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Q1. Balance of Payments of a country is a statement that records:-
a) Sources of Foreign Exchange b) Uses of Foreign Exchange c) Both a) and b) d) None of the above
Ans:- c) Explanation:- Balance of Payments is an accounting statement that records the foreign exchange transactions of a country with the rest of the world
Q2. The categories of transactions that are included in current account of Balance of Payments are:-
a) Exports and imports of goods b) (a) + Exports and Imports of services c) (b) + Income from and to abroad d) (c) + Transfers from and to abroad
Ans – d) Explanation:- Current Account of BoP records 1) export and imports of goods, services, income from and to abroad, unilateral transfers from and to abroad
Q3. Balance of Trade equals:-
a) Exports less imports b) Exports of goods less imports of goods c) Exports of services less imports of services d) None of the aboveShow Answer
Ans – b) Explanation:- Balance of Trade is the part of Current account of BoP. It is the differnce between Export and Import of physical goods
Q4. The categories of transactions that are included in the capital account of the Balance of Payments are:-
a) Investments from and to abroad b) Borrowings and lendings from and to abroad c) Changes in foreign exchange reserves d) All the above
Ans – d) Explanation:- Capital account of BoP records the financial transactions of a country in foreign exchange with the rest of the world that changes assets and liabilities status of a country. It includes three transactions. 1) Investments from and to abroad, 2) Borrowings and lendings from and to abroad, 3) Changes in foreign exchange reserves.
Q5. The measurement of Balance of Payments deficit is based on:-
a) Autonomous transactions b) Accommodating transactions c) Current account transactions d) Capital account transactions
Ans – a) Explanation:- Autonomous transactions are done for profit motive. Such transactions are the main cause of deficit in BoP.
Q6. Choose the correct statement from given below:
a) Balance of trade records the exports and imports of invisible items. b) A surplus in BoT can rectify the deficit in Bop. c) Accommodating items are only recorded in the capital account of the BOP. d) Import of machinery will be recorded in the capital account of BoP.
Ans – c) Explanation:- Accommodating transactionsa are only recorded in Capital Account. Main motive of such transactions are to settle the surplus and deficit of BoP due to autonomous transactions.
Q7.Choose the correct statement from given below.
a) Balance of Trade is a component of the capital account of Balance of Payments. b) Floating exchange rate is used to stabilize the price of foreign currency. c) Increase in the supply of foreign exchange results in a fall in its price d) Rise in the exchange rate leads to the revaluation of the currency.
Ans – c) Explanation:- Higher is the supply of foreign exchange, lesser is the foreign exchange rate.
Q8. Current accounts records all payments to rest of the world as_________and all receipts from rest of the world as______
a) Credit, Debit b) Debit, Credit c) Debit, Debit d) Credit, CreditShow Answer
Ans – b) Explanation:- Foreign exchange inflow is recorded on the credit side. The outflow of foreign exchange is recorded at the debit side of the BoP.
Q9. Balance on invisible trade is equal to
a) Export of goods – Import of goods b) Export of services – Import of services c) Import of goods – Export of goods d) Import of services – Export of goods
Ans – b) Explanation:- Invisible trade means trade of intangible goods like services
Q10. If value of visible exports is greater than the value of invisible imports, the balance relates to
a) Current account Bop b) Trade Deficit c) Capital account BoP d) Can’t be determinedr
Ans – d) Explanation:- Only visible exports are compared with visible imports and invisible exports are compared to invisible imports.
Q11. Balance of trade is a__________concept as compared to balance of payments.
a) narrower b) broader c) similar d) None of the above
Ans – a)
Explanation:- Balance of trade is the difference between exports and imports of visible goods. It is just a part of current account
Q12. If trade deficit is ₹ 1500 crores and import of goods are ₹ 3500 crores, value of export of goods will be ₹ 2000 crores?
a) True b) False c) Partially true d) Can’t be predicted
Ans – a)
Explanation:- Trade deficit = Imports of goods – Exports of goods
Q13. Trade deficit refers to the situation where
a) Export of goods is more than the import of goods b) export of goods is less than the import of goods c) export of services is more than the import of services d) export of services is less than the import of services
Ans – b)
Explanation:- When exports of goods is less than the imports of goods. it is the situation of Trade Deficit.
Q14. Uni-lateral transfers are included in
a) current account Bop b) capital account Bop c) Both a) and b) d) None of these
Ans – a)
Explanation:- Unilateral transfers are the part of invisible sections of Current account of BoP.
Q15. An Indian real estate company received rent from google in New York. This transaction would be recorded on____________side of_____________account.
a) credit, current b) debit, capital c) credit, capital d) debit, current
Ans – a)
Explanation:- It is an income out of Investment. It is recorded as income receipts at credit side under invisible trade in current account
Q16. A company located in India receives a loan from a company located abroad. How is this transaction recorded in India’s Balance of Payments Account?
a) Credit side of current account b) Debit side of current account c) Credit side of Capital account d) Debit side of Capital account
Ans – c)
Explanation:- It is financial transaction and increases the liabilities
Q17. An Indian Company located in India invests in a company located abroad. This transaction is entered in India’s Balance of Payments Account on:-
a) Credit side of current account b) Debit side of current account c) Credit side of Capital account d) Debit side of Capital account
Ans – d)
Explanation:- It is financial transaction and increases the assets of a country in rest of the world and results in outflow of foreign exchange
Q18. Foreign Exchange Transactions which are independent of other transactions in the Balance of Payments Account are called:
a) Current transactions b) Capital transactions c) Autonomous transactions d) Accommodating transactions
Ans – c)
Explanation:- Autonomous transactions are the transactions that are not influenced by other foreign exchange transactions. For example an Indian company wants to invest in USA rest state market.
