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NCERT Textual Exercises

ExErcisE 5.1 1. Forwhichofthesewouldyouuseahistogramtoshowthedata? (a) Thenumberoflettersfordifferentareasinapostman’sbag. (b) Theheightofcompetitorsinanathleticsmeet. (c) Thenumberofcassettesproducedby5companies. (d) Thenumberofpassengersboardingtrainsfrom7:00a.m. to7:00

p.m.atastation.Givereasonsforeach. 2. Theshopperswhocometoadepartmentalstorearemarkedas:man(M),

woman(W),boy(B)orgirl(G).Thefollowinglistgivestheshopperswhocameduringthefirsthourinthemorning:

WWWGBWWMGGMMWWWWGBMWBGGMWWMMWWWMWBWGMWWWWGWMMWWMWGWMGWMMBGGW

Makeafrequencydistributiontableusingtallymarks.Drawabargraphtoillustrateit.

3. Theweeklywages(inRs)of30workersinafactoryare.830,835,890,810,835,836,869,845,898,890,820,860,832,833,855,845,804,808,812,840,885,835,835,836,878,840,868,890,806,840

Usingtallymarksmakeafrequencytablewithintervalsas800–810,810–820andsoon.

4. DrawahistogramforthefrequencytablemadeforthedatainQuestion3,andanswerthefollowingquestions.

(i) Whichgrouphasthemaximumnumberofworkers? (ii) HowmanyworkersearnRs850andmore? (iii) HowmanyworkersearnlessthanRs850? 5. The number of hours forwhich students of a particular classwatched

televisionduringholidaysisshownthroughthegivengraph. Answerthefollowing. (i) Forhowmanyhoursdidthemaximumnumberofstudentswatch

TV? (ii) HowmanystudentswatchedTVforlessthan4hours?

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126

NCERT Textual Exercises

Test Yourself DH-1 1. Givenbelowaretheweightsofdifferentstudentsindataforms: 50,55,60,55,55,51,52,52,50,60,52,51,51,52,54,54,55,52,53,60,

51,51,52,55,55,54,53,52,54 Prepareafrequencytableusingtallymarks. 2. Thedistancebetweenathletesonarunningtrackaregivenbelow:

Distance 25-30 30-35 35-40 40-45 45-50Frequency 5 8 10 17 9

Prepareahistogram. 3. Givenbelowarethemarksobtainedby20students 30,61,55,34,28,30,60,56,35,35,30,61,60,55,56,30,60,61,28. (i) Findthelowestandhighestobservation. (ii) Prepareafrequencytableusingtallymarks. 4. Drawanappropriategraphtorepresentthefollowinginformation.

childrenwhoprefer

SchoolA SchoolB SchoolC SchoolD SchoolE

Pizza 45 55 35 15 25Samosa 55 25 40 20 10

5. Drawahitogramtorepresentthefollowingdatawhichgivestheheightsofthestudentsinaclass.

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127

NCERT Textual Exercises

Heights(incm) No.ofstudents124.5-127.5 4127.5-130.5 8130.5-133.5 15133.5-136.5 8136.5-139.5 7

6. Lookatthegraphdrawnbelowandanswerthequestionsgivenbelow.SaleofT.V.inashopfromJan.toDec.

(i) InwhichmonthwasthesaleofT.V.maximum. (ii) InwhichmonthwasthesaleofT.V.minimum. (iii) Inwhichmonths30T.V.weresold. (iv) Inwhichmonth45T.V.weresold. (v) Namethemonthsinwhich10T.V.weresold. (vi) HowmanyT.V.weresoldinthefirstquarteroftheyear. (vii) HowmanyT.V.weresoldinthesecondquarteroftheyear. (viii) HowmanyT.V.weresoldinthethirdquarteroftheyear. (ix) HowmanyT.V.weresoldinthefourthquarteroftheyear. (x) Inwhichquarter,thesalewasmaximumandinwhichitwasminimum.

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128

NCERT Textual Exercises

ExErcisE 5.2 1. Asurveywasmadetofindthetypeofmusicthatacertaingroupofyoung

peoplelikedinacity.Adjoiningpiechartshowsthefindingsofthissurvey.Fromthispiechartanswerthefollowing:

(i) If20peoplelikedclassicalmusic,howmanyyoungpeopleweresurveyed?

