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[1] Section A – Micro Economics 1. Give one example of normative statement. [1] 2. What is the area under price line equal to. [1] 3. What happens to profit/losses in the long run if firms are free to enter the industry? [1] 4. Factor ratio remains same under law of variable proportions. True or false. [1] 5. Why are firms said to be interdependent in an oligopoly market? Explain. [3] 6. Complete the following PPC and comment on the shape of a curve it is likely to attain. [3] Combinations Tea Coffee MRT MOC A 15 0 ________ B ________ 1 1 : 1 ________ C ________ 2 2 : 1 ________ D 9 ________ ________ ________ E 5 ________ ________ ________ F 0 5 5 : 1 ________ OR (a) Distinguish between microeconomics and macroeconomics with example. (b) Explain the central problem of 'for whom to produce' with example. 7. Raj buys more of good X either when it's price falls or when the price of its substitute rises. Distinguish between these two situations with the help of a diagram and a schedule. [4] 8. (a) Give example of a good which is normal good for one household and inferior good for another household. (b) When price of commodity falls by Rs. 2 per kg its quantity demaned increases by 2.5 kgs. Calculate the original and new demand if the price before change was Rs. 10 per unit and the shape of demand curve of a commodity is rectangular hyperbola. [2+2] 9. State two conditions of consumer equilibrium in equi-marginal utility analysis and find equilibrium in the following table when price of bread is Rs. 4, price of milk is Rs. 2 and consumers income is Rs. 16. [4] Combinations MU of bread MU of milk 1 16 14 (2018-19) Date : ___________ Duration : 3 Hrs. Max. Marks : 80 Class XI Economics Instructions: 4 All questions are compulsory. 4 Question numbers 1-4 and 13-16 carry the weightage of 1 mark. They need to be answered in single sentence. 4 Question numbers 5-6 and 17-18 carry the weightage of 3 marks. Answer to them should not exceed 60 words. 4 Question numbers 7-9 and 19-21 carry the weightage of 4 marks. Answer to them should not exceed 80 words. 4 Question numbers 10-12 and 22-24 carry the weightage of 6 marks. Answer to them should not exceed 120 words. 4 Use of calculators is not allowed. Sample Paper
Transcript
Page 1: Duration : 3 Hrs. Economics Max. Marks : 80 XI · 2019-05-30 · [3] 19. Represent the following data of faculty-wise distribution of students of a college for 3 different years by

[1]

Section A – Micro Economics1. Give one example of normative statement. [1]2. What is the area under price line equal to. [1]3. Whathappenstoprofit/lossesinthelongruniffirmsarefreetoentertheindustry? [1]4. Factor ratio remains same under law of variable proportions. True or false. [1]5. Whyarefirmssaidtobeinterdependentinanoligopolymarket?Explain. [3]6. CompletethefollowingPPCandcommentontheshapeofacurveitislikelytoattain. [3]

Combinations Tea Coffee MRT MOCA 15 0 – ________B ________ 1 1 : 1 ________C ________ 2 2 : 1 ________D 9 ________ ________ ________E 5 ________ ________ ________F 0 5 5 : 1 ________

OR (a) Distinguishbetweenmicroeconomicsandmacroeconomicswithexample. (b) Explainthecentralproblemof'forwhomtoproduce'withexample.7. RajbuysmoreofgoodXeitherwhenit'spricefallsorwhenthepriceofitssubstituterises.

Distinguishbetweenthesetwosituationswiththehelpofadiagramandaschedule. [4]8. (a) Giveexampleofagoodwhich isnormalgood foronehouseholdand inferiorgood for

another household. (b) WhenpriceofcommodityfallsbyRs.2perkgitsquantitydemanedincreasesby2.5kgs.

CalculatetheoriginalandnewdemandifthepricebeforechangewasRs.10perunitandtheshapeofdemandcurveofacommodityisrectangularhyperbola. [2+2]

9. State two conditions of consumer equilibrium in equi-marginal utility analysis and findequilibrium in the following tablewhenprice ofbread isRs.4,price ofmilk is Rs.2andconsumers income is Rs. 16. [4]

Combinations MU of bread MU of milk1 16 14

(2018-19)Date : ___________Duration : 3 Hrs.Max. Marks : 80

ClassXIEconomics

Instructions:4 All questions are compulsory.