Q19. Foreign Exchange Transactions dependent on other Foreign Exchange Transactions are called:
a) Current account transactions b) Capital account transactions c) Autonomous transactions d) Accommodating transactions
Ans – d)
Explanation:- Accommodating transactions are those that are undertaken as a consequence of the autonomous transactions
Q20. Which of the following statements is not true?
a) Borrowings from the Asia Development Bank by the government is an accommodating transaction. b) Loans given to Sri Lanka by the government are an accommodating transaction. c) Buying of machinery from Japan is an accommodating transaction d) Borrowing from the public is an accommodating transaction.
Ans – c)
Explanation:- Autonomous items refers to those Balance of Payment (BoP0 transactions which are undertaken for profit.
Q21. Who out of the following is included in “Residents” in BoP transactions?
a) Firms b) Foreign military personnel c) Government agencies d) Individuals
Ans – a),c),d)
Explanation:- Here residents means normal residents who has economic interest in the country
Q22. An accounting statement that provides a systematic record of all the economic transactions, between residents of a country and the rest of the world is________
a) Balance of Payments b) Balance of Trade c) Government Budget d) None of these
Ans – a)
Explanation:- BoP is the accounting statement that records the foreign exchange transactions of a country with the rest of the world.
Q23. Balance of Payments is a___________Concept.
a) Stock b) Flow c) Both a) and b) d) Neither a) nor b)
Ans – b)
Explanation:- BoP is prepared for a fiscal (accounting) year for 12 months.
Q24. Inflow of foreign exchange is recorded on the_________side.
a) Credit b) Debit c) Either a) or b) d) Neither a) nor b)
Ans – a),c),d)
Explanation:- Credit side of BoP records the inflow of foreign exchagne.
Q25. When receipts of foreign exchange are more than payments of foreign exchange, BOP is:
a) Balanced b) Surplus c) Deficit d) None of these
Ans – b),c),d)
Explanation:- When receipts of foreign exchange are more than payments. BoP results in surplus.
Q26. Unilateral Transfers are also known as:
a) Bilateral Transfers b) One-way Transfers c) Unrequited Transfers d) Neither a) nor b)
Ans – b)
Explanation:- Unilateral transfers are one way transactions. where one person does not receive anyting in return from another person.
Q27. Balance on ‘Balance of Trade’ can be:
a) Surplus b) Balanced c) Deficit d) Either a) or b) or c)
Ans – d)
Explanation:- Balance of trade is the difference between exports of goods and imports of goods. exports can be more, less and equal to imports of goods
Q28. Which of the following is a component of the Balance of Payment?
a) Current Account b) Capital Account c) Nominal Account d) Real Account
Ans – a),b)
Explanation:-
Q29. Export and import of goods is also known as:
a) Indivisible Trade b) Visible Trade c) One-sided Transactions d) Unrequited transfers
Ans – b)
Explanation:-
Q30. __________refers to the difference between exports and imports of visible items.
a) Balance of Payments b) Balance of Trade c) Both a) and b) d) Neither a) nor b)
Ans – b)
Q31. Autonomous transactions take place on
a) Real Account b) Capital Account c) Current Account d) None of these
Ans – b), c)
Explanation:-
Q32. ____________transactions are undertaken to cover the deficit or surplus in autonomous transactions.
a) current account b) current account c) Accommodating d) None of these
Ans – c)
Explanation:-
Q33. ________is the difference between value of goods sold to the rest of the world and value of goods imported from rest of the world.
a) Balance of Payment b) Balance of trade c) Balance of current account d) Balance of capital account
Ans – b)
Explanation:-
Q34. Gifts and remittances to abroad are recorded on the:
a) Credit side of current Account b) Debit side of Capital Account c) Debit side of current Account d) Credi side of Capital Account
Ans – c)
Q35. Export of the Machinery recorded on the:
a) Debit side of Current Account b) Credit side of Current Account c) Credit side of Capital Account d) Debit side of capital Account
Ans – b)
Q36. Surplus in BoP arises when
a) Autonomous Payments > Autonomous Receipts b) Accommodating Receipts > Accommodating Payments c) Accommodating Payments > Accommodating Receipts d) Autonomous Receipts > Autonomous Payments
Ans – d)
Q37. Balance of Trade is also known as:
a) Balance of Visible Trade b) Balance of Payments c) Trade Balance d) None of these
Ans – a)
Explanation:-
Q38. Import of Machinery is recorded in the_________Account and ‘Borrowings from abroad’ is recorded in the______Account.
a) Current, Capital b) Capital, Current c) Capital, Capital d) Current, Current
Ans – a)
Explanation:-
Q39. Foreign Exchange transactions are dependent on other foreign exchange transactions are called:
a) Current Account Transactions b) Capital Account Transactions c) Autonomous Transactions d) Accommodating Transaction
Ans – d)
Explanation:-
Q40. Foreign Exchange transactions which are independent of other transactions in the Balance of Payments Account are called:
a) Current Transactions b) Capital Transactions c) Autonomous Transactions d) Accommodating Transactions
NCERT MCQ ON I Excess Demand and Deficient Demand:
Q1._ is exercised through discussions, letters, and speeches to banks:
a) Moral suasion b) Selective Credit Controls c) Margin Requirements d) Open Market Operations
Ans – a)
Q2.Which of the following is not the reason for excess demand?
a) Fall in the propensity to consume b) Reduction in taxes c) Decrease in investments d) Deficit Financing
Ans – a),
Q3.Increase in cash reserve ratio will lead to:
a) Fall in Aggregate Demand b) Rise in Aggregate Demand c) No change in Aggregate Demand d) Reduces credit creating power of Commercial banks
Ans – a), d)
Q4.The gap by which actual aggregate demand exceeds the aggregate demand required to establish full employment equilibrium is known as _ .
