16
9.4 Relative Frequency
A Solidify/Practice Understanding
Task
Rachelisthinkingaboutthedatasheandhermom
collectedfortheaveragenumberoftextsaperson
sendseachdayandstartedthinkingthatperhapsatwo-waytableofthedatatheycollectedwould
helpconvincehermomthatshedoesnotsendanexcessiveamountoftextsforateenager.The
tableseparateseachdatapointbyage(teenagerandadult)andbytheaveragenumberoftextssent
(morethan100perdayorlessthan100perday).
Averageismorethan
100textssentperday
Averageislessthan100
textssentperday
Total
Teenager
20
4
24
Adult
2
22
24
Total
22
26
48
1. Writetwoobservationstatementsofthistwowaytable.
Tofurtherprovideevidence,Racheldecidedtodosomeresearch.Shefoundthatonly43%of
peoplewithphonessendover100textsperday.Shewasdisappointedthatthedatadidnot
supporthercaseandconfusedbecauseitdidnotseemtomatchwhatshefoundinhersurvey.
2. Whatquestionsdothesestatisticsraiseforyou?WhatdatashouldRachellookforto
supporthercase?
Afterlookingmorecloselyatthedata,Rachelfoundotherpercentageswithinthesamedatathat
seemedmoreaccuratewiththedatashecollectedfromherteenagefriends.
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MODELING DATA—9.4
17
SECONDARY MATH I // MODULE 9
MODELING DATA—9.4
3. HowmightRachelusethedatainthetwowaytabletofindpercentagesthatwouldbe
usefulforhercase?
PartII:OnceRachelrealizedtherearealotofwaystolookatasetofdatainatwowaytable,she
wasmotivatedtolearnaboutrelativefrequencytablesandconditionalfrequencies.Whenthedata
iswrittenasapercent,thisiscalledarelativefrequencytable.Inthissituation,the‘inner’values
representapercentandarecalledconditionalfrequencies.Theconditionalvaluesinarelative
frequencytablecanbecalculatedaspercentagesofoneofthefollowing:
• thewholetable(relativefrequencyoftable)
• therows(relativefrequencyofrows)
• thecolumns(relativefrequencyofcolumn)
SinceRachelwantstoemphasizethataperson’sagemakesadifferenceinthenumberoftextssent,
thefirstthingshedecidedtodoisfocusontheROWofvaluessoshecouldwriteconditional
statementsaboutthenumberoftextsapersonislikelytosendbasedontheirage.Thisiscalleda
relativefrequencyofrowtable.
4. Fillinthepercentageofteenagersforeachoftheconditionalfrequenciesinthehighlighted
rowbelow:
Row
Average is more
than 100 texts sent
per day
20
Average is less than
100 texts sent per day
Total
4
24
__ %
__%
100%
% of Adults
2
8%
22
92%
24
100%
% of People
22
46%
26
54%
48
100%
Teenager
% of
teenagers
SincethePERCENTAGEScreatedfocusonROWvalues,allconditionalobservationsarespecificto
theinformationintherow.Completethefollowingsentencefortherelativefrequencyofrow:
5. Ofallteenagersinthesurvey,_______%averagemorethan100textsperday.
6. Writeanotherstatementbasedontherelativefrequencyofrow:
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SECONDARY MATH I // MODULE 9
MODELING DATA—9.4
Belowistherelativefrequencyofcolumnusingthesamedata.Thistime,allofthepercentagesare
calculatedusingthedatainthecolumn.
Average is more than
Average is less than
Total
100
texts
sent
per
day
100
texts
sent
per
day
Teenagers
20
4
24
91%
15%
50%
Adults
2
22
24
9%
85%
50%
Total
22
26
48
100%
100%
100%
7. Writetwoconditionalstatementsusingtherelativefrequencyofcolumn.
Thisdatarepresentstherelativefrequencyofwholetable:
Averageismorethan100 Averageislessthan100
Total
textssentperday
textssentperday
%ofTeenagers
20
4
24
42%
8%
50%
%ofAdults
2
22
24
4%
46%
50%
%ofTotal
22
26
48
46%
54%
100%
8. Createtwoconditionaldistributionstatementsfortherelativefrequencyofwholetable.
9. Whatinformationishighlightedwhendataisinterpretedfromrelativefrequencytables?
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SECONDARY MATH I // MODULE 9
MODELING DATA—9.4
9.4 Relative Frequency – Teacher Notes
A Solidify Understanding Task
Purpose:Inthistaskstudentswillexaminedifferentwaystointerpretrelativefrequencytables
andwillwriteconditionaldistributionstatementsbasedontherelativefrequencyofrow,column,
orwholetable.UsingdatafromTextingBytheNumbers,studentswillseehowtwowaytablescan
showinformationthatisoftenhiddeninboxplotsorhistograms.Theywillalsolearnhow
conditionalfrequenciescanprovidespecificinformationaboutasubgroupofthedata(callingfor
moreprecisionofdescribingthedata).
CoreStandardsFocus:
S.ID.5Summarizecategoricaldatafortwocategoriesintwo-wayfrequencytables.Interpret
relativefrequenciesinthecontextofthedata(includingjoint,marginal,andconditionalrelative
frequencies).Recognizepossibleassociationsandtrendsinthedata.
RelatedStandards:S.ID.1,S.ID.2.S.ID.3
StandardsforMathematicalPracticeofFocusintheTask:
SMP2–Reasonabstractlyandquantitatively
SMP6–Attendtoprecision
SMP7–Lookandmakeuseofstructure
TheTeachingCycle:
Launch(WholeClass):
Aspartofaccessingbackgroundknowledge,youmaywishtoaskstudentswhattheyremember
aboutthedatafromthetaskTextingBytheNumbers.Thepurposeisonlytohavestudentsmention
datafromRachelandhermom,withcommentsrelatedtothestorythedatatold(specificsnot
needed).Readthescenariofromthistaskandhavestudentsanswerthefirstquestionbywriting
andsharingafewobservationsaboutthetwowaytable(reviewfromthetaskAfterSchoolActivity).
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SECONDARY MATH I // MODULE 9
MODELING DATA—9.4
Asstatementsareshared,writethemonstripsofpaper(canbesortedduringwholegroup
discussion).
Explore(SmallGroup):
Asstudentsworkthroughthetask,listenfortheirconjecturesaboutthedataRachelshouldfocus
ontomakehercase.Afterafewminutes,bringtheclassbacktogethertodiscussthetypesof
relativefrequencytables.Explainhoweachvalueisdeterminedintherelativefrequencyofrow.
Havestudentsworkinpairstocompletethesentenceframesandwriteconditionaldistribution
statementsforeachofthethreerelativefrequencytables.Givestudentstimetoconsiderallthree
tablesandcreatestatementsabouteachtable.Listenforunderstandingofeachrelativefrequency
table.Toassistinwritingsentences,remindstudentstopayattentiontothefocusofthetable
(whetherthefocusistherow,thecolumn,ortheentiretable).
Discuss(WholeClass):
Theintentionofthewholegroupdiscussionistohighlightthefollowing:
•
differencesbetweenrow,column,andwholetablerelativefrequencystatements
•
becomepreciseinourlanguageasweuseconditionalfrequencystatements
•
tellastoryusingtwowaytables.
Onewaytoorchestratethisdiscussionistoselectastudenttoshareaspecificrelativefrequencyof
columnstatementtheyhavecreated(letthemknowthisduringtheexplorephaseofthetask)and
havetheclassdetermineifthestatementisfromtherelativefrequencyofrow,column,orwhole
table.Thenaskastudenttoshareanotherrelativefrequencyofcolumnstatement.Askthegroup,
whatdoesthedataspecifictocolumntellus?
Movetoshowingtherelativefrequencyofrowstatementsandaskwhatdoesthedataspecificto
rowtellus?Continuediscussionwithrelativefrequencyofwholetable.
Toconclude,discussthelastquestionfromthetask:Whatinformationishighlightedwhendatais
interpretedfromrelativefrequencytables?Ifthereistime,alsodiscusshowtwowaytables
comparetootherunivariatemodelswehaveused(dotplots,boxplots,histograms).
AlignedReady,Set,Go:ModelingData9.4
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SECONDARY MATH I // MODULE 9
9.4
MODELING DATA – RSG 9.4
READY, SET, GO!
Name
PeriodDate
READY
Topic:Writingexplicitfunctionrulesforlinearrelationships
Writetheexplicitlinearfunctionforthegiveninformationbelow.
1.(3,7)(5,13)
2.Mikeearns$11.50anhour
3.(-5,-2)(1,10)
4.(-2,12)(6,8)
5.
6.
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SECONDARY MATH I // MODULE 9
9.4
MODELING DATA – RSG 9.4
SET
Topic:RelativeFrequencytables
Foreachtwo-waytablebelow,createtheindicatedrelativefrequencytableandalso
providetwoobservationswithregardtothedata.
7.Thistablerepresentssurveyresultsfromasampleofstudentsregardingmodeof
transportationtoandfromschool.
Walk
Bike
CarPool
Bus
Total
Boys
37
47
27
122
233
Girls
38
22
53
79
192
Total
75
69
80
201
425
Createtherelativefrequencyofcolumntable.Thenprovidetwoobservationstatements.
Walk
Bike
CarPool
Bus
Total
Boys
Girls
Total
100%
100%
100%
100%
100%
8.Thetwo-waytablecontainssurveydataregardingfamilysizeandpetownership.
NoPets
OwnonePet
Familiesof4orless
Familiesof5ormore
35
15
52
18
Total
50
70
Morethanone
pet
85
10
95
Total
172
43
215
Createtherelativefrequencyofrowtable.Thenprovidetwoobservationstatements.
Familiesof4orless
Familiesof5ormore
Total
NoPets
OwnonePet
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Morethanone
pet
Total
100%
100%
100%
21
SECONDARY MATH I // MODULE 9
9.4
MODELING DATA – RSG 9.4
9.Thetwo-waytablebelowcontainssurveydataaboutboysandgirlsshoes.
Athleticshoes
Boots
DressShoe Total
Girls
21
35
60
116
Boys
50
16
10
76
Total
71
51
70
192
Createtherelativefrequencyofwholetable.Thenprovidetwoobservationstatements.
Athleticshoes
Boots
DressShoe Total
Girls
Boys
Total
100%
GO
Topic:Onevariablestatisticalmeasuresandcomparisons
Foreachsetofdatadeterminethemean,median,mode,range,andstandard
deviation.Thencreateeitherabox-and-whiskerplotorahistogram.
10.23,24,25,20,25,29,24,25,30 11.20,24,10,35,25,29,24,25,33
12.Howdothedatasetsinproblems10and11comparetooneanother?
13.2,3,4,5,3,4,7,4,4
14.1,1,3,5,5,10,5,1,14
15.Howdothedatasetsinproblems13and14comparetooneanother?
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