4 Question numbers 1-4 and 13-16 carry the weightage of 1 mark. They need to be answered in single sentence.

4 Question numbers 5-6 and 17-18 carry the weightage of 3 marks. Answer to them should not exceed 60 words.

4 Question numbers 7-9 and 19-21 carry the weightage of 4 marks. Answer to them should not exceed 80 words.

4 Question numbers 10-12 and 22-24 carry the weightage of 6 marks. Answer to them should not exceed 120 words.

4 Use of calculators is not allowed.

Sample Paper

Page 2: Duration : 3 Hrs. Economics Max. Marks : 80 XI · 2019-05-30 · [3] 19. Represent the following data of faculty-wise distribution of students of a college for 3 different years by

[2]

2 12 103 8 84 4 65 2 36 0 1

OR Aconsumeriswillingtosacrifice3unitofXtoobtainonemoreunitofY.PriceofXandYare

Rs.6andRs.3respectively.Answerthefollowingquestions. (a) Istheconsumerinequilibrium.Whatwouldbehedotomaximisehissatisfactiongiven

the price of two commodities. (b) Higherindifferencecurvemeanshigherutility.Explain.10. (a) Completethefollowingtable: [6]

Output AFC TFC TVC MC01234

–––––

50––––

––

18–

20

–10–6–

(b) WhatisthebehaviourofTPandMPwhenmoreunitsofvariablefactorareemployedwithfixedfactorsintheshortrun.

11. (a) Find out the level of output at which the producer is in equilibrium under perfect competitionwhenpriceofacommodityisRs.20(usingfollowingschedule). [3+3]

Output 1 2 3 4 5 6 7TC 23 42 60 76 95 115 137

(b) SupplycurveistherisingportionofMCcurveoverandabovetheminimumofAVC?Doyouagree.Supportyouranswerwithreason.

12. (a) Aseveredroughtresultinadrasticfallintheoutputofrice.Analysehowwillitaffectthemarketpriceofwheat.

(b) Explaintheimplicationofceilingonpricebygovernment.Usediagram. [6]

Section B – Statistics

13. What is the difference between linear and curvilinear correlation. [1]14. Quartileisatypeof: [1] (a) Mathematicalaverage (b) Statisticalaverage (c) Partitionvalue (d) None15. Coefficientofvariationisapercentageexpressionof [1] (a) Meandeviation (b) Q.D. (c) S.D. (d) None16. Theindexofpricesisestimatedtobe112in2014.Incomparisontothebaseyearpricesin

2014arehigherbywhatpercentage. [1]17. Distinguishbetweenprimarydataandsecondarydata. [3]

OR Explainanythreequalitiesofagoodquestionnaire.18. Findthemissingitem,ifmeanofthefollowingseriesis50. [3]

Marks 30 35 40 ? 50 75No. of student 1 2 3 4 6 4

Page 3: Duration : 3 Hrs. Economics Max. Marks : 80 XI · 2019-05-30 · [3] 19. Represent the following data of faculty-wise distribution of students of a college for 3 different years by

[3]

19. Representthefollowingdataoffaculty-wisedistributionofstudentsofacollegefor3differentyearsbymultiplebardiagram. [4]

Year Arts Commerce Science200520062007

540650730

325410520

250275350

OR Show the following details of themonthly expenditure of two families given below by sub-

dividedbardiagramorcomponentbardiagram.