a) Deficient Demand b) Deflationary gap c) Inflationary gap d) Excess Demand
Ans – c)
Q5.“Change in Government Spending” is a part of:
a) Monetary Policy b) Fiscal Policy c) Either a) or b) d) Neither a) nor b)
Ans – b)
Q6.__ refers to the situation when aggregate supply falls showt of aggregate demand corresponding to full employment level of output in the economy.
a) Deficient Demand b) Excess Demand c) Inflationary Gap d) Deflationary gap
Ans – b)
Q7.Excess demand leads to:
a) Increase in the level of employment b) Decrease in the level of employemnt c) No change in the level of employment d) Increase in Price level
Ans – c), d)
Q8.Deficient Demand indicates:
a) Under employment equilibrium b) Over full employment equilibrium c) Full employment equilibrium d) None of these
Ans – a)
Q9.Monetary Policy is the policy of _ to control money supply and credit creation in the economy.
a) Central Government b) Central Bank c) Both a) and b) d) None of these
Ans – b)
Q10.During excess demand, central bank __ the margin.
a) Decreases b) Increases c) Removes d) Does not change
Ans – b)
Q11.If an economy is to control recession like most of the Euro Zone nations, which of the following can be appropriate:
a) Reducing Repo Rate b) Reducing CRR c) Both a) and b) d) None of a) and b)
Ans – c)
Q12.Aggregate demand can be increased by:
a) increasing bank rate b) selling government securities by Reserve Bank of India c) increasing cash reserve ratio d) none of the above
Ans – d)
Q13.The monetary policy generally targets to ensure _ .
a) Price stability in the economy b) Employment generation in the country c) Stable foreign relations d) Greater tax collections for the government
Ans – a)
Q14.Excess Demand can be controlled through:
a) Monetary Policy b) Fiscal Policy c) Both a) and b) d) Neither a) nor b)
Ans – c)
Q15.An economy is at full employment and AD is greater than AS, what will be the impact on price level in such an economy?
a) Rise b) Fall c) No change d) Both rise and fall
Ans – a)
Q16.Which of the following can be used to correct inflationary gap under Monetary Policy?
a) Increase in Taxation b) Reduce availability of credit c) Cut in Government Expenditure d) None of these
Ans – b)
Q17.Deficient Demand leads to:
a) Decrease in Planned Output b) Fall in General Prices c) Both a) and b) d) Rise in Employment Level
Ans – c)
Q18.During deflation, it is advisable to:
a) Lower the bank rate and purchase of securities in the open market b) Increase the bank rate and purchase of securities in the open market c) Lower the bank rate and sale of securities in the open market d) Increase the bank rate and sale of securities in the open market
Question 1. An index number which accounts for the relative importance of the items is known as (i) weighted index (ii) simple aggregative index (iii) simple average of relatives Answer: (i) An index number becomes a weighted index when the relative importance of items is taken care of weighted index is the weighted average of different goods.
Question 2. In most of the weighted index numbers the weight pertains to (i) base year (ii) current year (iii) both base and current year Answer: (i) In general, the base period weight is preferred in calculating the weighted index number but as per Laspeyre’s method it uses the base year quantity as weight, Paache uses current year quantities as weight and Fisher’s Index Method uses both base and current year quantities.
Question 3. The impact of change in the price of a commodity with little weight in the index will be (i) small (ii) large (iii) uncertain Answer: (i) An equal rise in the price of an item with little weight will have lower implications for the overall change in the price ;ndex than that of an Item with more weight.
Question 4. A consumer price index measures changes in (i) retail prices (ii) wholesale prices (iii) producers’prices Answer: (i) Consumer Price Index (CPI), also known as the cost of living index, measures the average change in retail prices which show the most accurate impact of price rise on the cost of living of common people.
Question 5. The item having the highest weight in consumer price index for industrial workers is (i) food (ii) housing (iii) clothing Answer: (i) As weight and Fisher’s index method uses both base and current year quantities. Food is given around 57% weight in CPI for industrial workers as it constitutes the major proportion of their total consumption.
Question 6. In general, inflation is calculated by using (i) wholesale price index (ii) consumer price index (iii) producer’s price index Answer: (i) The WPI is widely used to measure the rate of inflation. The weekly inflation rate is given by XtXt1Xt−1×100 where X, and Xt-1 to the WPI for the (t)th and (t- 1)th weeks.
Question 7. Why do we need an index number? Answer: Index number enables us to calculate a single measure of change of a large number of items. The index numbers are needed for the general and specific purpose they are
Measurement of Change in the Price Level or the Value of ‘ Money Index number measures the value of money during different periods of time as well as we can use it to know the Impact of the change in the value of money on different sections of society. It can be worked out to correct the inflationary and deflationary gaps in the system.
Information of Foreign Trade Index of export and import provides useful information regarding foreign trade which helps in formulating the policies of export and import.
Calculating Real Wages CPI are used in calculating the purchasing power of money and real wage as follows
Purchasing power of money = 1/Cost of living index
Real wage = (Money wage/Cost of living index) × 100
Measuring and Comparing Output Index of Industrial Production (IIP) gives us a quantitative figure about the change in production in the industrial sector and thus helps in comparing industrial output in different periods. Similarly, agricultural production index provides us an estimate of the production index provides us an estimate of the production in agricultural sector.
Policy Making of Government With the help of index numbers government determines the minatory and fiscal prey and take nassery steps to develop the country.
Indicating Stock Prices Sensex and NIFT are index numbers of share prices on BSE and NSE respectively. They serve as a useful guide for investors in the stock market. If the sensex and nifty are rising, investors have positive expectations about the future performance of the economy and it is an appropriate time for investment.
Question 8. What are the desirable properties of the base period? Answer: Base period should have the following properties
The base year should be a normal period and periods in which extraordinary events have occurred should not be taken as base periods as they are not appropriate for general comparisons.
