should be incellsAllandBll.Activate the Cha rt Wizard,selecttheXY (Sca tt er )chartusing the'Scatter-with datapoints connected by smoothedlines'type, andclick~.ForData Range, highlightthe data in cellsA4toALland click~ Clickthe Cha rt Titleandtype 'ACCELERA TE DMOTION'.Click andenterTime(s) andDistan ce(cm) inValu e(X) and Value (Y)respectively.Hit~SelectAs object inand click~Notewere thevaluesstarton the x-exis.
Wenowneed to inputthe x-vetues.Clickon thegraphtoactivatetheeditwindow and clickonanydata value(itwillchangecolor).Rightclickthemouse ona datavalue, selectSourceData,andtheSeriestab.Now clickinthe X-Va lue s entrybox,hig hlight (enter) the rangeB4:BIl,andclickOK.The truedatavaluesare reflected on the graph
Tomakethe graph more readable,wewill do someeditingas inprevious activities.First, change the scale on the x-axis sothatAuto Maxi mum is 7and the Major Un itis1.Highlig htbothof the axesforemphasis.To addgrid linesto the graph, beginbyclicking on thegraph.backgroundtoactivate it.Rightclickthe mouse, select Cha rt Options,andtheGrid lincstab. SelectMajo r Grid li nesfo rbo ththeXandY axesand clickOK.Size andmove thegraphso that the upperrightcorne r isin cell.'\.15 to preparetoanalyze the data
Part2· Analyzethe dataandredo the chart
Whe nanalyzin gexperime ntal data, wewouldliketohave a st raight-linegraph Thegraphof the data appear s tobe a segme ntofa parabo la. This indic atesthat thex-axis datashouldbe raisedtoa power.Squarethe time incolu mnCto try to geta straightline Enterthe header"T ime!"in column C3.TypeTime2in the cell.Highlight the2, selectForm a t,Cells,Fo nt, click Superscri pl,andOK. In cellC4,type=B4"2.This formulamaythe nbe copied to therangeC5:Cl lasin aprevio us activity.Ano therquick way to copy th.isis to firstselectcellC4.Then, clickonthe sma llsq uare box in the bonom rightcornerofthecellanddrag itdown to cell CI I.Youarenow readytodraw a new graph forDistanc e versusTimeSquared.
Begin bycopyingtheoldchan.Click the chart, select Copy, andmo ve to cell A35andselect Paste.A duplicatechartwillappearforediting.
Toent er the time squareddata, click in the chart to activate theedit window.
Activatethe datapoints andrightclick apoint. SelectSoun:e Dat aand clickinthe X Valuesline.Deletethecontentsof thisline.Enter (highlig ht )therangeC4:Cl land clickOK.Wenow havea straightline,but the scaleon thex-axis onlygoes to7.
For somefina l to uches. editthex-axis tochangeMaximum10SOandtheMajor Un it to 10.The n, weneed to changeTime toTime' inthe titleandonthe x-axis.Double click the cursor after the'e' in time soitappears as a flashing vertical bar.Type a'2' and then highlightit.SelectFormet, SelectedAmTitle,Su pe rsc ri pt,andOK.Repea tthis in the titleanddickouts idethechartto turn off the editbo x.Savethe work.
Pan 3·Getting theequat ions
Togetthe equationofthe functionforgraphone, wemustfirstdeterminethe equationoftheline in theDistance versusTime'graph.That is. wemust getthe slope andy-interce pt (paramet ers) forthe equationofthe line.
The equation of a lineis traditio na llywritten as Y=mX +b where'm're presents slopeand'b 'represents theinterceptofrhey-axis.OurY valuerepresentsDistance0 andOUfXvaluerepresents Time'OfT1.Thefunctionisdefinedbythe equatio n D,.mTl+b.Solet' s find theslopeandinterceptofthey-axls .
MovetocellG3and type'GraphParameters'.Type'Slo pe'inGS.Activatethe adjacent cellOS.SelectInsert.,Function, and selectSutiu ica tSelectSlopefrom the FunctionNam elist and clickOK.ClickinthelineforKnown
rs
and high.lightthe range with.distance data.Click intheKnown X' slineand select the Timeldataand se lectOK.Theslopeis approximately 2.Type"Intercept" in cellG6andmoveto cell 86.SelectInsert, Funclion,andselect Statistical- SelectInterce ptfrom theFunctionNamelist and clickOK.Clickin the lineforKnow n Y's and highlightthe range with distance data.ClickintheKnownX'! lineand selecttheTime~data and selectOK.The interceptis approximatelyo.
The linehas theequation Y=2 X+o.The relationshipbetween distance andtime in the experimentis nowD=2T~.The graph'sslopeof2 is equalto ha lf the acceleration of the ballor the ball'saccelerationdowntheincline is4cmls~.
Part4·{rsjng the equations
The newequationcan now beusedto eliminatetheerrorsthat occurred with the experimen taldata.We can findthecorrectdistancesthecart wouldobtai n on thisincline if experime nta l errorswereeliminat ed.IncellDJ,type'CorrectedDistances '.In cellD4, use the formula by typing-Z· C4.CopythisformulatocellsD5:Dll.The resulting valuesgive the line ofbest fit andcan be addedtothe graph.
To add thelineof bestfit from the data.highlight the valuesin ColumnDand select copy.Clickon thechartarea ofgraph 2 andclickpaste.A new lineofbest fitis placed onthegraph,Excel can alsoadd a line of bestbitto a chart. Clicka pointonthe chart andthenright click the mouse onthepoint.SelectAdd Trendline,choosethe Typetab, clickLinear, and dickOK.Notetheoverlapco nfirms ourwork.
Now for some finishing touches.Movethegraph parametersdown alongsidethe secondgraph.UsePrintPreviewto view your work.Closeand move andsizethe charts sothat it all appearsonone shee t.Type yourgroupnumber and names inthe upper right cells.Save theworksheet.Printitby selecti ngFile,Print,andensuri ng thatActive Sheet{s) isactivated in the printdialogu e box.
Pan 5· Analysis·Extrapolat ionandintemolatio n Answer each of the following:
Usethesecond graphto estimatehow farthe can will travelin 3.5 secondsand in 8seconds. (Hint:Can you changethe verticaland horizontal scales?) 2. How far shouldthecart actuallyrollin 3.5 seconds and in8seconds? [Hint:
Begin inBIZand use the copy commandas required to haveExcel find it) Explainwhat you didto find the values.
How long will ittake the can to travelexactly 80 ern?Ho w long does it take to travel 250 ern?(Hint:UseExcel andstaninDI3.Reme mber,you are solving for timeTinD-2Tl.)
4. For a steeper incline,thefo llo wing data was recorded for a cart rolling down it ACCELERA TE DMOTIONEXPERllvIENT
Distanc e versus Time Data
D1STAN CE(c m) TIME(s)
o
02.9 I
11.5 2
25.8 3
49 .1 4
73.2 5
104 _5 6
14 9.4 7
Use the previousExcel worksheetto find theequatio n of the function againusing the corrected distances.Completely update the charts and repeat each of questions 1,2,and 3.