Item of Expenditure (Expenditure) Family A (income 25,000) Family B (income 40,000)

FoodClothingHouse RentMiscellaneousSavings

10,0005,0004,0004,5001,500

12,00010,0006,0008,0004,000

20. Findoutmodeofthefollowingseries. [4]

Size 8 9 10 11 12 13 14 15Frequency 5 6 8 7 9 8 9 6

21. ForthefollowingdatacalculateStandardDeviationtakingassumedmean=24.5. [4]

Class 10 – 19 20 – 29 30 – 39 40–49 50 – 59Frequency 4 5 6 2 3

22. Drawa‘lessthan’ogiveand‘morethan’ogivecurvesforthefollowingfrequencydistribution: [6]

Marks 0–10 10–20 20–30 30–40 40-50 50-60No. of Student 3 4 8 10 3 2

23. From the following data, calculate price index numbers of 2007 with 1993 as base by (i)Laspeyre’sMethod(ii)Paasche’sMethod,(iii)Fisher’sMethod. [6]

Marks Base Year (1993) Current Year (2007)Commodity Price (`) p0 Quantity q0 Price (`) p1 Quantity q1

ABCD

20504020

8101520

40605020

651525

24. CalculatethecoefficientofcorrelationofthefollowingdatabytheSpearman’sRankCorrelationmethod: [6]

X 19 24 12 23 19 16Y 9 22 20 14 22 18

OR CalculatethecoefficientofcorrelationforthefollowingdatabytheActualMeanMethod.

X 12 15 18 21 24 27 30Y 6 8 10 12 14 16 18

vvvvv

Page 4: Duration : 3 Hrs. Economics Max. Marks : 80 XI · 2019-05-30 · [3] 19. Represent the following data of faculty-wise distribution of students of a college for 3 different years by

[4]

(2018-19)Date : ___________Duration : 3 Hrs.Max. Marks : 80

ClassXIEconomics

1. MinimumwagsshouldbeguaranteedbytheGovernmentinalleconomicactivities.

2. TR

3. Firmswillearnnumbernormalprofitinthelongrunifentry&existorefree.

4. False,factorratiochangesasmoreofvariablefactorsareemployedwithfixedfactors.

5. Thisisbecausewhenthenumberofcompetitorsisfew,anychangeinprice,outputofproductbyafirmwillhavedirecteffectonthesalesofrivals,whowillthenretaliatebychangingtheirownprices,outputoradvertisingtechniqueasthecasemaybe.Itis,therefore,clearthatanoligopolisticfirmmustconsidernotonlythemarketdemandforitsproduct,butalsothereactionsofotherfirmsintheindustrytotakeanymajordecision.

6.

Combination Tea Coffee MRT MOC

A 15 0 - -

B 14 1 1 : 1 1

C 12 2 2 : 1 2

D 9 3 3 : 1 3

E 5 4 4:1 4

F 0 5 5 : 1 5

OR (a)

MICROECONOMICS MACROECONOMICS

1. It is thestudyof individualeconomicunits, likepriceofaparticularcommodity,outputofafirm,etc.

1.Itisthestudyofaneconomyasawholeornationalaggregateslikeinflation,nationalincomeetc.

2.Pricedeterminationandallocationofresourcesisthemainorcentralproblem.Thus,itisalsocalledasPrice-theory

2. Determination of level of income and output is the mainofcentralproblem.Thus,itisalsocalledasTheoryofIncomeandEmpowerment.

3. It is analysed through demand and supply of aparticularorgood/factor.

3. It is analysed through aggregate demand andaggregatesupplyintheeconomy.

4.Itdealswithhowtoattainconsumerequilibrium,producerequilibrium,etc.

4.Itdealswiththedeterminationofequilibriumlevelofnationalincome,output,etc.

(b) For Whom to Produce? Once the problems of ‘what’ and ‘how’ to produce are solved, the goods are thenproduced.Becausetheresourcesandtheresultingoutputofgoodsislimited,thethirdbasiceconomicdecision,whichmustbetakenis‘forwhomtoproduce’.‘Forwhomtoproduce’meanshowthenationalproduceistobedistributedamongthemembersofthesociety.Inotherwords,forwhomtoproducemeanswhoshouldgethowmuchofthetotalamountofgoodsandservicesproducedintheeconomy.Thus,thethirdproblemistheproblemsharingofthenationalproduce.