Extreme values should not be selected as base period.
The period should not be too far in the past as comparison with current period cannot be done with such base year as policies, economic and social conditions change with time.
Base period should be updated periodically.
Question 9. Why is it essential to have different CPI for different categories of consumers? Answer: The Consumer Price Index (CPI) in India is calculated for different categories as under
CPI for industrial workers.
CPI for urban non-manual employees.
CPI for agricultural labourers.
The reason behind calculation of three different CPIs is that the consumption pattern of the three groups (i.e., industrial workers, urban non-manual workers and agricultural labourers) differs significantly from each other. Therefore, to assess the impact of the price change on the cost of living of the three groups, component items included in the index need to be given different weights for each of the group. This necessitates the calculation of different CPI for different categories of consumers.
Question 10. What does a consumer price index for industrial workers measure? Answer: Consumer price index for industrial workers measures the average change in retail prices of a basket of commodities which an industrial worker generally consumes. Consumer price index for industrial workers is increasingly being considered the appropriate indicator of general inflation, which shows the most accurate impact of price rise on the cost of living of common people.
The items included in CPI (Consumer Price Index) for industrial workers are food, pan, supari, tobacco, fuel and lighting, housing, colthing, and miscellaneous expenses with food being accorded the highest weight. This implies that the food price changes have a significant impact on the CPI.
Question 11. What is the difference between a price index and a quantity index? Answer: The difference between a price index and a quantity index is as follows
Price index numbers measure and allow for comparison of the prices of certain goods while quantity index number measure the changes in the physical volume of production, construction or employment.
Price index numbers are more widely used as compared to quantity index numbers.
Price index is known as unweighted index number while quantity index number is known was weighted index numbers.
Question 12. Is the change in any price reflected in a price index number? Answer: No, the change in any price is not reflected in a price index number. Price index numbers measure and permit comparison of the prices of certain goods included in the basket being used to compare prices in the base period with prices in the current period. Moreover, an equal rise in the price of an item with large weight and that of an item with low weight will have different implications for the overall change in the price index.
Question 13. Can the CPI number for urban non-manual emplyees represent the changes in the cost of living of the President of India? Answer: The CPI for the urban non-manual employees cannot represent the changes in the cost of living of the President of India. This is because the consumption basket of an average non-manual employee does not consist of the items that would be a part of the consumption basket of the President of India.
Question 14. The monthly per capita expenditure incurred by workers for an industrial centre during 1980 and 2005 on the following items are given below. The weights of these items are 75, 10, 5, 6 and 4 respectively. Prepare a weghted index number for cost of living for 2005 with 1980 as the base. Answer:
Question 15. Read the following table carefully and give your comments. Answer: Index of Industrial Production Base 1993-94 The following conclusions can be made by analysing the above table
Manufacturing industry has the highest weight of 79.58% in Index of Industrial Production (IIP) while mining and quarrying and electricity industries account for 10.73% and 10.69% respectively.
Manufacturing Industry has registered the highest growth among all industrial sectors in both the years 1996-97 and 2003-04.
Mining and quarrying has registered the lowest growth rate in both the years.
The General Index shows that industrial increased by 30.8% in 1996.-97 as compared to 1993-94 and by 89% in 2003-04.
Question 16. Try to list the important items of consumption in your family. Answer: (This is a general example. You can use the actual consumption items in your family). The following items constitute the total consumption needs for a family
Food
Clothing
House-Rent/EMI of Housing loan
Education
Electricity
Entertainment and recreation
Miscellaneous expenses
Question 17. If the salary of a person in the base year is ? 4,000 per annum and the current year salary is ? 6,000 by how much should his salary rise to maintanin the same standard of living if the CPI is 400? Answer: Base CPI = ₹ 100 Current CPI = ₹400 Base Year Salary = ₹ 4,000 Current Year Salary = ₹ 6,000 When Base CPI is ₹100, then the salary is = ₹ 4,000 Current salary equivalent to base year salary = (Base year salary/100) × CPI of current year When Current CPI is ₹ 400, then the salary should be = 4,000100×400 = ₹ 16,000 100 Thus, his salary should be X 16,000 to maintain his purchasing power. Therefore, in the current year his salary should increase by ₹ 16,000 – ₹ 6,000 = ₹ 10,000 so as to maintain the same level of living in the current year as that of the base year.
Question 18. The consumer price index for June, 2005 was 125. The food index was 120 and that of other items What is the percentage of the total weight given to food? Answer: Let the total weight = 100 W1 denotes weight of food W2 denotes weight of other items So, Multiplying both sides of Eq. (i) by 135 and subtracting Eq. (ii) from (i) we get So, W1 = 100015 = 66.67 Substituting the value of in the Eq. (i), we get W1 + W2 = 100 or 6667 + W2 = 100 W2 = 33.33 Therefore, percentage of total weight given to food is 66.67% and other items 33.33%.
Question 19. An enquiry into the budgets of the middle class families in a certain city gave the following information What is the cost of living index of 2004 as compared with 1995? Answer: Cost of Living Index = 134.50 Thus, the price rose by 34.50% during 1995 and 2004.
Question 20. Record the daily expenditure quantities bought and prices paid per unit of the daily purchases of your family for two weeks. How has the price change affected your family? Answer: This is a practical exercise. Record the daily expenditure, quantities bought and prices paid per unit of the daily purchases of your family for two weeks and try to analyse if quantities purchased decrease with rise in price of the respective items and also note if the percentage change in quantity brought about by a percentage change in price differ for different types of items.
