2 Findthemeanofeachsetofdata.

a) 2,5,8,4,11

b) 0,3,9,2,2,11,15,32,7

c) 2,8,5,12,4

d) 17,24,15,42,63,71,7

3 Findthemedianofeachsetofdata.

a) 2,4,5,8,11

b) 2,5,8,4,11

c) 0,11,3,5,2,19

d) 44,40,41,49

e) 17,9,35,3,0,42

Understandanduse the mean,medianandmode

1 Herearefivetowersofcubes.

a) Whatisthemostcommonnumberofcubesusedinatower?

Whichaverageisthis?Circleyouranswer.

mode� median� mean

b) Thetowersareinascendingorderofheight.

Howmanycubesareinthemiddletower?

Whichaverageisthis?Circleyouranswer.

mode� median� mean

c) Thecubesareredistributedsothatthefivetowersarenowallthe

sameheight.

Howmanycubesareineachtowernow?

Whichaverageisthis?Circleyouranswer.

mode� median� mean

d) Completethesentences.

Themediannumberofcubesusedis

Themodalnumberofcubesusedis

Themeannumberofcubesusedis

©WhiteRoseMaths2020

A supporting video can be found at https://vimeo.com/432450580

6 Sixnumbershaveamodeof19,ameanof12andamedianof14

a) Fillinthecardstoshowwhatthenumberscouldbe.

b) Whatistherangeofyoursetofnumbers?

Compareyourrangewithapartner’s.

7 Themeanofthissetofdatais10.5

z+1 0 21 13 21 z 7 8

a) Workoutthevalueofz.

z=

b) Workoutthemedian,modeandrangeofthedata.

median mode range

c) Aninthcardisadded.

Themeanisnow12

Whatisthevalueoftheninthcard?

8 Writeanexpressionforthemeanofthecards.

3x 5x 7x 9x 2x 13x

4 Findthemodeofeachsetofdata.

a) 3,5,1,3,2,9,3

b) 17,11,9,9,17,6,9

c) 26.3,14.1,15.8,14.1,26.3,19.7,20.6

d) 0,1,2,3,4,5,6,7

e) red,blue,red,orange,yellow,green,yellow,blue,red,red,white

5 Themeanofthissetofdatais13

047112135

Doraisworkingoutthemeanofadifferentsetofdata.

158122236

ShowthatDoraiscorrect.

©WhiteRoseMaths2020

I don’t need to do any calculations. I know

that the mean is 14

2 Thetableshowsthenumberoflettersinthefirst100wordsinanew

children’sbook.

Numberofletters Numberofwords

1 11

2 15

3 22

4 17

5 12

6 11

7 9

8 3

a) Circlethemodalnumberoflettersinaword.

8 22 3 4

Foreachoftheanswersyouhavenotcircled,discusswithapartner

whysomebodymightthinktheyarethemode.

b) Circletherangeofthenumberoflettersinaword.

7 8 19 21

Foreachoftheanswersyouhavenotcircled,discusswithapartner

whysomebodymightthinktheyaretherange.

c) Evaisworkingoutthemeanofthedatainthetable.

HowcanyoutellstraightawaythatEvaisincorrect?

d) Workoutthemeanofthedatainthetable.

Find themean from an ungroupedfrequency table

1 Thedatashowstheagesof40peopleatanexerciseclass.

1 7 1 7 1 7 1 7 1 7 1 7 1 7

1 8 1 8 1 8 1 8 1 8

19 19 19 19 19 19 19 19 19

20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20

Annie,AmirandDexterareworkingoutthemeanofthedatausing

differentmethods.

Annie'smethod Addallthenumbersupanddividebyhow

manythereare.

Amir'smethod Workout7×17+5×18+9×19+19×20

andthendividebyhowmanynumbersthereare.

Dexter'smethod Useatable.

Age Frequency

17 7

18 5

19 9

20 19

Chooseonemethodtoworkoutthemean.