Thedistributionofnationaloutputandincomeisdoneinthefollowingtwoways: (i) Inter-Personal distribution: Thisimpliesdistributionamongindividualsinthesociety (ii) Factoral distribution: This impliesdistributionamongdifferent factorsofproduction,namely, land,

labour,capitalandentrepreneur. Themainquestionrevolvesaroundthatwhetherdistributionpromotesequalityornot.Promotionofequality

inthesocietywouldrequireequitabledistributionofoutputintheeconomy.Thiswouldleadtoagreatersocialwelfarebutatthesametime,maydiminishtheincentivetoproducemore.Ontheotherhand,inequalitywillinduceahigherlevelofproductionandthus,ahighergrowthratefortheeconomy.Thechoicevariesindifferenteconomicsystems.While,socialisteconomywoulddefinitelypromotesocialwelfarebyequaldistribution,acapitaleconomywouldleadtounequaldistributionbutahighergrowthrate.

Hints/Solutions to Sample Paper

Page 5: Duration : 3 Hrs. Economics Max. Marks : 80 XI · 2019-05-30 · [3] 19. Represent the following data of faculty-wise distribution of students of a college for 3 different years by

[5]

7. IncreaseinDemandVsExpansionofDemand

BASIS INCREASE IN DEMAND EXPANSION OF DEMAND

Meaning Increase in demand means rise in quantitydemandeddue tochange in factorsother thanownpriceofthegood.Here,consumerdemandsmorequantityatthesameprice.

Expansion of demand means rise inquantitydemandedduetofallinpriceofthecommodityitself.

Reasons 1.Favourablechangeintaste2.Increaseinpriceofsubstitutegoods.3.Fallinpriceofcomplementarygoods4. Increase in income of consumers (incase of

normalgoods)5. Fall in income of consumers (in case of inferior

goods.)

Itiscausedbyfallinpriceofthecommodityitself

Shift vs Movement

Thereisrightwardshiftindemandcurve.Thisisbecausethereisachangeindemand.

There is a downward movement along thedemand curve. This is because there is changeinquantitydemanded.

Schedule and dig.

8. (a) Agoodcanbeanormalgoodfortheconsumeratsomelevelsofincomeandaninferiorgoodatotherlevelsofincome.Forexample,atverylowlevelsofincome,asincomeofaconsumerincreases,heincreasesdemandforcoarsecerealsbecausehislevelofconsumptionisbelowtheminimum.Butafteracertainlevelofincome,anyincreaseinincomeoftheconsumerwillreducehisconsumptionofcoarsecerealslikemaize,bajraetc.becausehewillnowsubstitutesuperiorcerealslikewheatandrice.

(b) Pricebeforechange=P=10/unit

Changeinprice=DP=2/kg

IncreaseinQ.d=DQ=2.5kg

∈d=1 [givenrectangularhyperbola]

∆∆QP

PQ

d× = ε

2 52

10 1.× =

Q

P=10

P1=8

4P=2q=?

<19> 2.5 q1=?

Q=12.5kg

Originaldemand=12.5kg

Newdemand=Q+DQ=12.5+2.5=15kg

Page 6: Duration : 3 Hrs. Economics Max. Marks : 80 XI · 2019-05-30 · [3] 19. Represent the following data of faculty-wise distribution of students of a college for 3 different years by

[6]

9.

Combination MU of breadMU of bread in terms of money

MUr

Mu in terms of money

1

2

3

4

5

6

16

12

8

4

2

0

4

3

2

1

0.5

0

14

10

8

6

3

1

7

5

4

3

1.5

0.5 Consumerwillbeinequilibriumwhenbeconsumers2unitofbreads&4unitsofmilkbecauseatthisconsumption

bundle.

MUPx

MUr r= = = =Pr

124

62

3 units.

&Also4.2+2.4=16 consumer spent all of his income.

OR

(a) Noconsumerisnotinequilibriumor MRS≠MRε 3 ≠ 2 (b) Asconsumeriswillingtosacrificemoreunitof4thenwhatmarketrequired

(i) The consumer will consume more of x.