Question 21. Given the following data Source Economic Survey, Government of India 2004-2005 (i) Calculate the inflation rates using different index numbers. (ii) Comment on the relative values of the index numbers. (iii) Are they comparable? Answer: (i) (a) Inflation using CPI of Industrial Workers
(b) Inflation using CPI of Non-maunal Employees (c) Inflation using CPI of Agricultural Labourers
(d) Inflation using WPI (ii) The inflation rate calculated using CPI industrial worker with the base year 1982 is the highest and inflation rate calculated using WPI with the base year 1993-94 is the least. (iii) No the index number are not comparable because of the following reasons
Base periods for CPI of industrial workers, urban non-manual workers, agricultural labourers and WPI are different.
Commodities and their weightage in different index number may be different.
Question 1. The unit of correlation coefficient between height in feet and weight in kgs is (a) kg/feet (b) percentage (c) non-existent Answer: (c) Correlation coefficient (r) has no unit. It is a pure number. It meansss units of measurement are not part of r.
Question 2. The range of simple correlation coefficient is (a) 0 to infinity (b) minus one to plus one (c) minus infinity to infinity Answer: (b) The value of the correlation coefficient lies between minus one and plus one, -1 ≤ r ≤ 1. If the value of r is outside this range it indicates error in calculation.
Question 3. If rXY is positive the relation between X and Y is of the type (a) when Y increases X increases (b) when Y decreases X increases (c) when Y increases X does not change Answer: (a) If r is positive the two variables move in the same direction. e.g., when the price of coffee rises, the demand for tea also rises as coffee is a substitute of tea. Therefore, the r between price of coffee and demand for tea will be positive
Question 4. If rXY = 0, the variable X and Y are (a) linearly related (b) not linearly related (c) independent Answer: (b) If rXY = 0, it means the two variables are uncorrelated and there is no linear relation between them. However, other types of relation may be there and they may not be independent.
Question 5. Of the following three measures which can measure any type of relationship? (a) Karl Pearson’s coefficient of correlation (b) Spearman’s rank correlation (c) Scatter diagram Answer: (c) The scatter diagram gives a visual presentation of the relationship and is not confined to linear relations. Karl Pearson’s coefficient of correlation and Spearman’s rank correlation are strictly the measures of linear relationship.
Question 6. If precisely measured data are available the simple correlation coefficient is (a) more accurate than rank correlation coefficient (b) less accurate than rank correlation coefficient (c) as accurate as the rank correlation coefficient Answer: (a) Rank correlation should be used only when the variables cannot be measured precisely, generally it is not as accurate as the simple correlation coefficient as all the information concerning the data is not utilised in this.
Question 7. Why is r preferred to covariance as a measure of association? Answer: Both, correlation coefficient and covariance measure the degree of linear relationship between two variables, but correlation coefficient is generally preferred to covariance due to the following reasons
The correlation coefficient (r) has no unit.
The correlation coefficient is independent of origin as well as scale.
Question 8. Can r lie outside the -1 and 1 range depending on the type of data? Answer: No the value of the correlation coefficient lies between minus one and plus one, -1 ≤ r ≤ 1. If the value of r is outside this range in any type of data, it indicates error in calculation.
Question 9. Does correlation imply causation? Answer: No, correlation measures do not imply causation. Correlation measures co-variation and not causation. Correlation does not imply cause and effect relation. The knowledge of correlation only gives us an idea of the direction and intensity of change in a variable when the correlated variable changes. The presence of correlation between two variables X and Y simply means that when the value of one variable is found to change in one direction, the value of the other variable is found to change either in the same direction (i.epositive change) or in the opposite direction (i.e., negative change), in a definite way.
Question 10. When is rank correlation more precise than simple correlation coefficient? Answer: Rank correlation is more precise than simple correlation coefficient in the following situations
When the Measurements of the Variables are Suspect e.g., in a remote village where measuring rods or weighing scales are not available, height and weight of people cannot be measured precisely but the people can be easily ranked in terms of height and weight.
When Data is Qualitative It is difficult to quantify qualities such as fairness, honesty etc. Ranking may be a better alternative to quantification of qualities.
When Data has Extreme Values Sometimes the correlation coefficient between two variables with extreme values may be quite different from the coefficient without the extreme values. Under these circumstances rank correlation provides a better alternative to simple correlation.
Question 11. Does zero correlation mean independence? Answer: No, zero correlation does not mean independence. If there is zero correlation (rXY = 0), it means the two variables are uncorrelated and there is no linear relation between them. However, other types of relation may be there and they may not be independent.
Question 12. Can simple correlation coefficient measure any type of relationship? Answer: No, simple correlation coefficient can measure only linear relationship.
Question 13. List some variables where accurate measurement is difficult. Answer: Accurate measurement is difficult in case of
Qualitative variables such as beauty, intelligence, honesty, etc.
It is also difficult to measure subjective variables such as poverty, development, etc which are interpreted differently by different people.
Question 14. Interpret the values of r as 1, -1 and 0. Answer:
If r = 0 the two variables are uncorrelated. There is no linear relation between them. However, other types of relation may be there and hence the variables may not be independent.
If r= 1 the correlation is perfectly positive. The relation between them is exact in the sense that if one increases, the other also increases in the same proportion and if one decreases, the other also decreases in the same proportion.
If r = -1 the correlation is perfectly negative. The relation between them is exact in the sense that if one increases, the other decreases in the same proportion and if one decreases, the other increases in the same proportion.
Question 15. Why does rank correlation coefficient differ from Pearsonian correlation coefficient? Answer: Rank correlation coefficient differs from Pearsonian correlation coefficient in the following ways
Rank correlation coefficient is generally lower or equal to Karl Pearson’s coefficient.
Rank correlation coefficient is preferred to measure the correlation between qualitative variables as these variables cannot be measured precisely.
The rank correlation coefficient uses ranks instead of the full set of observations that leads to some loss of information.
If extreme values are present in the data, then the rank correlation coefficient is more precise and reliable.
Question 16. Calculate the correlation coefficient between the heights of fathers in inches (X) and their sons (Y). Answer: Note Answer: printed in NCERT is incorrect.
