NAME:___________________________ Math7.2,Period____________

Mr.Rogove Date:__________

LinearFunctionsandStatisticsStudyGuide1

Statistics Study Guide

Instructions:Thisstudyguidecoversthematerialthatwillbeonournexttestcoveringmostlystatistics.Doyourbestandturninthecompletedstudyguidewhenyoutakeyourtest.Thanks!

SCATTER PLOT Ascatterplotisagraphofbivariatenumericaldata.PatternsinScatterPlots:Ifyoucanseethevalueofonevariabletendtovaryinapredictablewayasthevaluesoftheothervariablechanges,thereisastatisticalrelationship.LinearRelationship:Ifthedatalookslikeitisvaryingalongastraightline,wecansaythereisalinearrelationship.

Non-LinearRelationship:Ifthedataisvaryingalongacurve,orapatternotherthanastraightline,itissaidtobenon-linear.

PositiveTrend:ifthedatamoveinapatternupandtotheright,thereisapositivetrend.

NegativeTrend:Ifthedatamoveinapatterndownandtotheleft,thereisanegativetrend.

LinearRelationship

Chest Girth (cm)

Wei

ght

(kg)

170160150140130120110100900

350

300

250

200

150

100

0

NonLinearRelationship

Shell Length (mm)

Age

(ye

ars)

1501251007550250

4.5

4.0

3.5

3.0

2.5

2.0

1.5

1.0

0.5

0.0

Positivetrendinthedata

x

y

350300250200150100500

5

4

3

2

1

0

Negativetrendinthedata

x

y

35302520151050

6

5

4

3

2

1

0

NAME:___________________________ Math7.2,Period____________

Mr.Rogove Date:__________

LinearFunctionsandStatisticsStudyGuide2

IndependentVariable:thisistheexplanatoryvariableorthepredictorvariable.Thisisthevariablethatisnotchangedbytheactionoftheothervariables.Thisisthex-value,onthehorizontalaxis.DependentVariable:Thisisresponsevariableorthepredictedvariable.Thisisthevariablethatyouaretryingtomakepredictionsabout.Thisisthey-valueontheverticalaxis.Independentv.DependentVariable:Wecanusetheinformationabouttheindependentvariabletomakepredictionsaboutthevaluesofthedependentvariable(y-axis).LineofBestFit:Thisisastraightlinethatrepresentsthetrendinthedata.Thelineofbestfitshouldbedrawnasclosetoasmanypointsonthegraphaspossible.Wecanwriteanequationforthislinebyidentifyingtwopointsontheline,findingaslopeanday-intercept.Theslopeofthelineofbestfitmeasurestheimpactthattheexplanatoryvariablehasontheresponsevariable.They-interceptisthevalueoftheresponsevariablewhentheexplanatoryvariablehasnoeffect.Inlinearmodels,they-interceptmightnotmakesenseinthecontextoftherealworldsituation.

NAME:___________________________ Math7.2,Period____________

Mr.Rogove Date:__________

LinearFunctionsandStatisticsStudyGuide3

BIVARIATE CATEGORICAL DATA AND TWO WAY TABLES

CategoricalVariables:Variablesthatrepresentdataevaluatedusingspecificcategoriesordescriptions.BivariateCategoricalDataisorganizedandsummarizedinatwo-wayfrequencytable.

RelativeFrequency:Adescriptionofthefrequencyoftheoccurrencesofeachofthepiecesofcategoricaldatainrelationtothewhole.Thisisaproportionmeasuredbythefollowingfraction:!"#$%#&'(

!"!#$.

Example:TheproportionofallstudentswhoaremaleANDpreferredsaltysnacksis!"!"or0.17

RowRelativeFrequency:Adescriptionofthefrequencyoftheoccurrencesofpiecesofcategoricaldatainrelationtothetotalofarow.Thisisaproportionmeasuredbythefollowingfraction:!"#$%#&'(

!"# !"!#$.

Example:Theproportionoffemalestudentswholikehealthyfoodis!"!"or0.25.

ColumnRelativeFrequency:Adescriptionofthefrequencyoftheoccurrencesofpiecesofcategoricaldatainrelationtothetotalofacolumn.Thisisaproportionmeasuredbythefollowingfraction: !"#$%#&'(

!"#$%& !"!#$.

Example:Ofthestudentswholikecandybarstheproportionofthemwhoareboysis !

!!or0.82.

FavoriteSnack

CandyBar

BakedGoods

Salty Spicy Healthy Total

Gender Male

9 10 15 5 8 47

Female

2 13 14 1 10 40

Total

11 23 29 6 18 87

NAME:___________________________ Math7.2,Period____________

Mr.Rogove Date:__________

LinearFunctionsandStatisticsStudyGuide4

ProblemSet.2.BelowisdatathatmeasuresminutesNicoleplayedinbasketballgamesandthenumberofpointsshescored.

MinutesPlayed

PointsScored

MinutesPlayed

PointsScored

15 7 12 818 12 23 169 6 15 1221 14 10 14

a.Drawascatterplotofthedataaboveinthespaceprovidedbelow.Clearlylabelyourgraph.b.Whatpattern(s)doyounoticeinthedata?Linearpositiverelationship.It’salsoproportionalsinceitgoesthroughtheorigin.c.Drawalineofbestfitonthegraphabove.Writetheequationforthelinebelow.Showhowyoudeterminedtheequationusingcalculations.Ithinkareasonablelineofbestfitwouldgothrough 12,8 and 18, 12 ,andsotheslopeofthatlinewouldbe !"!!

!"!!"= !

!= !

!,whichwouldmaketheequation𝑦 = !

!𝑥 +

𝑏…substitutein 12, 8 𝑓𝑜𝑟 𝑥 and 𝑦 and you get 8 = !!12 + 𝑏, 𝑏 = 0

Equationis𝑦 = !

!𝑥

d.VerballydescribetherelationshipbetweenthenumberofminutesNicoleplaysandthenumberofpointsshescores.Whatdoestheslopemeaninthecontextofthesituation?Theslopeis2/3whichmeansthatwillscoreabout2pointsforevery3minutessheplays,or2/3orapointperminute.

Time(inminutes)

Points

NAME:___________________________ Math7.2,Period____________

Mr.Rogove Date:__________

LinearFunctionsandStatisticsStudyGuide5

3.ThetableshowsthenumberofactivewoodpeckerclustersinapartoftheDeSotoNationalForestinMississippi.Year 2005 2006 2007 2008 2009 2010 2011 2012 2013ActiveClusters

22 24 27 27 34 40 42 45 51

a.Createascatterplotofthedata.Representthex-axisasthenumberofyearssince2005.b.Onereasonablelineofbestfitgoesthroughthe2007and2011data.Findtheequationofthatline.The2007datais 2, 27 andthe2011datais 6, 42 …sowefindslope:!"!!"

!!!= !"

!.

Now,tofindy-intercept,pluginacoordinateandtheslope:𝑦 = 𝑚𝑥 + 𝑏 27 = 2 !"

!+ 𝑏

27 = !"

!+ 𝑏 à𝑏 = !"

!

𝒚 =𝟏𝟓𝟒 𝒙+

𝟑𝟗𝟐

c.Predictthenumberofactiveclustersin2020.2020is15since2005,sothex-valuewouldbe15…weneedtofindywhen𝑥 = 15.

𝑦 =154 15 +

392

𝑦 =2254 +

784 𝑦

=3034 = 75

34

Thereshouldbeabout76activeclustersin2020.

Yearssince2005

ActiveClusters

NAME:___________________________ Math7.2,Period____________

Mr.Rogove Date:__________

LinearFunctionsandStatisticsStudyGuide6

4.Asurveywasconductedof400peoplethataskedthemquestionsabouttheirgenderandtheirpreferredfootwear.Someoftheresultsareasfollows:• 240peoplesurveyedwerefemale.

• 160peoplesurveyedpreferredsneakers.

• 80peoplesurveyedpreferredheels • 40peoplesurveyedpreferredsandals

• 60femalespreferredsneakers • 78femalespreferredheels• 32malespreferredsandals a.Completethetwo-wayfrequencytablethatsummarizesthedataonfootwearandgender.

FootwearPreference Sneakers Heels Sandals Flats/Dress

ShoesTotal

Female 60 78 8 94 240

Male 100 2 32 26 160

Total 160 80 40 120 400

b.Whatproportionoftheparticipantsisfemale?240/400or.60c.Iftherewerenoassociationbetweengenderandfootwearpreference,shouldyouexpectmorefemalesthanmalestoprefersneakersorfewerfemalesthanmalestoprefersneakers?Iwouldexpectmorefemalestoprefersneakersbecausetherearemorefemalessurveyed.d.Makeatableoftherowrelativefrequenciesofeachfootweartypeforthemaleandfemalerow.

FootwearPreference Sneakers Heels Sandals Flats/Dress

ShoesTotal

Female .25 .33 .03 .39 1.00

Male .63 .01 .20 .16 1.00

Total .40 .20 .10 .30 1.00

e.Ifyouchoseasurveyparticipantatrandom,whatkindoffootwearwouldyouexpectthemtoprefer?Explain.Sneakersbecausetheyarethemostpopularoverall.160studentsprefersneakers.f.Ifyouknowthattherandomlyselectedparticipantwasafemale,wouldthischangethepredictionfrompart(e)?Whyorwhynot?Whatassociationscanyoucanmakebetweenthevariables?Yes,itwouldprobablybeflatsordressshoes.Morethanyou’dthink,womenpreferflat/heels.

NAME:___________________________ Math7.2,Period____________

Mr.Rogove Date:__________

LinearFunctionsandStatisticsStudyGuide7

5.Asurveyof587thgradestudentswasconductedthataskedmanyinterestingquestionsaboutgenderandsalsapreference.Someresultsareasfollows:• 12studentstotallikedhotsalsa

• 11studentslikedmediumsalsa

• 13boyslikemildsalsa

• 6boysdon’tlikesalsaatall

• 15studentsdon’tlikesalsa

• Only2girlslikemediumsalsa

• 9boyslikehotsalsa

a.Completethetwo-wayfrequencytablethatsummarizesthedataonsalsapreferenceandgender. SalsaPreference

Nosalsa Mild Medium Hot Total

Male 6 13 9 9 37

Female 9 7 2 3 21

Total 15 20 11 12 58

b.Whatproportionoftheparticipantsarefemaleswholikedonotlikesalsaatall?9/58or.16c.Iftherewerenoassociationbetweengenderandsalsapreference,wouldyouexpecttofindthatmoregirlsdonotlikesalsaormoreboysdonotlikesalsa?Explainyouranswer.Iwouldexpectthatmoreboyswouldn’tlikesalsabecausetherearemoreboyssurveyedoverall.d.CreateaROWrelativefrequencytableofvaluesforsalsapreferenceforeachgender. SalsaPreference

Nosalsa Mild Medium Hot Total

Male .16 .35 .24 .24 1.00

Female .43 .33 .10 .14 1.00

Total .26 .35 .19 .21 1.00

e.Arethereanyassociationsyoucanmakebetweensalsapreferenceandgender?Whatarethey?Itlookslikethere’sanassociationbetweengenderandthosedonotlikesalsa—ifyoudon’tlikesalsayou’remorelikelytobeagirl.Whilenotasstrong,therelookstobeanassociationbetweengenderandmediumandhotinthatboysaremorelikelythangirlstolikemediumandhotsalsa.

NAME:___________________________ Math7.2,Period____________

Mr.Rogove Date:__________

LinearFunctionsandStatisticsStudyGuide8

6.Inthesamesurveyweaskedstudentsabouttheamountofsleeptheygotandthetimetheywenttobed.Belowaretheresultsinatwowaytable. BEDTIME

Between

8PM-9PM

Between

9-10PM

After10PM Total

Sleep

each

night

Lessthan6 0 0 1 1

Between6and

8

2 18 7 27

Morethan8 8 21 1 30

TOTAL 10 39 9 58

a.Makeaconclusion(basedonmath)abouttheassociationbetweengoingtobedafter10PMandgettinglessthan8hoursofsleep.Writeafewsentencesexplainingyourthoughts.Ifyougotobedafter10PM,you’remorelikelytogetlessthan8hoursofsleep.Whilelessthanhalfofallrespondents(28/58)reportedgettinglessthan8hoursofsleep,thosewhowenttobedafter10PMoverwhelmingly(8/9)gotlessthan8hoursofsleep.b.CreateaCOLUMNrelativefrequencytablebelow BEDTIME

Between

8PM-9PM

Between

9-10PM

After10PM Total

Sleep

each

night

Lessthan6 0 0 .11 .02

Between6and

8

.20 .46 .78 .46

Morethan8 .80 .54 .11 .52

TOTAL 1 1 1 1

c.Basedonyourcolumnrelativefrequencytable,forwhichbedtimecategoryistheretheleastassociationwiththeamountofsleep?Explainthis.Becausethe9-10PMbedtimerelativefrequenciesmostcloselyresemblethetotalrelativefrequency,Iwouldsaythatcolumnhastheleastassociation…Ifyougotobedbetween9-10PM,itprovideslittleinformationonhowmanyhoursofsleepyoumightget.