(ii) MarginalutilityofxfallsduetolawofDMU.

(iii) MRSxy falls.

(iv) HewillconsumermoreofxtillsMRSx4=MRE.

(c) Thisisbecauseahigherindifferencecurverepresentsmorequantityofboththegoodsoratleastofonegood.Sinceweassumethataconsumerhasmonotonicpreferencesi.e.,moregoodsmeansmoreutility,ahigherICrepresentingmoreamountofgoods,showsahigherlevelofutility.

10. (a)

Output AFC TFC TVC MC

0

1

2

3

4

50

25

16.67

12.5

50

50

50

50

50

10

18

24

20

10

8

6

4

(b) Referstudymatebook

11. (a)

Output TC MC Price AR TR = P × Q MR

1

2

3

4

5

6

7

23

42

60

76

95

115

137

23

19

18

16

19

20

22

20

20

20

20

20

20

20

20

40

60

80

100

120

140

20

20

20

20

20

20

20Atoutput levels1stand6thunits,bothMRandMCareequal,which is20 inboththecases.Butproducer is inequilibriumat6thunitonlywhereprofitismaximum(100)

(b) Referstudymate

Page 7: Duration : 3 Hrs. Economics Max. Marks : 80 XI · 2019-05-30 · [3] 19. Represent the following data of faculty-wise distribution of students of a college for 3 different years by

[7]

12. (a)

E1

E

P1

P

Price ( )`(Wheat)

SQ Q1

D

QD and Qs of wheat Ø Demand&wheatRises(Demandshitrightwards Ø Situationofexcessdemandinthemarginal Ø Excessdemandleadstoriseinpriceduetocompetitionamongbuyers Ø Marketpricerises Ø Whenpricerisesexpansioninsupplyandcontractionindemandtillnewequilibriumisestablishtillε1. (b) Shortage: Sincethepriceissetbelowtheequilibriumprice,thereisexcessdemandinthemarket.Allofthe

consumers’needs,cannotbemetbecauseproducerssupplylessatalowerprice.Thus,thereisashortageinthemarket.

Black marketing:Ablackmarketisareinwhichthegoodsaresoldillegallyatahigherpricethanfixedbythegovernment.Sincethereisashortageinthemarketduetopriceceiling,producerstrytoexploittheconsumers.Since thedemandcannotbemetcompletely,someconsumersare ready topayahigherprice for thegoodneeded.Ontheotherhand,somesellersarealsointerestedingettingahigherpricetogetmoreprofits.Inthisway,bothbuyersandsellersindulgeinillegaltransaction.Asaresult,thepricesometimesrisesevenabovetheequilibriumpriceandtheentirepurposeofpriceceilingislost.

Rationing: Sincethereisashortageinthemarkettheconsumerscannotgetallwhattheywant.Becauseoflimitedsupply,thegovernmentdistributestheessentialgoodsinlimitedquantitiestotheconsumersatthecontrolprice.Thisisknownasrationingandisdonethroughrationshops.Forthis,governmenthasestablishedPublic Distribution System (PDS). Itisnecessarytoaccompanypriceceilingwithrationingsoastoprotecttheconsumersandpreventemergenceofblackmarket.

13. Linearcorrelationissaidtoexistiftheamountofchangeinonevariabletendstobearaconstantratiototheamountofchangeintheothervariable.

Innonlinearorcurvilinearcorrelation,theamountofchangeinonevariabledoesnotbearaconstantratiototheamountofchargeintheotherrelatedvariable.

14. (c)

15. (d)

16. 12%

17.

Basic Primary Data Secondary Data

Time factor Itrequireslongertimefordatacollection. Secondarydatarequireslesstime.

Cost Factor Thecollectionofprimarydatarequiresaconsiderableamountofmoneyandpersonalsaswholeplanofinvestigationisinitiated.

Thecollectionofsecondarydataischeaperasitistakenfrompublishedorunpublishedmaterial.

Reliability and suitability

Primarydataismorereliableandsuitabletotheenquiryastheinvestigatorhimselfcollectsit.

Secondarydataislessreliableandlesssuitable as someone else has collected the data whichmaynotservethepurpose.

Precautions Thereisnogreatneedforprecautionswhileusingprimarydata.

Secondarydatashouldbeusedwithgreatcareand caution.

OrganizationFactor

Collectionofprimarydatarequireselaborateorganizationsetup.

Thereisnoneedfororganizationalsetupincaseofsecondarydata.

Thebasicdifferencebetweenprimarydataandsecondarydataisof‘degree’.

Thedatacollectedbyonewillbeprimary,butthesamedatausedbyanotherwillmakeitsecondary.Forexample,datacollectedbyMinistryofHumanResourcewith

(a) NumberofQuestions:Thenumberofquestionsshouldbeassmallaspossible.Longquestionnairesdiscouragepeoplefromcompletingthem.Onlythosequestionswhichhaveadirectrelevancetotheproblembeinclude.

(b) SimpleandshortQuestions:Thequestionsshouldbeclear,brief,andunambiguous.Thequestionshouldbeframedinsuchamannerthattheiranswerarespecificandprecise.

(c) Avoid Questions requiring calculations: The questions relating tomathematical computations or questionswhichforcetherespondenttorecollectfromhismemoryshouldnotbeasked.Forexample,informantsshouldnotbeaskedyearlyincome,sinceinmostofthecasestheyarepaidmonthly.

Page 8: Duration : 3 Hrs. Economics Max. Marks : 80 XI · 2019-05-30 · [3] 19. Represent the following data of faculty-wise distribution of students of a college for 3 different years by

[8]

18. Letthemissingitembex

Calculation of Missing item

Marks(X) No.ofstudents(f) fX

303540x

5075

123464

30701204x

300300

∑f =20 ∑f X=820+4x

X

fXf

= ∑∑

50 820 4

20=

+ x

50×20=820+4x x=45marks MissingMarks=45Marks19.

OR

20. Thefrequenciesoftwoitems:12and14havethehighestfrequencyof9.So,groupingoffrequencyisessential.Themethodofgroupingwillbeusedfordeterminationofmode.

Page 9: Duration : 3 Hrs. Economics Max. Marks : 80 XI · 2019-05-30 · [3] 19. Represent the following data of faculty-wise distribution of students of a college for 3 different years by

[9]

Table 1 : Grouping Table

Size(X)

Frequency(f)

In two’s In Three’s

Column I Column II Column II ColumnIV ColumnV ColumnVI

89101112131415

56879896

} 11

} 15

} 17

} 15

}14 } 16

}17

} 19

}24} 21

} 26

} 19

} 23

Table 2 : Analysis Table

ColumnNo. 8 9 10 11 12 13 14 15

I

II

III

IV

V

VI

Total – – 1 2 5 4 3 –

Thesize12isoccuringmaximumnumberoftimes(5times).So,Mode=12.Ans.Mode=12

21. Thisisacaseofinclusiveclass-intervals.So,ithastobeconvertedintoexclusiveseries.

MarksX No.ofstudents

f

Mid-point

m

d=m–A

A=24.5d X A

C′ =

C=10

fd′ d′2 t′d2

9.5 – 19.5

19.5 – 29.5

29.5 – 39.5

39.5–49.5

49.5–59.5

4

5

6

2

3

14.5

24.5(A)

34.5

44.5

54.5

–10

0

+10

+20

+30

–1

0

+1

+2

+3

–4

0

+6

+4

+9

1

0

1

4

9

4

0

6

8

27

N=Σf=20 Σfd′=15 Σfd′2=45

(i) Standard deviation ( )σ =′−

×∑ ∑fd

Nfd

NC

2 2

Σfd′2=45;N=20;Σfd′=15;C=10

σ = −

× = − × = × =

4520

1520

10 2 25 5625 10 1 6875 10 12 992

. . . .

Page 10: Duration : 3 Hrs. Economics Max. Marks : 80 XI · 2019-05-30 · [3] 19. Represent the following data of faculty-wise distribution of students of a college for 3 different years by

[10]

22. For ‘Lessthan’and‘Morethan’ogivecurves,frequencydistributionwillbeconvertedintocumulativefrequencyasshowninthefollowingtable:

Cumulative Frequency Distribution

Marks No.ofstudent Marks No.ofstudents

Less than 10

Less than 20

Less than 30

Lessthan40

Less than 50

Less than 60

3

7

15

25

28

30

Morethan0

Morethan10

Morethan20

Morethan30

Morethan40

Morethan50

30

27

23

15

5

2

Byplotting lessthancumulative frequencyagainsttheupper limitof theclass-intervalandmorethancumulativefrequencyagainstthelowerlimitoftheclass-interval,wegetthefollowing‘lessthan’and‘morethan’ogivecurves(seefigure)

23. ConstructionofPriceIndexNumbers

BaseYear(1993) CurrentYear(2007)

Commodity Price(`)p0

Quantityq0

Price(`)p1

Quantityq1

p0q0 p0q1 p1q0 p1q1

A

B

C

D

20

50

40

20

8

10

15

20

40

60

50

20

6

5

15

25

160

500

600

400

120

250

600

500

320

600

750

400

240

300

750

500

Σp0q0

=1,660

Σp0q1

=1,470

Σp1q0

=2,070

Σp1q1

=1,790

(i) Laspeyre’sMethod

P

p qp q01

1 0

0 0

100 2 0701 660

100 124 69= × = × =∑∑

,,

.

(ii) Paasche’sMethod

P

p qp q01

1 1

0 1

100 1 7901 470

100 121 77= × = × =∑∑

,,

.

(iii) Fisher’sMethod

P

p qp q

p qp q01

1 0

0 0

1 1

0 1

100= × ×∑∑

∑∑

= × × = × = × =

2 0701 660

1 7901 470

100 1 51835 100 1 2322 100 123 22,,

,,

. . .

Ans.(i)Laspeyre’s=124.69;(ii)Paasche’s=121.77;(iii)Fisher’s=123.22.

Page 11: Duration : 3 Hrs. Economics Max. Marks : 80 XI · 2019-05-30 · [3] 19. Represent the following data of faculty-wise distribution of students of a college for 3 different years by

[11]

24. Calculation of Rank Correlation

X Y R1 R2 (R1 – R2)

D

D2

19

24

12

23

19

16

9

22

20

14

22

18

3.5

6

1

5

3.5

2

1

5.5

4

2

5.5

3

+2.5

+0.5

–3

+3

–2

–1

6.25

0.25

9

9

4

1

N=6 ΣD2=29.50

Here,number19isrepeatedtwiceinseriesXandnumber22isrepeatedtwiceinseriesY.Therefore,inX,m=2andinY,m=2.

rD m m m m

N Nk = −+ − + − +

−1

6 112

112

2 2 3

3

Σ ( ) ( ) ...........

∑D2=29.50;N=6

= −

+ − + −

−1

6 29 50 112

2 2 112

2 2

6 6

3 3

3

. ( ) ( )

= −+ +

= −×

=1 6 29 50 0 5 0 5210

1 6 30 5210

0 128( . . . ) . .

Ans.RankCoefficientofcorrelation=0.128.Thereisverylowdegreeofpositivecorrelation.OR

CalculationofCoefficientofCorrelation(ActualMeanMethod)

X-Series Y-Series

xyX x X X= − x2 Y y Y Y= − y2

12

15

18

21

24

27

30

–9

–6

–3

0

+3

+6

+9

81

36

9

0

9

36

81

6

8

10

12

14

16

18

–6

–4

–2

0

+2

+4

+6

36

16

4

0

4

16

36

54

24

6

0

6

24

54

∑X=147 ∑x=252 ∑Y=84 ∑y2=112 ∑xy=168

X XN

Y YN

Y XY

X Y

=∑

= =

=∑

= =

=∑

∑ × ∑=

×=

1477

21

847

12

168232 112

16828 2242 2 ,

== =168168

1

vvvvv


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