Question 17. Calculate the correlation coefficient between X and Y and comment on their relationship. Answer:
As the value of r is zero, so there is no linear correlation between X and Y.
Question 18. Calculate the correlation coefficient between X and Y and comment on their relationship. Solution As the correlation coefficient between the two variables is + 1, so the two variables are perfectly positive correlated
Answer: Dispersion is the measure of the extent to which different items tend to dispense away from the central tendency.
Question 2
What is the coefficient of dispersion?
Answer: The coefficient of dispersion shows different data percentage or relative value. The coefficient of dispersion is known as a relative measure of dispersion.
Question 3
Define range.
Answer: Range is the variance between the lowest and highest value in a series. Therefore, Range = Highest value in the series – Lowest value in the series.
Question 4
Explain the interquartile range.
Answer: In a series, the difference between the first Quartile (Q1) and third Quartile (Q3) is known as the interquartile range.
Question 5
What is the quartile deviation?
Answer: Half of the interquartile range is Quartile deviation. It can also be mentioned as semi-inter quartile range.
Question 6
What is the coefficient of quartile deviation formula?
Answer: For calculating the coefficient of quartile deviation, the formula applied is.
Q3−Q1/ Q3+Q1
Question 7
Define mean deviation.
Answer: A mathematics average of the deviations of all the principles taken from some average value (mean, median, mode) of the series, ignoring signs (+ or -) of the deviation is mean deviation.
Question 8
What is standard deviation?
Answer: The square root of the arithmetic mean of the squared deviations of the items from their mean value.
Question 9
What is a Lorenz curve?
Answer: Lorenz curve is a curve that shows the actual distribution deviation (of income or wealth) from the line exhibiting equal distribution.
Question 10
Define variance.
Answer: Variance is another measure of dispersion. Variance is the square of the standard deviation.
Question 11. A measure of dispersion is a good supplement to the central value in understanding a frequency distribution. Comment. Answer: Dispersion is the extent to which values in a distribution differ from the avarage of the distribution. Knowledge of only average is insufficient as it does not reflect the quantum of variation in values.
Measures of dispersion enhance the understanding of a distribution considerably by providing information about how much the actual value of items in a series deviate from the central value, e.g., per capita income gives only the average income but a measure of dispersion can tell you about income inequalities, thereby improving the understanding of the relative living standards of different sections of the society. Through value of dispersion one can better understand the distribution.
Thus a measure of dispersion is a good supplement to the central value in understanding a frequency distribution.
Question 12. Which measure of dispersion is the best and how? Answer: Standard Deviation is considered to be the best measure of dispersion and is therefore the most widely used measure of dispersion.
It is based on all values and thus provides information about the complete series. Because of this reason, a change in even one value affects the value of standard deviation.
It is independent of origin but not of scale.
It is us’eful in advanced statistical calculations like comparison of variability in two data sets.
It can be used in testing of hypothesis.
It is capable of further algebraic treatment.
Question 13. Some measures of dispersion depend upon the spread of values whereas some calculate the variation of values from a central value. Do you agree? Answer: Yes, it is true that some measures of dispersion depend upon the spread of values, whereas some calculate the variation of values from the central value. Range and Quartile Deviation measure the dispersion by calculating the spread within which the value lie. Mean Deviation and Standard Deviation calculate the extent to which the values differ from the average or the central value.
Question 14. In town, 25% of the persons earned more than ₹ 45,000 whereas 75% earned more than 18,000. Calculate the absolute and relative values of dispersion. Answer: 25% of the persons earned more than ₹ 45,000. This implies that upper quartile Q3 = 45,000 75% earned more than 18,000. This implies that lower quartile Q1 =18,000 Absolute Measure of Dispersion = Q3 – Q1 = 45,000 – 18,000 = 27,000 Relative Measure of Dispersion Co-efficient of Quartile Deviation
Question 15. The yield of wheat and rice per acre for 10 districts of a state is as under Calculate for each crop, (i) Range (ii) QD (iii) Mean’Deviation about Mean (iv) Mean Deviation about Median (v) Standard Deviation (vi) Which crop has greater variation? (vii) Compare the value of different measures for each crop. Answer: (i) Range (a) Wheat Highest value of distribution (H) = 25 Lowest value of distribution (L) = 9 Range = H – L = 25 – 9 = 16 (b) Rice Highest value of distribution (H) = 34 Lowest value of distribution (L)=12 Range = H – L = 34 – 12 = 22 (ii) Quartile Deviation (a) Wheat Arranging the production of wheat in increasing order 9, 10, 10, 12, 15, 16, 18, 19, 21, 25 Q1 = N+14th item = 10+14th item = 114th item = 2.75th item = Size of 2nd item + 0.75 (size of 3rd item – size of 2nd item) = 10 + 0.75(10 – 10) = 10 + 0.75 × 0 = 10 Q3 = 3(N+1)4th item = 3(10+1)4th item = 334th item = 8.25th = Size of 8th item + 0.25 (size of 9th item – size of 8th item) = 19 + 0.25(21 – 19) = 19 + 0.25 × 2 = 19 + 0.50 = 19.50 Quartile Deviation = Q3−Q12=19.50−102=9.502 = 4.75 (b) Rice Arranging the data of production of rice 12, 12, 12, 15, 18, 18, 22, 23, 29, 34 item Q1 = N+14th item = 10+14th item = 2.75 th item = Size of 2nd item + 0.75 (size of 3rd item – size of 2nd item) = 12 + 0.75(12 – 12) = 12 + 0.75 × 0 = 12 = 8.25th item = Size of 8th item + 0.25 (size of 9th item – size of 8th item) = 23 + 0.25(29 – 23) = 23 + 0.25 × 6 = 23 + 1.5 = 24.5 Quartile Deviation = Q3−Q12=24.5−122=12.502 = 6.25
(iii) Mean Deviation about Mean (a) Wheat
(b) Rice
(iv) Mean Deviation about Median (a) Wheat
(b) Rice
(v) Standard Deviation (a) Wheat
(b) Rice
(vi) Coefficient of Variation (a) Wheat CV =σX¯¯¯¯¯×100=5.0415.5×100 = 32.51 (b) Rice CV =σX×100=7.1619.5×100 = 36.71 Rice crop has greater variation as the coefficient of variation is higher for rice as compared to that of wheat. (vii) Rice crop has higher Range, Quartile Deviation, Mean Deviation about Mean, Mean Deviation about Median, Standard Deviation and Coefficient of Variation.
