Averages and range - Corbettmaths · Mode, Median, Mean and Range Videos 50, 53, 56, 57 on Corbettmaths Question 1: The length of nine caterpillars are listed below 9cm 4cm 8cm 10cm

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!Mode,Median,MeanandRangeVideos50,53,56,57onCorbettmaths

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�Question1: Workoutthemodefortheeachofthefollowing

(a)5,6,6,7,8,10 (b)1,1,1,4,6,8,12 (c)5,5,7,7,7,8,8,9

(d) 5,7,3,5,8,9,10,2 (e)8,3,3,4,6,8,13,3,18 (f)12,14,15,17,15(g)2.3,2.6,2.8,2.7,2.8,2.7,2.4,2.3,2.1,2.3 (h)−2,−1,5,8,−2,2,−1,9,−1,1,2,−1

Question2: Thebarchartshowstheshoesizes ofagroupofstudents.

(a) Howmanystudentsintotalarethere?

(b) Whatisthemodalshoesize?

Question3: Workoutthemodefortheeachofthefollowing

(a) 8,1,1,7,2,1,5,9,4,1,5,5,9,6,4,3,2,3,1,1,9,8,7,3,2,4,5,1,1,9,1

(b) 8,9,7,3,4,7,9,3,4,5,1,2,2,1,3,0,0,8,1,4,7,8,6,6,3,3,3,1,3,3,5

Question4: Thetallychartshowsthefavouritesportofthestudentsinaclass.

(a) Whatisthemodalsport?

(b) Howmanystudentsareintheclass?

(c) Howmanymorestudentslikedfootballthanrugby?

Question5: MrsGreengivesherclassatest.Theresultsareshowninthebarchartbelow.

(a) Whatisthemodalgrade?

(b) Howmanystudentssatthetest?

AgradeCoraboveisa“pass.”

(c) Whatfractionofthestudentspassedthetest?

Examples

Workout:TheMode

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!Mode,Median,MeanandRangeVideos50,53,56,57onCorbettmaths

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� Question1: Workoutthemedianfortheeachofthefollowing

(a)5,1,4,6,8 (b)9,1,3,6,7,8,9 (c)6,4,7,1,3,8,1,10

(d) 7,3,8,9,6,5 (e)9,8,6,6,6,7,1,2,6,8 (f)−4,5,−7,−1,2,0,9

(g) 20,30,10,20,40,50,60,10,80,30 (h)49,34,12,10,53,20,65,34,90,100,33

(i)6.2,6.8,6.6,7.2,6.4,7.4,5.8 (j)124,53,39,230,155,180

Question2: Shownaretheagesandweightsof5dogs.

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(a) Whichdoghasthemedianage?

(b) Whichdoghasthemedianweight?

Question3: Theheightofsomefootballersarelistedbelow:

1.81m,1.78m,1.88m,1.79m,1.86m,1.85m,1.78m,1.93m

(a) Workoutthemedianheight

(b) Whatisthemodalheight?

Question4: Writedown[ivenumberswithamedianof7

Question5: Writedowneightnumberswithamedianof10

Question6: Writedownfourdifferentnumberswithamedianof4.5

Question7: Writedownsixdifferentnumberswithamedianof0

Examples

Workout:TheMedian

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!Mode,Median,MeanandRangeVideos50,53,56,57onCorbettmaths

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� Question1: Findthemeanforeachofthesetsofdatabelow

(a) 4,9,7,10,5 (b)2,8,6,3,12,7,4 (c)3,2,1,3,2,2,1,3,1,2,3,2,1

(d) 1,8,7,5,6,4,7,6 (e)20,30,24,32 (f)12,8,14,5,1,3,0,8,10,11

(g) 9,−3,−6,5,0 (h)1.4,2.8,2.4,2.5,2.8,3.1,1.1

Question2: Abasketballteamplays8matches. Thenumberofpointstheyscoreineachmatchare: 62,68,67,79,82,50,74,62

(a) Workoutthemeannumberofpointsscored

(b) Writedownthemodalnumberofpointsscored

(c)Writedownthemediannumberofpointsscored

Question3: MrHollandgiveshisclassatest.Theresultsare: 34%,44%,75%,21%,98%,86%,71%,76%,63%,55%

(a) Workoutthemeanmark

(b) Workoutthemedianmark

(c)Howmanystudentsscoredabovethemeanmark?

Question4: Fivehousesonastreetaresoldin2016.Theysellfor £175,000 £184,000 £150,000 £201,000 £191,000

Calculatethemeanprice.

Question5: Themeanoffournumbersis10.Threeofthenumbersare9,11and7. Workoutthefourthnumber.

Question6: Themeanofsixnumbersis5.Fiveofthenumbersare6,6,5,3and1. Workoutthesixthnumber.

Question7: Themeanof[ivenumbersis8.2.Fourofthenumbersare8,10,12and10. Workoutthe[ifthnumber.

Examples

Workout:TheMean

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Question1: Findtherangeforeachofthefollowing

(a) 5,9,1,5,7,4,3 (b)6,7,10,8,9,9 (c)21,15,19,24,30,26

(d) 210,250,260,180,240 (e)6.2,7.3,8.8,1.5,4.1 (f)3,1,2,1,3,4,5,0,1

(g) −5,1,3,6,−8,1 (h)−6,−10,−2,−9 (i)0,7,9,−21,10,−4

(j) 7,9,−2,13,9,8,20,−8,1 (k)−10,−6,−15,−9,−8,−7,8,−3

Question2: Therangeforalistofnumbersis7.Thesmallestvalueis4. Whatisthelargestvalueinthelist?

Question3: Therangeforalistofnumbersis8.Thelargestvalueis13. Whatisthesmallestvalueinthelist?

Question4: Therangeforalistofnumbersis1.Thelargestvalueis4. Whatisthesmallestvalueinthelist?

Question5: Therangeforalistofnumbersis27.Thesmallestvalueis87. Whatisthelargestvalueinthelist?

Question6: ThenumberofpointsthatRandalstownRugbyClubscoredineightmatchesare 24,17,19,35,9,43,15,30.

(a) Workouttherangeofthenumberofpointsscored.

(b) Workoutthemedianofthenumberofpointsscored.

Question7: Thetableshowsthemiddaytemperatureover[ivedays. Eachtemperatureisindegreescelsius.

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(a) Workouttherangeofthetemperatures.

(b) Workoutthemeantemperature.

Examples

Workout:TheRange

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!Mode,Median,MeanandRangeVideos50,53,56,57onCorbettmaths

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Question1: Thelengthofninecaterpillarsarelistedbelow

9cm4cm8cm10cm7cm5cm13cm10cm6cm

(a) Findthemode(b) Findthemedian(c) Findthemean(d) Findtherange

Question2: Jamesplayssixgamesofdarts. Hisscoresare120,71,80,14,90,117

ShouldJamesusethemeanorthemediantogivehimthehighestaveragescore?

Question3: Shownaretheweightsof3puppies.

(a) Workoutrangeoftheweights

(b) Workoutthemedianweight

(c)Workoutthemeanweight

Question4: Theamountofwaterinsomecontainersare:

2litres,330ml,0.08litres,0.7litres,75ml,5000ml,0.15litres

(a) Workoutthemedian(b)Findtherange

Question5: Themedianheightof11footballersis1.85m. Onlyonefootballerhasaheightof1.85m Howmanyfootballershaveaheightunder1.85m?

Question6: Writedownsevennumbersthathavearangeof10andameanof12.

Question7: Writedownsixnumbersthathaveamedianof8,ameanof9andarangeof13

Question8: Fivenumbershavearangeof14. Fourofthenumbersare20,22,31and25. Workoutthetwodifferentpossiblevaluesforthe[ifthnumber.

Apply

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Question9: BelfastGiantshaveplayed5matchesandthemeannumberofgoalsscoredis3 Whentheyplaythe6thmatch,themeanincreasesto4.

Howmanygoalswerescoredinthe6thmatch?

Question10: Jamesisacarsalesman. Hehasatargetofselling5carsadayfromMondaytoFriday. OverMondaytoThursday,hehassoldameanof6carsaday. HowmanycarsmusthesellonFridaytomeethistarget?

Question11: Ateachersurveysagroupofstudents. Heaskshowmuchpocketmoneytheyreceiveeachweek.Theyrespond

£5£8£4£50£6£8£7.50£10£8£7

(a) Workoutthemedian(b) Workoutthemean(c) Whichaverage,themedianorthemean,ismostsuitableforthisdata?

Question12:Asetofsixnumbershaveamedianof9. Allofthenumbersareeven. Therangeofthenumbersis8. Themodeofthenumbersis6.

Writedownapossiblesetofsixnumbers.

Question13: Shownbeloware[ivecardswhicharearrangedinorderfromsmallesttolargest

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Therangeofthecardsis6. Themedianofthecardsis7. Themeanofthecardsis8. Workoutthe4missingnumbers.

�Answers

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