(ii) Whichtypeofmusicislikedbythemaximumnumberofpeople? (iii) Ifacassettecompanyweretomake1000CD’s,howmanyofeach

typewouldtheymake?

2. Agroupof360peoplewereaskedtovotefortheirfavouriteseasonfromthethreeseasonsrainy,winterandsummer.

(i) Whichseasongotthemostvotes? (ii) Findthecentralangleofeachsector. (iii) Drawapiecharttoshowthisinformation.

Season No. of votes

Summer

Rainy

Winter

90

120

150

3. Drawapiechartshowingthefollowinginformation.Thetableshowsthecolourspreferredbyagroupofpeople.

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NCERT Textual Exercises

Colours Number of PeopleBlue

Green

Red

Yellow

18

9

6

3Total 36

Findtheproportionofeachsector.Forexample,Blueis1836

12

== ;Greenis936

14

== andsoon.Usthistofindthecorrespondingangles.

4. TheadjoiningpiechartgivesthemarksscoredinanexaminationbyastudentinHindi,English,Mathematics,SocialScienceandScience. If the totalmarksobtainedbythestudentswere540,answerthefollowingquestions.

(i) Inwhichsubjectdidthestudentscore105marks?(Hint:for540marks,thecentralangle=360°.So,for105marks,whatisthecentralangle?)

(ii) HowmanymoremarkswereobtainedbythestudentinMathematicsthaninHindi?

(iii) ExaminewhetherthesumofthemarksobtainedinSocialScienceandMathematicsismorethanthatinScienceandHindi.(Hint:Juststudythecentralangles).

5. Thenumberofstudentsinahostel,speakingdifferentlanguagesisgivenbelow.Displaythedatainapiechart.Language Hindi English Marathi Tamil Bengali TotalNo.ofStudents

40 12 9 7 4 72

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NCERT Textual Exercises

Test Yourself DH-2 1. Thegivenpie-chartshowsthegameslikedbyClassVIIIstudentsreadand

answer,thequestionsgivenbelow:

Thereare180studentslikeBasketball. (i) HowmanystudentslikeBasketball. (ii) HowmanymorestudentsareinterestedinBadmintonthaninCricket? (iii) FindtheratioofthestudentswholikeTennistothatwholikeBasket

ball. 2. Gyaneshspends20%ofhisincomeonhouserent,30%onhouseholditems,

10%onhisdaughters fees,25%onhissavingand15%onhisvehicle'spetrol.

(i) Representtheaboveinformationintabularform. (ii) Presentthisinformationonapiechart. 3. Thepiechartshowsthecoloursselectedbyfamilytobepaintedontheir

walls.Readthischartandanswerthefollowing:

(i) Whichisthefavouritecolourofthefamily? (ii) Whichcolourwereequallylikedbythefamily? (iii) Whichcolourislikedtheleast? 4. GivenisthepiechartshowingthemarksobtainedbyIshitainherexams. Calculatehermarksinallthesubjectifsheobtainedatotalof216marks.

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NCERT Textual Exercises and Assignm

ents

ExErcisE 5.3 1. Listtheoutcomesyoucanseeintheseexperiments. (a) Spinningawheel (b) Tossingtwocoinstogether

2. Whenadieisthrown,listtheoutcomesofaneventofgetting (i) (a) aprimenumber (b) notaprimenumber. (ii) (a) anumbergreaterthan5 (b) anumbernotgreaterthan5. 3. Findthe (a) ProbabilityofthepointerstoppingonDin(Question1-(a))? (b) Probabilityofgettinganacefromawellshuffleddeckof52playing

cards? (c) Probabilityofgettingaredapple.(Seefigurebelow)

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132

NCERT Textual Exercises and Assignm

ents 4. Numbers1to10arewrittenontenseparateslips(onenumberononeslip),

kept in aboxandmixedwell.One slip is chosen from theboxwithoutlookingintoit.Whatistheprobabilityof

(i) gettinganumber6? (ii) gettinganumberlessthan6? (iii) gettinganumbergreaterthan6? (iv) gettinga1-digitnumber? 5. If youhave a spinningwheelwith 3 green sectors, 1 blue sector and1

redsector,what is theprobabilityofgettingagreensector?What is theprobabilityofgettinganonbluesector?

6. FindtheprobabilitiesoftheeventsgiveninQuestion2.

Test Yourself DH-3 1. Findtheprobabilityofgettingatleastoneheadintossingacointwice. 2. Iftwounbiaseddicearethrownthenfindtheprobabilityofgettingasum

of5. 3. Acoinistossed10timesandoutcomesareobservedasH,T,H,H,T,H,T,

H,H Calculatethepercentagechanceofoccurrenceofhead(H)andTail(T). 4. Twooctagonaldicewithnumbers1-8arethrowntogether (i) Findtheprobabilitythat5and6areshownonthedice. (ii) Findtheprobabilitythatsumoftwonumbersis10. (iii) Findtheprobabilitythatboththenumbersareeven. (iv) Findtheprobabilitythatanoddandanevennumbersarepresented

inthethrow. (v) Findtheprobabilitythat6isnotshownoneitherofthedice. 5. Aboxofstationeryitemshas6pencilsand4rubbers.Onepieceofthese

itemisremovedatrandom.Calculatetheprobabilitythattheitemremovedwillbe

(i) Arubber (ii) Apencil 6. Adiceisthrown12timesandoutcomesare 1,6,2,3,3,4,4,5,4,3,4,2 Findtheprobabilityofmostcommonoutcome.

Data Handling

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NCERT Textual Exercises and Assignm

ents 7. Acoinisthrown20timesandoutcomesobservedare T,T,H,H,H,T,T,T,T,H,H,T,H,H,T,H,T,H,H,T CalculatethepercentagechanceofoccurrenceofHead(H)andTail(T). 8. Alkatossesacointhreetimesfindtheprobabilityof (i) headsshowingupallthethreetimes. (ii) tailsshowingupallthethreetimes. (iii) thecoinsshowingupsamesideallthethreetimes. (iv) tailsshowinguptwotimesandheadonce. (v) headsshowinguptwotimesandtailsonce.

Data Handling

136

NCERT Textual Exercises and Assignments

Exercise – 5.1 1. Since,Histogramisagraphicalrepresentationofdata,ifdatarepresentedinmannerofclass

interval. Therefore,forcase(b)and(d),wewoulduseahistogramtoshowthedata,becauseinthese

case,datacanbedividedintoclass-intervals. Incase(b),agroupofcompetitionshavingdifferentheightsinanathleticsmeet. Incase(d),thenumberofpassengersboardingtrainsinanintervalofonehouratastation. 2. Thefrequencydistributiontableisasfollows:

Theillustrationofdatabybar-graphisasfollows:

30252015105

W M B GShoppers

Num

ber o

f sho

pers

3. Therepresentationofdatabyfrequencydistributiontableusingtallymarksisasfollows:

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137

ClassIntervals

Tally Marks Frequency

800–810

810 820–

820 830–

830 840–

840 850–

850 860–

860 870–

870 880–

880 890–

880 900–

Total

3

2

1

9

5

1

3

1

1

4

30 4. (i) 830–840grouphasthemaximumnumberofworkers. (ii) 10workerscanearnmorethan`850. (iii) 20workersearnlessthan`850.

10

9

8

7

6

5

4

3

2

1

O

800 810

–

810 820

–

820 830

–

830 840

–

840 850

–

850 860

–

860 870

–

870 880

–

880 890

–

880 900

–

Num

ber

of

Shoper

s

Wages

5. (i) ThemaximumnumberofstudentswatchedT.V.for4–5hours. (ii) 34studentswatchedT.V.forlessthan4hours. (iii) 14studentsspentmorethan5hoursinwatchingT.V.

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138

Test Yourself (DH-1) 3. lowestobservation=28 highestobservation=61 6. (i) July (ii) MarchandMay (iii) January,April,June,August,September,December (iv) October (v) MarchandMay (vi) 60T.V. (vii) 70T.V. (viii) 110T.V. (ix) 95T.V. (x) 3rdquartersalewasmaximumandinIstquartersalewasminimum.

Exercise – 5.2 1. (i) 10%represents100people

Therefore20%represents = × =100 2010

200 people

Hence,200peopleweresurveyed. (ii) Lightmusicislikedbythemaximumnumberofpeople.

(iii)CD'sofclassicalmusic = × =10 1000100

100

CD'sofsemi-classicalmusic = × =20 1000100

200

CD'soflightmusic = × =40 1000100

400

CD'soflightmusic = × =30 1000100

300

2. (i) Winterseasongotthemostvotes.

(ii) Centralangleofsummerseason =°× °

°= °90 360

36090

Centralangleofrainyseason = °× °°

= °120 360360

120

Centralangleofwinterseason =°× °

°= °150 360

360150

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139

(iii)

3. Here,centralangle=360°andtotalnumberofpeople=36

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140

4.

(i) Thestudentscored105marksinHindi (ii) MarksobtainedinMathematics=135. MarksobtainedinHindi=105 Difference=135–105=30 Thus,30moremarkswereobtainedbythestudentinmathematicstheninHindi (iii)ThesumofmarksinSocialScienceandmathematics =97.5+138=232.5 ThesumofmarksinScienceandHindi=120+105=225 Yes,thesumofthemarksinSocialScienceandMathematicsismorethanthatinScience

andHindi. 5.

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141

Piechartatabovegivendataisasfollows

Test Yourself (DH-2) 1. (i) 30 (ii) 10 (iii) 4:3 3. (i) Pink (ii) LemonandBlue (iii) Green 4. S.St.–54 English–42 Maths–60 Science–42 Hindi–18

Exercise – 5.3 1. (a) TherearefourlettersA,B,CandDinaspinningwheel.Sothereare4outcomes. (b) Whentwocoinsaretossedtogether.TherearefourpossibleoutcomesHH,HT,TH,TT.

(HereHTmeansheadonfirstcoinandtailonsecondcoinandsoon) 2. (i) (a) Outcomesofeventofgettingaprimenumberare1,4and6. (b) Outcomesofeventofnotgettingaprimenumberare1,4and6. (ii) (a) Outcomesofeventofgettinganumbergreaterthan5is6. (b) Outcomesofeventofnotgettinganumbergreaterthen5are1,2,3,4and5. 3. (a) Inaspinningwheel,therearefivepointersA,A,B,C,D.Sotherearefiveoutcomes. PointerstopsatDwhichisoneoutcome.

Data Handling

142

BA

A

DC

SotheprobabilityofthepointerstoppingonD= 15

(b) Thereare4acesinadeckof52playingcards.So,therearefoureventsofgettinganace.

So,probabilityofgettinganace nth

2

(c) Totalnumberofapples=7 Numberofredapples=4

Probabilityofgettingredapple nth+

12

4. (i) Outcomeofgettinganumber6fromtenseparateslipsisone.

Therefore,probabilityofgettinganumberMedianobservation observation

=

+ +

n nth th

2 21

2 (ii) Numberslessthan6are1,2,3,4and5whicharefive.Sothereare5outcomes.

Therefore,probabilityofgettinganumberlessthan nth+

12

(iii)Numbergreaterthan6outoftenthatare7,8,9,10.Sothereare4possibleoutcomes.

Therefore,probabilityofgettinganumbergreaterthan 11 12+

th

(iv)Onedigitnumbersare1,2,3,4,5,6,7,8,9outoften.

Therefore,probabilityofgettinga1-digitnumber 122

th

5. Therearefivesectors.Threesectorsaregreennoutoffivesectors. Therefore,probabilityofgettingagreensector 81 Thereisonebluesectoroutoffivesectors. Non-bluesectors=5–1=4sectors Therefore,probabilityofgettinganon-bluesector 81 9=

Data Handling

143

6. Whenadieisthrown,therearetotalsixoutcomes,i.e.,1,2,3,4,5,and6. (i) (a) 2,3,5areprimenumbers.Sothereare3outcomesoutof6. Therefore,probabilityofgettingaprimenumber 11025 (b) 1,4,6arenottheprimenumbers.Sothereare3outcomesoutof6. Therefore,probabilityofgettingaprimenumber 11025 5 3 7 105= × × =( ) (ii) (a) Only6isgreaterthan5.sotheisoneoutcomeoutof6. Therefore,probabilityofgettinganumbergreaterthan 5329 (b) Numbersnotgreaterthan5are1,2,3,4and5.Sothereare5outcomesoutof6. Therefore,probabilityofnotgettinganumbergreaterthan 5329 73=

Test Yourself (DH-3)

1. 78

2. 4

3619

==

3. H ==2003

%

T ==100

3%

4. (i)164

(ii)764

(iii)14 (iv)

1264

5. (i)25 (ii)

35

6. 4 7. Head–50% Tail–50%

8. (i)18 (ii)

18

(iii)14 (iv)

38

(iv) 38