Question 16. A batsman is to be selected for a cricket team. The choice is between X and Y on the basis of their scores in five previous scores which are Which batsman should be selected if we want, (i) a higher run-getter, or (ii) a more reliable batsman in the team? Answer: Batsman X
(i) Average of Batsman X is higher than that of Batsman Y, so he should be selected if we want a high scorer. (ii) The Batsman Y is more reliable than Batsman X. This is because the coefficient of variation of Batsman X is higher than that of Batsman Y.
Question 17. To check the quality of two brands of light bulbs, their life in burning hours was estimated as under for 100 bulbs of each brand. (i) Which brand gives higher life? (ii) Which brand is more dependable? Answer: For Brand A For Brand B
Q14. The size of land holdings of 380 families in a village is given below. Find the median size of land holdings.
Size of Land Holdings (in acres)
Less than 100
100-200
200-300
300-400
400 and above
Number of families
40
89
148
64
39
Answer
Size of Land Holdings Class Interval
Number of families(f)
Cumulative frequency (CF)
0-100
40
40
100-200
89
129
200-300
148
277
300-400
64
341
400-500
39
380
Total
Σf = 380
Σf = N = 380 Median = Size of (N/2)th item = 380/2 = 190th item It lies in class 200-300. Median size of land holdings = 241.22 acres
Q15. The following series relates to the daily income of workers employed in a firm. Compute (a) highest income of lowest 50% workers (b) minimum income earned by the top 25% workers and (c) maximum income earned by lowest 25% workers.
Daily Income (in Rs)
10-14
15-19
20-24
25-29
30-34
35-39
Number of workers
5
10
15
20
10
5
(Hint: Compute median, lower quartile and upper quartile.)
Answer
Daily Income (in Rs) Class Interval
No of workers(f)
Cumulative frequency (CF)
9.5-14.5
5
5
14.5-19.5
10
15
19.5-24.5
15
30
24.5-29.5
20
50
29.5-34.5
10
60
34.5-39.5
5
65
Total
Σf = 65
(a) Σf = N = 65 Median = Size of (N/2)th item = 65/2 = 32.5th item It lies in class 24.5-29.5. Highest income of lowest 50% workers = Rs 25.12
(b) First, we need to find Q1 Class interval of Q1 = (N/4)th items = (65/4)th items = 16.25th item It lies in class 19.5-24.5. Minimum income earned by the top 25% workers = Rs 19.92
(c) First, we need to find Q3 Class interval of Q3 = 3 (N/4)th items = 3 (65/4)th items = 3 × 16.25th item = 48.75th item It lies in class 24.5-29.5. Maximum income earned by lowest 25% workers = Rs 29.19
Q16. The following table gives production yield in kg. per hectare of wheat of 150 farms in a village. Calculate the mean, median and mode values.
Production yield (kg. per hectare)
50-53
53-56
56-59
59-62
62-65
65-68
68-71
71-74
74-77
Number of workers
3
8
14
30
36
28
16
10
5
Answer
Production Yield (kg. per hectare)
No. of farms Frequency (f)
Mid Class (x)
fx
Cumulative frequency (CF)
50-53
3
51.5
154.5
3
53-56
8
54.5
436
11
56-59
14
57.5
805
25
59-62
30
60.5
1815
55
62-65
36
63.5
2286
91
65-68
28
66.5
1862
119
68-71
16
69.5
1112
135
71-74
10
72.5
725
145
74-77
5
75.5
377.5
150
Σf = 150
Σfx = 9573
Mean = Σfx/Σf = 9573/150 = 63.82 hectare Modal Class = 62-65
Answer: The presentation of data is a representation of data in an attractively and transparent manner that everybody understands and analyses.
Q2.What is tabulation?
Answer: Tabulation means presenting data in tabular form.
Q3.Define table.
Answer: Table refers to the systematic representation of data with rows and columns.
Q4.Explain a simple table.
Answer: A simple table only displays one characteristic of the data.
Q5.What is a complex table?
Answer: It is a table that shows more than one characteristic of the data.
Q6.Define a derived table.
Answer: A derived data is something where the information is not displayed according to the way it was collected. It is first into rations or percentages and then presented.
Q7.What are the two principal parts of a table?
Answer: The two principal parts of a table are (i) Table number and (ii) Title
Q8.What are the different kinds of a table?
Answer: Tables can be classified into three parts. (i) Purpose (ii) Originality, and (iii) Construction
Q9.What are the two types of complex table?
Answer: The two types of a complex table are (i) Double or two-way table and (ii) Manifold table
Q10.What are a different forms of presentation of data?
Answer: The different form of presentation of data are (i) Textual and descriptive presentation (ii) Tabular presentation, and (iii) Diagrammatic presentation
Q11. What kinds of diagrams are more effective in representing the following? (i) Monthly rainfall in a year (ii) Composition of the population of Delhi by religion (iii) Components of cost in a factory
Answer (i) Monthly rainfall in a year – simple bar diagram as only one variable i.e. monthly rainfall is to be present and compared visually. (ii) Composition of the population of Delhi by religion – Simple bar diagram Plotting different religion on the x-axis and the number of people on the y-axis, one can easily compare the number of the population religion-wise. (iii) Components of cost in a factory – Pie chart as entire circle represents the total cost and various components of costsare shown by different portions of the circle.