Whydidyouchoosethismethod?

Talkaboutitwithapartner.

©WhiteRoseMaths2020

H

1 1 + 1 5 + 2 2 + 1 7 + 1 2 + 1 1 + 9 + 3 = 1 0 01008

= 1 2 . 5

A supporting video can be found at https://vimeo.com/432450753

5 Ateacherasksanumberofstudentssixspellingquestions.

Thetableshowstheresults.

Numberofcorrectspellings 0 1 2 3 4 5 6

Numberofstudents 1 6 8 11 6 4

Theteachercalculatesthatthemeannumberofcorrectspellingswas3.4

Findthemissingdatainthetable.

6 ThreeYear9classessitamentalarithmetictest.

Thetableshowsthenumberofstudentsineachclassandthemean

numberofquestionseachclassgetscorrect.

ClassNumberof

students

Meannumberof

correctanswers

9A 32 23

9B 25 18

9C 20 15

Workouttheoverallmeanforallthestudents.

3 Thetableshowsthenumberofbedroomsin1,000housesinatown.

Thetableisincomplete.

Numberofbedrooms 1 2 3 4 5 6

Numberofhouses 33 124 237 380 186

a) Howmanyhouseshavesixbedrooms?

b) Statethemodalnumberofbedrooms.

c) Findthemeannumberofbedroomsperhouse.

4 Rosieplaysforalocalfootballteam.

Thefrequencydiagramshowshowmanygoalstheteamscoredinitsfirst

twentygames.

a) Findthenumberofgoalsscoredintotalinthetwentygames.

b) Findthemeannumberofgoalsscoredpergame.

©WhiteRoseMaths2020

0 1 2 3 40

1

2

3

4

6

5

7

8

numberofgoalsscoredingame

nu

mb

ero

fg

am

es

3 ThetableshowsMrGlover’smonthlyphonebillsovertwoyears.

Completethetable.

Phonebill,x(£) Frequency Midpoint frequency×midpoint

0≤x<10 7 5 7×5=35

10≤x<20 9 15 9×15=

20≤x<30 5

30≤x<40 3

Completethecalculationtofindanestimateofthemeanofhisphonebills.

estimateofmean≈totalcost

totalfrequency= =

4 Thetableshowsinformationabouttheamountoftimeagroupof

studentsspentonlineoneevening.

Completethetable.

Timeonline,

h(hours)Frequency Midpoint frequency×midpoint

0≤h<1 2 0.5

1≤h<2 12

2≤h<3 7

3≤h<4 5

4≤h<6 4

Completethecalculationtofindanestimateofthemeantimespentonline.

estimateofmean≈totaltime

totalfrequency= =

Find themean from agroupedfrequency table

1 Whatnumberisatthemidpointofeachnumberline?

a)

0 10

d)

11 20

b)

1 5

e)

20 30

c)

10 20

f)

41 50

2 Writethemidpointsoftheclassintervals.

a) 0≤x<10 c) 10≤x<20 e) 20≤x<40

b) 1≤x<10 d) 11≤x<20 f) 21≤x<40

©WhiteRoseMaths2020

H

A supporting video can be found at https://vimeo.com/432450874

7 Thetableshowstheamountoftimepeopletooktogetoutof

anescaperoom.

Time,t(minutes) Frequency Midpoint

0<t≤15 3

22.5 225

595

12 45

50<t≤60 1,100

a) Fillinanymissinginformationinthetable.

b) Writethemodalclassofthetimetaken.

c) Workoutanestimateforthemeantimetaken.

d)

DoyouagreewithMo?

Explainyouranswer.

5 Thetableshowssomeinformationaboutthemassesof30pets.

Mass,m(kg) Frequency

0≤m<2 8

2≤m<5 4

5≤m<10 12

10≤m<15 5

15≤m<25 1

a) Workoutanestimateforthemeanmassofthepets.

b) Writethemodalclassofthemasses.

6 Thetableshowssomeinformationaboutthewaitingtimesatapostoffice

onelunchtime.

Waitingtime,t(minutes) 0≤t<3 3≤t<4 4≤t<5 5≤t<10

Frequency 20 15 8 2

Workoutanestimateforthemeanwaitingtime.

©WhiteRoseMaths2020

I think the intervals should be 0 ≤ t < 15 not

0 < t ≤ 15, so the answer will be wrong.

2 Tommycomestoschooleitherbybusorbycar.

Hecompareshistraveltimes(inminutes)bybusandbycar.

Mean Range

Bus 16 7

Car 12 18

a) Onaverage,whichmethodoftransportisfaster?

Howdoyouknow?

b) Whichmethodoftransporthastheleastconsistentjourneytimes?

Howdoyouknow?

3 FilipandBrettaretrainingfora200msprint.

Thetimes(inseconds)fortheirpracticerunsareshown.

Filip 27 25 26 25 29 26 25 27 25

Brett 25 24 31 32 29 29 27 30 30

a) Whohasthefastestpracticeruntime?

b) Workoutthemedianpracticeruntimeforeachstudent.

Filip Brett

c) Workouttherangeofpracticeruntimesforeachstudent.

Filip Brett

d) Whohasthebestmedianrunningtime?

e) Whoisthemostconsistent?

Comparedistributionsusing averagesand the range

1 Aclasshasaspellingtesteveryweek.

Herearetheresultsoffourstudentsoverasix-weekperiod.

Teddy 688948 Esther 267899

Rosie 777777 Scott 867876

a) Workoutthemeanresultofeachstudent.

Teddy Rosie Esther Scott

b) Workouttherangeofresultsforeachstudent.

Teddy Rosie Esther Scott

c) Whichstudenthadthegreatestmean?

d) Whichstudentwasthemostconsistent?

e) Whodoyouthinkrevisedforthetests?

©WhiteRoseMaths2020

A supporting video can be found at https://vimeo.com/432451003

6 ThetableshowsthescoresofagroupofstudentsinEnglishand

Sciencetests.

English 47 36 72 42 51 78 38 47 38 52

Science 58 67 74 59 68 66 68 59 63 24

a) Completethetable.

Mean Median Range

Englishmarks

Sciencemarks

b) Useanaverageandtherangetomaketwocomparisonsbetweenthe

EnglishandSciencemarks.

1.

2.

7 Atacharity10,000mrace,twentyexperiencedrunnersfinishwith

ameantimeof48minutesandarangeof10minutes.

Herearethetimes(inminutes)oftenfirst-timerunnersintherace.

62 70 58 75 66 57 59 98 72 61

Maketwocomparisonsbetweentheexperiencedandfirst-timerunners.

1.

2.

Willyourcomparisonschangeiftherunnerwhotook98minutesisnot

includedinthedata?

4 Aboys’rugbyteamplayssevengames.

Hereisthenumberofpointstheyscoreineachgame.

14 31 12 27 22 45 16

a) Findthemedianofthenumberofpointsscored.

b) Findtherangeofthenumberofpointsscored.

Agirls’rugbyteamalsoplayssevengames.

Theirmedianscoreis28pointsandtherangeoftheirscoresis44points.

c) Usethemedianandrangetocomparetheperformancesoftheboys’

rugbyteamandthegirls’rugbyteam.

Median:

Range:

5 ForanEnglishassignment,Nijahiscomparingthenumberofwordsin

thirtysentencesoftwodifferentauthors.

Numberofwordsin

shortestsentence

Numberofwordsin

longestsentence

Mediannumberof

wordspersentence

AuthorA 6 15 10

AuthorB 10 23 14

a) Workouttherangeofthenumberofwordspersentencefor

eachauthor.

authorA authorB

b) Maketwocomparisonsaboutthenumberofwordspersentence

writtenbytheauthors.

1.�

2.� ©WhiteRoseMaths2020