Q12. Suppose you want to emphasise the increase in the share of urban non-workers and lower level of urbanisation in India as shown in Example 4.2. How would you do it in the tabular form? Answer
Urban non workers
Rural Non Workers
Total Non workers
19 crores
42 crores
62 crores
The number of rural non-workers is greater than urban non-workers. The higher number of rural non-workers indicates lower level of urbanisation in India according to 2001 Census data.
Q13. How does the procedure of drawing a histogram differ when class intervals are unequal in comparison to equal class intervals in a frequency table? Answer When the class intervals are equal then by normal method we can make histogram which has equal width of rectangle. When the class intervals are unequal, heights of rectangles are to be adjusted to yield comparable measurements by using frequency density (class frequency divided by width of the class interval) instead of absolute frequency.
Q14. The Indian Sugar Mills Association reported that, ‘Sugar production during the first fortnight of December 2001 was about 3,87,000 tonnes, as against 3,78,000 tonnes during the same fortnight last year (2000). The off-take of sugar from factories during the first fortnight of December 2001 was 2,83,000 tonnes for internal consumption and 41,000 tonnes for exports as against 1,54,000 tonnes for internal consumption and nil for exports during the same fortnight last season.’ (i) Present the data in tabular form. (ii) Suppose you were to present these data in diagrammatic form which of the diagrams would you use and why? (iii) Present these data diagrammatically. Answer
(i)
Sugar Production in India
Date
Total Production (tonnes)
Internal Consumption (tonnes)
Export of sugar (tonnes)
December, 2000
3,78,000
1,54,000
–
December, 2000
3,27,000
2,83,000
41,000
(ii) To present these data in diagrammatic form we can use multiple bar diagram because these are effective in comparing two or more sets of data.
(iii)
Q15. The following table shows the estimated sectoral real growth rates (percentage change over the previous year) in GDP at factor cost.
Represent the data as multiple time series graphs. Answer
Q1. What is a variable? Distinguish between a discrete and a continuous variable.
Answer
A characteristic, number, or quantity whose value changes overtime is called variable. For example: weight, income etc. It can be either discrete or continuous.
Discrete Variable
Continuous Variable
• A variable that takes only whole number as its value is called discrete variable.
• These variables increase in jumps or in complete numbers.
• For example- Number of people in a family, number of students in a class, etc.
• A variable that can take any value, within a reasonable limit is called a continuous variable.
• These variables assume a range of values or increase in fractions and not in jumps.
• For example- age, height, weight, etc.
Q2. Explain the ‘exclusive’ and ‘inclusive’ methods used in classification of data. Answer
Exclusive method: The classes, by this method, are formed in such a way that the upper class limit of one class equals the lower class limit of the next class for example, 0-10, 10-20, and so on . Thus, the continuity of the data is maintained. The upper class limit is excluded but the lower class limit of a class is included in the interval. This method is most appropriate for data of continuous variables.
Inclusive method: This method does not exclude the upper class limit in a class interval. It includes the upper class in a class. Thus both class limits are parts of the class interval for example, 1-5, 6-10, 11-15 and so on. The interval 1-5 includes both the limits i.e. 1 and 5.
Q3. Use the data in Table 3.2 that relate to monthly household expenditure (in Rs) on food of 50 households and obtain the range of monthly household expenditure on food.
(i) Obtain the range of monthly household expenditure on food.
Answer
Range = Highest Value – Lowest Value Highest Value = 5090 Lowest Value = 1007 So, Range = 5090 – 1007 = 4083
Q4.Divide the range into appropriate number of class intervals and obtain the frequency distribution of expenditure. Answer
Q5. Find the number of households whose monthly expenditure on food is(a) less than Rs 2000(b) more than Rs 3000 c) between Rs 1500 and Rs 2500
Answer
(a) Number of households whose monthly expenditure on food is less than Rs 2000 = 20 + 13 = 33
(b) Number of households whose monthly expenditure on food is more than Rs 3000 = 2+1+2+0+1 = 6 (c) Number of households whose monthly expenditure on food is between Rs 1500 and Rs 2500 = 13 + 6 = 19 Page No: 39
Q6. In a city 45 families were surveyed for the number of domestic appliances they used. Prepare a frequency array based on their replies as recorded below.
Answer
No. of Domestic Appliances
No. of Households
0
1
1
7
2
15
3
12
4
5
5
2
6
2
7
1
Total
45
Q7.. What is ‘loss of information’ in classified data?
Answer
The classified data summarises the raw data making it concise and comprehensible, it does not show the details that are found in raw data. Once the data are grouped into classes, an individual observation has no significance in further statistical calculations. Further, the statistical calculations are based on the values of the class marks, ignoring the exact observations of the data leading to the problem of loss of information.
Q8. Do you agree that classified data is better than raw data?
Answer
The raw data are usually large an fragmented, it is very difficult to draw any meaningful conclusion from them. Classification makes the raw data comprehensible by surprising them into groups. When facts of similar characteristics are placed in the same class, it enables one to locate them easily, make comparison, and draw inferences without any difficulty. Therefore, classified data is better than raw data
Q9. Distinguish between Univariate and Bivariate frequency distribution. Answer
The frequency distribution of a single variable is called a Univariate Distribution. Income of people, marks scored by students, etc. are examples of Univariate Distribution.
The frequency distribution of two variables is called Bivariate distribution. Sales and advertisement expenditure, weight and height of individuals, etc. are examples of Bivariate distribution.
Q10. Prepare a frequency distribution by inclusive method taking class interval of 7 from the following data:
