An earlier Assistant Statistical Officer subject paper, all 150 questions in the paper’s own words. Under each, Show answer gives the right option, the working that gets there, and the page on this site that teaches the topic. Its questions fall under the same ten items of the Paper-II syllabus — see the syllabus map. Also solved: the paper of 29 April 2025.
Source. The Commission’s question paper preview “ECOSTATS 0411S2”, created 2022-11-04 (the PDF), which marks the correct option of every question in green, with a tick. It states: 150 questions, duration 150 minutes, total marks 150, negative marks 0.33 per wrong answer. In this PDF every question and option is printed as a picture, English above Telugu, with no text behind it; the English is transcribed here from those pictures. The numbering and the answer marked are read from the PDF itself.
How to read it. The answer shown is the right option among those printed, with the working that gets there. Where a question or an option is loosely printed, the working says how it is read.
By item of the Paper-II syllabus. Each question is placed in the item it tests; the reasoning-style questions sit with the subject they reason about.
“Production is the outcome of the combined activity of the four factors of production”.
With reference to the above statement, which of the following is/are NOT considered as factors of production?
(i) Land
(ii) Labour
(iii) Capital
(iv) Organisation
(v) Service
Answer: (4) (v) only
The four factors of production are land, labour, capital and organisation (enterprise); each earns rent, wages, interest and profit. A service is an output, not a factor.
Study this: National Income and the National Accounts — Economics (Unit 2)
Two goods X and Y are said to be ______ if the price of good X is inversely related to the demand of good Y.
Answer: (2) complementary
Complements are used together (car and petrol): a rise in the price of X lowers the demand for Y. For substitutes the relation runs the other way — a dearer X raises the demand for Y.
Study this: Price Determination, Market Structures and Factor Incomes — Economics (Unit 1)
Which of the following statements are true/false?
(i) Inferior goods have positive income effect.
(ii) Inferior goods have negative income effect.
Answer: (4) Statement (i) is false and statement (ii) is true
For an inferior good demand falls as income rises, so its income effect is negative: (i) is false and (ii) is true.
Study this: Price Determination, Market Structures and Factor Incomes — Economics (Unit 1)
Which of the following statements is FALSE regarding degree of price elasticity of demand?
Answer: (1) Perfectly Elastic Demand: ($E_d = 1$)
Perfectly elastic demand has $E_d = \infty$ (a horizontal demand curve); $E_d = 1$ is unit elasticity. The other three are stated correctly.
Study this: Price Determination, Market Structures and Factor Incomes — Economics (Unit 1)
A ______ competition is a market situation, in which many firms compete with each other to sell their closely-related differentiated products.
Answer: (3) monopolistic
Many firms selling close but differentiated products (brands of soap, toothpaste) is monopolistic competition. Perfect competition has identical products, oligopoly a few firms.
Study this: Price Determination, Market Structures and Factor Incomes — Economics (Unit 1)
If the nominal GDP = ₹18,000 crores and the real GDP = ₹12,000 crores, calculate the GDP deflator.
Answer: (2) 1.5 or 150%
GDP deflator $= \dfrac{\text{nominal GDP}}{\text{real GDP}} = \dfrac{18{,}000}{12{,}000} = 1.5$, or 150%.
Study this: National Income and the National Accounts — Economics (Unit 2)
Which of the following is NOT a method of measurement of National Income?
Answer: (4) Cost Accounting Method
National income is measured by the value added (product), income and expenditure methods. Cost accounting is a branch of accounting, not a method of measuring it.
Study this: National Income and the National Accounts — Economics (Unit 2)
If the disposable income is ₹100 and consumption expenditure is ₹80, calculate the Average Propensity to Save (APS)?
Answer: (1) 20%
Saving $= 100 - 80 = 20$, so APS $= S/Y = 20/100 = 20\%$.
Not taught on this site yet — see where this site is thinnest.
The part of investment (increase or decrease) which takes place due to a change in the level of national income is termed as ______.
Answer: (3) induced investment
Investment that responds to a change in income (or output) is induced investment. Autonomous investment does not depend on income; gross and net differ only by depreciation.
Not taught on this site yet — see where this site is thinnest.
Which of the following statements are correct/incorrect regarding items excluded from money supply of a country?
(i) The cash held by commercial banks is included in money supply.
(ii) The stock of monetary gold held in reserves as a backing to paper currency is included in money supply.
Answer: (1) Both statements (i) and (ii) are incorrect.
Both statements name items that are excluded from the money supply. Cash held by the banks themselves is not money in the hands of the public, so (i), which says it is included, is incorrect. The monetary gold kept as backing for the currency is not in circulation either, so (ii), which says it is included, is incorrect too. Both statements are incorrect.
Study this: Money, Banking and Credit Creation — Economics (Unit 3)
Which of the following is/are considered as primary function(s) of money?
(i) Medium of exchange
(ii) Measure of value
(iii) Store of value
(iv) Transfer of value
Answer: (2) (i) and (ii) only
The primary (main) functions are medium of exchange and measure of value. Store of value and transfer of value (standard of deferred payment) are the secondary functions.
Study this: Money, Banking and Credit Creation — Economics (Unit 3)
Which of the following are correct regarding measures of money supply?
(i) $M_1$ = Currency-notes and coins with the public (excluding cash in hand of all commercial banks) + Demand deposits (excluding inter-bank deposits) of all commercial banks and cooperative banks + Other deposits held with the RBI
(ii) $M_2$ = $M_1$ + Savings deposits with post office savings banks
(iii) $M_3$ = $M_2$ + Time deposits of all cooperative banks only
(iv) $M_4$ = $M_3$ + Total deposits with the post office savings banks excluding National Savings Certificates.
Answer: (1) (i), (ii) and (iv) only
The RBI’s old four measures: $M_1$ as stated in (i); $M_2 = M_1 +$ savings deposits with post office savings banks; $M_4 = M_3 +$ all post office deposits except National Savings Certificates. (iii) is wrong: $M_3 = M_1 +$ net time deposits of all banks, commercial and cooperative, not $M_2$ plus cooperative banks only.
Study this: Money, Banking and Credit Creation — Economics (Unit 3)
Compute credit multiplier and total credit money created by the banking system, if the required reserve ratio is 10% for every ₹1,00,000 deposited in the banking system.
Answer: (1) 10 and ₹10,00,000
Credit multiplier $= 1/\text{RRR} = 1/0.10 = 10$, so a deposit of ₹1,00,000 supports $10 \times 1{,}00{,}000 = \text{₹}10{,}00{,}000$ of total deposits.
Study this: Money, Banking and Credit Creation — Economics (Unit 3)
Which of the following is correct with regard to Reserve Money?
Answer: (1) Reserve Money = Currency in circulation + Bankers’ deposits with RBI + Other deposits with RBI
Reserve money (M0, high-powered money) is currency in circulation plus the banks’ deposits with the RBI plus other deposits with the RBI. Deposits with the SBI are ordinary bank deposits.
Not taught on this site yet — see where this site is thinnest.
Calculate narrow money ($M_1$) from the following data.
| Particulars | In ₹ crores |
|---|---|
| Currency with public | 90,000 |
| Demand deposits with banking system | 2,00,000 |
| Time deposits with banking system | 2,20,000 |
| Other deposits with RBI | 2,80,000 |
| Saving deposits of post office saving banks | 60,000 |
Answer: (1) ₹5,70,000 crores
$M_1 =$ currency with the public $+$ demand deposits $+$ other deposits with the RBI $= 90{,}000 + 2{,}00{,}000 + 2{,}80{,}000 = \text{₹}5{,}70{,}000$ crores. Time deposits and post office savings deposits belong to broader measures.
Study this: Money, Banking and Credit Creation — Economics (Unit 3)
Which of the following statements are true/false?
(i) A government budget is an annual statement showing item wise estimates of receipts and expenditures during a fiscal year.
(ii) James Wilson presented India’s first budget on 18 February 1880.
Answer: (1) Statement (i) is true and statement (ii) is false
(i) is the definition of the annual financial statement. (ii) is false: James Wilson presented India’s first budget in 1860, not in 1880.
Study this: Public Finance, Budgets and Deficits — Economics (Unit 4)
Which of the following is/are considered as source(s) of non-tax revenue of the central government?
(i) Interest received on loans given by the government to the state.
(ii) Profits or dividends received by public enterprises like BHEL, LIC etc.
(iii) Grants or donations received by the government from international organizations.
Answer: (1) (i), (ii) and (iii)
Non-tax revenue is what the government earns without taxing: interest on its loans, dividends and profits of public enterprises, fees, and grants received. All three qualify.
Study this: Public Finance, Budgets and Deficits — Economics (Unit 4)
Calculate budget deficit from the following data:
| Items | In ₹ crores |
|---|---|
| Revenue receipts | 40,000 |
| Revenue expenditure | 30,000 |
| Capital receipts | 30,000 |
| Capital expenditure | 50,000 |
Answer: (3) ₹10,000 crores
Budget deficit $=$ total expenditure $-$ total receipts $= (30{,}000 + 50{,}000) - (40{,}000 + 30{,}000) = \text{₹}10{,}000$ crores.
Study this: Public Finance, Budgets and Deficits — Economics (Unit 4)
Which of the following statements is FALSE?
Answer: (2) A direct quote is the number of units of a foreign currency exchangeable for one unit of home currency.
A direct quote is the number of units of home currency per unit of foreign currency (so many rupees to the dollar). Units of foreign currency per unit of home currency is an indirect quote, so statement 2 is the false one.
Study this: International Economics: Trade, Balance of Payments and the Institutions — Economics (Unit 5)
The balance of trade surplus of a country is ₹800 crores. If the value of imports is ₹9,000 crores, find the value of exports.
Answer: (1) ₹9,800 crores
Balance of trade $=$ exports $-$ imports, so exports $= 800 + 9{,}000 = \text{₹}9{,}800$ crores.
Study this: International Economics: Trade, Balance of Payments and the Institutions — Economics (Unit 5)
Which of the following statements are true/false?
(i) The balance of payment of a country is a systematic record of all economic transactions between the residents of a country and rest of the world, during a year.
(ii) The current account records exports and imports of goods and services and unilateral transfers.
Answer: (1) Both statements (i) and (ii) are true
Both are the textbook definitions: the balance of payments records all economic transactions with the rest of the world in a year, and the current account holds goods, services and unilateral transfers.
Study this: International Economics: Trade, Balance of Payments and the Institutions — Economics (Unit 5)
The ______ account includes all international economic transactions with income or payment flows occurring within the current year and the ______ account is made up of transfers of financial assets and the acquisition and disposal of non-produced or non-financial assets.
Answer: (1) current; capital
Flows belonging to the current year (trade, income, transfers) go to the current account; transfers of financial assets and non-produced, non-financial assets go to the capital account.
Study this: International Economics: Trade, Balance of Payments and the Institutions — Economics (Unit 5)
The International Monetary Fund was established in ______ at the Bretton Woods Conference.
Answer: (2) 1944
The IMF was set up at the Bretton Woods Conference of July 1944, where its Articles of Agreement were drawn up. It came formally into being in December 1945 and began work in 1947, but the question ties the date to the conference: 1944.
Study this: International Economics: Trade, Balance of Payments and the Institutions — Economics (Unit 5)
The World Bank Group includes which of the following?
(i) International Bank for Reconstruction and Development (IBRD)
(ii) International Development Association (IDA)
(iii) International Finance Corporation (IFC)
(iv) Multilateral Investment Guarantee Agency (MIGA)
(v) International Centre for Settlement of Investment Disputes (ICSID)
Answer: (4) (i), (ii), (iii), (iv) and (v)
The World Bank Group has five institutions: IBRD, IDA, IFC, MIGA and ICSID.
Study this: International Economics: Trade, Balance of Payments and the Institutions — Economics (Unit 5)
Which of the following institutions was renamed as the World Bank?
Answer: (1) International Bank for Reconstruction and Development
The International Bank for Reconstruction and Development, founded at Bretton Woods, is the institution known as the World Bank (with IDA it forms the World Bank proper).
Study this: International Economics: Trade, Balance of Payments and the Institutions — Economics (Unit 5)
Which of the following statements are true/false regarding trade?
(i) Internal trade refers to buying and selling of goods and services within the boundaries of a nation.
(ii) The buying and selling of goods and services in large quantities for the purpose of resale or intermediate use is known as wholesale trade.
Answer: (1) Both statements (i) and (ii) are true
Both are the standard definitions: internal (home) trade is within a country’s borders, and buying and selling in bulk for resale or further use is wholesale trade.
Not taught on this site yet — see where this site is thinnest.
The stock of skill, ability, expertise, education and knowledge embodied in the people of a country is called ______.
Answer: (2) human capital
The stock of skill, education and knowledge in people is human capital. Human capital formation is the process of adding to that stock.
Study this: International Economics: Trade, Balance of Payments and the Institutions — Economics (Unit 5)
______ unemployment exists in an economy due to movement of people from one job to another and in the process, they remain unemployment for some times.
Answer: (4) Frictional
Unemployment while people move between jobs is frictional. Seasonal follows the season, cyclical follows the business cycle, and visible (open) unemployment is joblessness that can be seen and counted.
Study this: The Indian Economy: Poverty, Unemployment, Inequality and Planning — Economics (Unit 6)
As per the 2011 Census, the density of population in India is ___ persons per sq. km.
Answer: (1) 382
Census 2011 put India’s density at 382 persons per sq. km (up from 325 in 2001).
Study this: Applied Statistics Unit 4 — Vital Statistics
As per the 2011 Census, the number of males was pegged at ______ million and the population of females stood at ______ million.
Answer: (1) 623.7; 586.5
Census 2011 (provisional totals): 623.7 million males and 586.5 million females, 1,210.2 million in all.
Study this: Applied Statistics Unit 4 — Vital Statistics
India’s population as per the 2011 Census is:
Answer: (1) 1210.2 million
Census 2011 (provisional totals): 1,210.2 million (121.02 crore). 1,028 million was the 2001 figure.
Study this: Applied Statistics Unit 4 — Vital Statistics
______ gave the concept of the poverty line in pre-independent India.
Answer: (2) Dadabhai Naoroji
Dadabhai Naoroji, in Poverty and Un-British Rule in India, first estimated a poverty line for India, from the cost of a subsistence diet.
Study this: The Indian Economy: Poverty, Unemployment, Inequality and Planning — Economics (Unit 6)
For the estimation of the poverty line, who among the following coined the term ‘jail cost of living’?
Answer: (3) Dadabhai Naoroji
Naoroji based his estimate on the cost of the diet given to prisoners — the ‘jail cost of living’.
Study this: The Indian Economy: Poverty, Unemployment, Inequality and Planning — Economics (Unit 6)
______ unemployment refers to a situation wherein more people are engaged in any economic activity than required.
Answer: (1) Disguised
When more people work on a job than it needs, so that some could leave without output falling (their marginal product is zero), the unemployment is disguised. It is common on family farms.
Study this: The Indian Economy: Poverty, Unemployment, Inequality and Planning — Economics (Unit 6)
Which of the following statements are true/false?
(i) Occasionally poor are those who are rich most of the time but may sometimes have a patch of bad luck; may remain below the poverty line. They are called the usually poor.
(ii) Transient poor are those who regularly move in and out of poverty.
Answer: (2) Statement (i) is false and statement (ii) is true.
Statement (i) describes people who are rich most of the time but slip below the poverty line after a patch of bad luck. They are the occasionally poor, not the usually poor, who are among the chronic poor; so (i) is false. Statement (ii) says the transient poor are those who move in and out of poverty, which is what makes their poverty transient: the churning poor move in and out regularly, the occasionally poor now and then. So (ii) is true.
Study this: The Indian Economy: Poverty, Unemployment, Inequality and Planning — Economics (Unit 6)
Calculate fiscal deficit from the following particulars.
| Items | In ₹ crores |
|---|---|
| Estimated total expenditure of the government | 1,50,000 |
| Revenue receipts of the government | 1,20,000 |
| Non-debt capital receipt of the government | 10,000 |
Answer: (1) ₹20,000 crores
Fiscal deficit $=$ total expenditure $-$ (revenue receipts $+$ non-debt capital receipts) $= 1{,}50{,}000 - (1{,}20{,}000 + 10{,}000) = \text{₹}20{,}000$ crores.
Study this: Public Finance, Budgets and Deficits — Economics (Unit 4)
The Fiscal Responsibility and Budget Management Act to correct fiscal imbalances was passed in:
Answer: (2) 2003
The Fiscal Responsibility and Budget Management Act was passed in 2003 (it came into force in 2004).
Not taught on this site yet — see where this site is thinnest.
Which of the following options is correct regarding the First and Second Five-Year Plans?
Answer: (1), the table marked (1)
The First Plan ran from 1951 to 1956 and the Second from 1956 to 1961.
Study this: The Indian Economy: Poverty, Unemployment, Inequality and Planning — Economics (Unit 6)
The Nehru-Mahalanobis model was started in the ______ Five-Year Plan.
Answer: (2) Second
The Second Plan (1956–61) was built on P.C. Mahalanobis’s model, with its stress on heavy industry.
Study this: The Indian Economy: Poverty, Unemployment, Inequality and Planning — Economics (Unit 6)
The Government of India constituted the NITI Aayog in ______. NITI stands for ______.
Answer: (1) 2015; National Institution for Transforming India
NITI Aayog, the National Institution for Transforming India, replaced the Planning Commission on 1 January 2015.
Study this: The Indian Economy: Poverty, Unemployment, Inequality and Planning — Economics (Unit 6)
Who among the following is considered as the ‘Indian Father of the Green Revolution’?
Answer: (3) Dr. MS Swaminathan
M.S. Swaminathan led the introduction of high-yielding wheat and rice in India and is called the father of its Green Revolution.
Not taught on this site yet — see where this site is thinnest.
The first ever National Agriculture Policy was announced in:
Answer: (3) July 2000
The first National Agricultural Policy was announced in July 2000.
Not taught on this site yet — see where this site is thinnest.
Which of the following are major provisions of the Industrial Policy Resolution, 1956?
(i) Provision of Licensing
(ii) Expansion of Public Sector
(iii) Emphasis on Small Industries
Answer: (1) (i), (ii) and (iii)
The 1956 Resolution enlarged the public sector (Schedules A, B and C), kept industrial licensing for the private sector, and gave a special place to small and village industries.
Not taught on this site yet — see where this site is thinnest.
Which of the following transactions will be added when the starting point is debit, i.e. favourable balance as per cash book.
Answer: (1) Cheques issued but not presented for payment
Starting from a debit (favourable) cash-book balance, cheques issued but not yet presented have been deducted in the cash book but not yet by the bank, so they are added. The other three are deducted.
Study this: Bank Reconciliation Statement — Financial Accounting (Unit 4)
Which of the following concepts states that the transactions of business are recorded in the books of the business on the assumption that it is a continuing enterprise?
Answer: (2) Going Concern
Recording on the assumption that the business will continue indefinitely is the going concern concept; it is why assets are carried at cost less depreciation rather than at sale value.
Study this: What Accounting Is: Concepts, Conventions and the Rules of Debit and Credit — Financial Accounting (Unit 1)
The ______ accounting concept state that personal expenses of a proprietor or partners should be debited to the Drawing Account.
Answer: (1) Separate Business Entity
Business entity: the business is separate from its owner, so the owner’s personal expenses paid by the business are drawings, not business expenses.
Study this: What Accounting Is: Concepts, Conventions and the Rules of Debit and Credit — Financial Accounting (Unit 1)
ABC Ltd. follows the diminishing balance method of depreciation for depreciating machinery year after year due to the ______ convention.
Answer: (3) Consistency
Keeping to the same method from year to year, so that one year’s accounts compare with the next, is the convention of consistency.
Study this: What Accounting Is: Concepts, Conventions and the Rules of Debit and Credit — Financial Accounting (Unit 1)
‘The owner of a firm records his daily medical expenses in the firm’s Income Statement.’
With reference to the above statement, indicate which of the following accounting principles has the owner violated?
Answer: (1) Separate Business Entity
The owner’s medical bills are personal, and charging them to the firm mixes the owner with the business: it breaks the business entity concept.
Study this: What Accounting Is: Concepts, Conventions and the Rules of Debit and Credit — Financial Accounting (Unit 1)
Under which accounting concept are qualitative transactions NOT recorded in the books of account?
Answer: (1) Money Measurement
Only what can be measured in money is recorded; qualitative facts (staff morale, a manager’s skill) are left out. That is the money measurement concept.
Study this: What Accounting Is: Concepts, Conventions and the Rules of Debit and Credit — Financial Accounting (Unit 1)
Pass the necessary journal entry for the following transaction.
Issued cheque of ₹39,000 to Pranab, a creditor, in settlement of his account of ₹40,000.
Answer: (1) Pranab A/c Dr. ₹40,000
To Bank A/c ₹39,000
To Discount received A/c ₹1,000
Pranab’s account is closed by debiting the full ₹40,000; the bank pays ₹39,000 and the ₹1,000 he allowed is a gain: Pranab A/c Dr. 40,000, To Bank A/c 39,000, To Discount received A/c 1,000.
Study this: Journal and Ledger: the Accounting Process Worked End to End — Financial Accounting (Unit 2)
Repair expenses paid on the repair of an old machine purchased should be ______.
Answer: (1) debited to the Machinery A/c
Repairs needed to make a second-hand machine fit for use are part of the cost of acquiring it, so they are capitalised: debited to the Machinery A/c. Repairs during use would go to a Repairs A/c.
Not taught on this site yet — see where this site is thinnest.
Which of the following statements are true/false?
(i) Cash account is a real account.
(ii) Bank account is a real account.
Answer: (4) Statement (i) is true and statement (ii) is false.
The cash account is a real account (an asset). The bank account is a personal account — the bank is an artificial person — so (ii) is false.
Study this: What Accounting Is: Concepts, Conventions and the Rules of Debit and Credit — Financial Accounting (Unit 1)
Which of the following transactions will be deducted when the starting point is credit, i.e. favourable balance as per the bank statement or pass book?
Answer: (2) Cheques issued but not presented for payment.
Starting from a credit (favourable) pass-book balance, cheques issued but not yet presented will still reduce the bank balance, so they are deducted. The other three are added.
Study this: Bank Reconciliation Statement — Financial Accounting (Unit 4)
The Bank Reconciliation Statement is prepared as on 31 March 2021 starting with credit balance as per the bank pass book. State whether the following transactions will be shown in the Bank Reconciliation Statement by adding or deducting it from the given balance.
(i) Bank had collected interest and credited the account with ₹1,000.
(ii) Bill of exchange for ₹10,000 realized by the bank was not recorded in the cash book.
Answer: (1) Both transactions (i) and (ii) will be deducted from the bank pass book.
Both are credits the bank has made that the cash book does not yet show, so the pass book is higher; starting from its balance, both are deducted.
Study this: Bank Reconciliation Statement — Financial Accounting (Unit 4)
Identify which of the following transactions are shown as a Debit or Credit balance in a Trial Balance.
(i) Cash in hand
(ii) Rent outstanding
(iii) Creditors
(iv) Bank overdraft
(v) Sundry debtors
(vi) Bills receivable
(vii) Goodwill
(viii) Sales
Answer: (2) Debit balance: (i), (v), (vi) and (vii)
Credit balance: (ii), (iii), (iv) and (viii)
Assets and expenses are debit balances: cash, sundry debtors, bills receivable and goodwill. Liabilities and gains are credit balances: rent outstanding, creditors, bank overdraft and sales.
Study this: Trial Balance, Errors and Final Accounts — Financial Accounting (Unit 5)
Loss on sale of an old car used for business is ______.
Answer: (1) debited to the Profit and Loss Account
A loss on the sale of a fixed asset is a capital loss charged against the year’s profit: debited to the Profit and Loss Account (the asset account is credited to close it).
Study this: Depreciation, Reserves, Single Entry and Non-Trading Concerns — Financial Accounting (Unit 6)
Rectify the following two journal entries.
(i) A purchase of goods from Ram amounting to ₹1,500 has been wrongly passed through the sales book.
(ii) A credit sale of goods of ₹1,200 to Ramesh has been wrongly passed through the purchase book.
Answer: (1) (i) Purchases A/c Dr. ₹1,500
Sales A/c Dr. ₹1,500
To Ram A/c ₹3,000
(ii) Ramesh A/c Dr. ₹2,400
To Purchases A/c ₹1,200
To Sales A/c ₹1,200
(i) The purchase was posted as a sale: Ram was debited and Sales credited ₹1,500. Undo it and post it right: Purchases Dr. 1,500 and Sales Dr. 1,500, To Ram 3,000. (ii) The sale was posted as a purchase: Purchases debited and Ramesh credited ₹1,200. So Ramesh Dr. 2,400, To Purchases 1,200, To Sales 1,200.
Study this: Trial Balance, Errors and Final Accounts — Financial Accounting (Unit 5)
Mr. Mehra purchased a machine on 1 December 2021 for ₹5,00,000. He paid ₹20,000 for loading and carriage expenses to bring the machine to the factory. He further incurred ₹35,000 for installing the machine in the factory. Calculate the amount that will be debited to the Machinery Account.
Answer: (4) ₹5,55,000
Everything spent to bring an asset to use is capitalised: $5{,}00{,}000 + 20{,}000 + 35{,}000 = \text{₹}5{,}55{,}000$.
Not taught on this site yet — see where this site is thinnest.
The cost of a machine is ₹20,000 and the rate of depreciation is 10%. The company follows the diminishing balance method of depreciation. The useful life of the machine is 5 years. Calculate the amount of depreciation that will be charged to the Profit and Loss Account in the 3rd year.
Answer: (2) ₹1,620
At 10% on the diminishing balance: year 1 ₹2,000 (book value 18,000), year 2 ₹1,800 (16,200), year 3 $0.10 \times 16{,}200 = \text{₹}1{,}620$.
Study this: Depreciation, Reserves, Single Entry and Non-Trading Concerns — Financial Accounting (Unit 6)
Garima maintains books on the single entry system. She presented the following information.
Calculate the profit or loss made by Garima during the period.
Answer: (1) Profit made during the period = ₹9,000
Profit $=$ closing capital $-$ opening capital $+$ drawings $-$ fresh capital $= 33{,}800 - 30{,}400 + 9{,}600 - 4{,}000 = \text{₹}9{,}000$.
Study this: Depreciation, Reserves, Single Entry and Non-Trading Concerns — Financial Accounting (Unit 6)
Karl Pearson’s correlation coefficient is independent of:
Statement I: change of scale
Statement II: change of origin
Which option is correct?
Answer: (3) Both statements I and II are correct.
$r$ is unchanged by a change of origin and by a change of scale (up to its sign, if a scale factor is negative), so both statements hold.
Study this: Statistical Methods Unit 2 — Correlation
For the computation of Karl Pearson’s correlation coefficient:
Statement I: the two variables have to be measured on either an interval or ratio scale
Statement II: the two variables cannot be measured in entirely different units
Which option is correct?
Answer: (1) Only statement I is correct.
Pearson’s $r$ needs interval or ratio data (I). It is a pure number, so the two variables may well be in entirely different units — height in cm, weight in kg; II is false.
Study this: Statistical Methods Unit 2 — Correlation
The Spearman’s correlation coefficient between marks of two subjects for five students for the following data is:
| Roll No. | 1 | 2 | 3 | 4 | 5 |
|---|---|---|---|---|---|
| Mathematics | 56 | 45 | 61 | 58 | 76 |
| Statistics | 66 | 40 | 65 | 59 | 67 |
Answer: (2) 0.70
Ranks in mathematics 2, 1, 4, 3, 5 and in statistics 4, 1, 3, 2, 5; $d = -2, 0, 1, 1, 0$, $\sum d^2 = 6$. $\rho = 1 - \dfrac{6 \times 6}{5(25 - 1)} = 1 - 0.3 = 0.70$.
Study this: Statistical Methods Unit 2 — Correlation
The Pearson’s correlation coefficient of the given data having following calculations is:
$n = 5, \sum x = 260, \sum y = 16.5, \sum xy = 859, \sum x^2 = 13530, \sum y^2 = 54.55$
Answer: (4) 1.00
$r = \dfrac{n\sum xy - \sum x \sum y}{\sqrt{(n\sum x^2 - (\sum x)^2)(n\sum y^2 - (\sum y)^2)}} = \dfrac{4295 - 4290}{\sqrt{(67650 - 67600)(272.75 - 272.25)}} = \dfrac{5}{\sqrt{50 \times 0.5}} = 1$.
Study this: Statistical Methods Unit 2 — Correlation
The correlation coefficient from two lines of regression $Y + X = 5$ and $Y + 2X = 3$ is:
Answer: (4) 0.707
Taking $Y + X = 5$ as the line of $Y$ on $X$ gives $b_{yx} = -1$, and $Y + 2X = 3$ as $X$ on $Y$, $X = (3 - Y)/2$, gives $b_{xy} = -\tfrac{1}{2}$. (The other way round the product would be 2, more than 1, which is impossible.) So $r^2 = b_{yx}b_{xy} = 0.5$ and $|r| = 0.707$. Both coefficients are negative, so $r$ itself is $-0.707$; option 4 gives its size.
Study this: Statistical Methods Unit 3 — Concurrent Deviation, Multiple & Partial Correlation
The arithmetic mean of both regression coefficients is:
Answer: (1) greater than and equal to correlation coefficient
The two regression coefficients have the same sign as $r$, and $b_{yx}b_{xy} = r^2$. For $r \gt 0$ the arithmetic mean of two positive numbers is at least their geometric mean: $\tfrac{1}{2}(b_{yx}+b_{xy}) \ge \sqrt{b_{yx}b_{xy}} = r$, with equality only when $b_{yx} = b_{xy}$. So the mean of the regression coefficients is greater than or equal to the correlation coefficient (for a negative $r$ the same holds of their numerical values).
Study this: Statistical Methods Unit 3 — Concurrent Deviation, Multiple & Partial Correlation
When the overall sample dispersion is purely due to dispersion among the categories and not at all due to dispersion within the individual categories, then the value of the correlation ratio is:
Answer: (3) 1
The correlation ratio is $\eta^2 = $ (dispersion between the categories) $/$ (total dispersion). With no dispersion within the categories, the two are equal and $\eta = 1$.
Study this: Statistical Methods Unit 3 — Concurrent Deviation, Multiple & Partial Correlation
If the interclass correlation coefficient is 0.782, then the exams can be rated with ______ reliability by different raters.
Answer: (3) good
Agreement between different raters scoring the same exams is measured by the intraclass correlation (the paper writes “interclass”). On the usual guideline (Koo and Li, 2016), below 0.5 is poor, 0.5 to 0.75 moderate, 0.75 to 0.9 good, and above 0.9 excellent. 0.782 is good.
Study this: Statistical Methods Unit 3 — Concurrent Deviation, Multiple & Partial Correlation
For $n$ pairs from an uncorrelated bivariate normal distribution, the sampling distribution of the studentised Pearson's correlation coefficient follows:
Answer: (2) student $t$ -distribution with degree of freedom $n - 2$
If $\rho = 0$, $t = \dfrac{r\sqrt{n-2}}{\sqrt{1-r^2}}$ follows Student’s $t$ with $n - 2$ degrees of freedom (two are used up estimating the two means).
Not taught on this site yet — see where this site is thinnest.
For data (size $n$ ) that follow a bivariate normal distribution with zero population correlation ( $\rho = 0$ ), the exact density function $f(r)$ for the sample correlation coefficient $r$ of a normal bivariate is:
Answer: (4) $f(r) = \dfrac{(1-r^2)^{\frac{n-4}{2}}}{B\left(\frac{1}{2},\frac{1}{2}(n-2)\right)}$; $B$ is beta function
Under $\rho = 0$ the density of $r$ is $f(r) = \dfrac{(1-r^2)^{(n-4)/2}}{B\left(\frac{1}{2}, \frac{n-2}{2}\right)}$, $-1 \le r \le 1$ — the density that gives the $t$ result above.
Not taught on this site yet — see where this site is thinnest.
The Laspeyre’s price index from the following data is:
| Commodity | Base period | Current period | ||
|---|---|---|---|---|
| Price | Quantity | Price | Quantity | |
| Sugar | 2 | 10 | 4 | 5 |
| Salt | 5 | 12 | 6 | 10 |
| Tea | 4 | 20 | 5 | 15 |
| Snack | 2 | 15 | 3 | 10 |
Answer: (2) 135.3
Laspeyres uses base-year quantities: $\dfrac{\sum p_1q_0}{\sum p_0q_0} \times 100 = \dfrac{40 + 72 + 100 + 45}{20 + 60 + 80 + 30} \times 100 = \dfrac{257}{190} \times 100 = 135.3$.
Study this: Applied Statistics Unit 3 — Index Numbers
The Paasche’s quantity index from the following data is:
| Commodity | Base period | Current period | ||
|---|---|---|---|---|
| Price | Quantity | Price | Quantity | |
| Sugar | 10 | 8 | 11 | 10 |
| Salt | 15 | 6 | 9 | 12 |
| Tea | 8 | 12 | 17 | 20 |
Answer: (3) 161.27
Paasche’s quantity index weights by current prices: $\dfrac{\sum q_1p_1}{\sum q_0p_1} \times 100 = \dfrac{110 + 108 + 340}{88 + 54 + 204} \times 100 = \dfrac{558}{346} \times 100 = 161.27$.
Study this: Applied Statistics Unit 3 — Index Numbers
If the price index number satisfies $P_{01} \times P_{12} \times P_{20} = 1$ , then the index number follows the:
Answer: (3) circular test
$P_{01} \times P_{12} \times P_{20} = 1$ — going round the cycle of years brings the index back to where it started — is the circular test.
Study this: Applied Statistics Unit 3 — Index Numbers
The cost of living index number is constructed by the:
(I) Aggregate expenditure method
(II) Family Budget method
Which option is correct?
Answer: (3) Both (I) and (II)
A cost of living index is built by either the aggregate expenditure method (weights are base-year quantities) or the family budget method (a weighted mean of price relatives, the weights being base-year expenditure).
Study this: Applied Statistics Unit 3 — Index Numbers
The value of third quartile $Q_3$ for the following marks 25, 47, 34, 52, 23, 62, 29, 57 of 8 students in Statistics is:
Answer: (3) 55.75
In order: 23, 25, 29, 34, 47, 52, 57, 62. $Q_3$ is the $\tfrac{3(n+1)}{4} = 6.75$th value $= 52 + 0.75(57 - 52) = 55.75$.
Study this: Descriptive Statistics Unit 3 — Measures of Central Tendency
The yearly earnings of investment manager for the past 6 years are 4%, 6%, 7%, 8%, 8.2%, 9%. The range is:
Answer: (2) 5%
Range $=$ largest $-$ smallest $= 9\% - 4\% = 5\%$.
Study this: Descriptive Statistics Unit 4 — Measures of Dispersion
The profit for 4-quarters of a year are 40,000, 20,000, 60,000, and 80,000, respectively. The mean absolute deviation is:
Answer: (3) 20,000
Mean $= 2{,}00{,}000/4 = 50{,}000$; absolute deviations 10,000, 30,000, 10,000, 30,000; their mean is 20,000.
Study this: Descriptive Statistics Unit 4 — Measures of Dispersion
The coefficient of range for the following data is:
43, 53, 61, 74, 65, 82, 73, 46, 60, 63
Answer: (3) 0.312
Coefficient of range $= \dfrac{L - S}{L + S} = \dfrac{82 - 43}{82 + 43} = \dfrac{39}{125} = 0.312$.
Study this: Descriptive Statistics Unit 4 — Measures of Dispersion
If the coefficient of quartile deviation of the students’ marks is 0.57 and the third quartile $Q_3$ is 31, then the first quartile $Q_1$ is:
Answer: (3) 8.5
$\dfrac{Q_3 - Q_1}{Q_3 + Q_1} = 0.57$ gives $31 - Q_1 = 0.57(31 + Q_1)$, so $1.57\,Q_1 = 13.33$ and $Q_1 \approx 8.5$.
Study this: Descriptive Statistics Unit 4 — Measures of Dispersion
If the coefficient of standard deviation is 0.40 and the mean is 5 for the given data, then the variance is equal to:
Answer: (3) 4.0
Coefficient of standard deviation $= \sigma/\bar{x}$, so $\sigma = 0.40 \times 5 = 2$ and the variance is 4.
Study this: Descriptive Statistics Unit 4 — Measures of Dispersion
For the data of 50 employees' earnings, the coefficient of mean deviation and mean deviation are 0.3 and 15,000, respectively, the mean earning is:
Answer: (3) 50,000
Coefficient of mean deviation $=$ MD $/$ mean, so mean $= 15{,}000/0.3 = 50{,}000$.
Study this: Descriptive Statistics Unit 4 — Measures of Dispersion
In a town, 25% of the persons earned more than ₹45,000. If the quartile deviation is 13500, then the 75% of the persons earned is more than ______.
Answer: (4) 18000
25% earn more than ₹45,000, so $Q_3 = 45{,}000$. QD $= (Q_3 - Q_1)/2 = 13{,}500$ gives $Q_1 = 18{,}000$, and 75% earn more than $Q_1$.
Study this: Descriptive Statistics Unit 4 — Measures of Dispersion
If the arithmetic mean and the geometric mean of two numbers are 12 and 6, then the harmonic mean is:
Answer: (2) 3
For two numbers $G^2 = AH$, so $H = G^2/A = 36/12 = 3$.
Study this: Descriptive Statistics Unit 3 — Measures of Central Tendency
For the three numbers 2, $a$ , $b$ , the arithmetic mean is $\frac{14}{3}$ and the geometric mean is 4. The value of $a$ and $b$ respectively are:
Answer: (1) (4, 8)
Mean $14/3$: $2 + a + b = 14$, $a + b = 12$. GM 4: $2ab = 64$, $ab = 32$. So $a, b$ are 4 and 8.
Study this: Descriptive Statistics Unit 3 — Measures of Central Tendency
If the harmonic mean and arithmetic mean respectively of three numbers in arithmetic progression are 54/11 and 6, then the geometric mean of those numbers is:
Answer: (3) $(162)^{\frac{1}{3}}$
Write the numbers $6 - d, 6, 6 + d$. $\dfrac{3}{\frac{1}{6-d} + \frac{1}{6} + \frac{1}{6+d}} = \dfrac{54}{11}$ gives $\dfrac{12}{36 - d^2} = \dfrac{4}{9}$, so $36 - d^2 = 27$. GM $= \big(6(36 - d^2)\big)^{1/3} = (162)^{1/3}$.
Study this: Descriptive Statistics Unit 3 — Measures of Central Tendency
The median of the following data is:
| Class | 40-44 | 44-46 | 46-48 | 48-52 | 52-58 | 58-60 |
|---|---|---|---|---|---|---|
| Frequency | 4 | 6 | 8 | 12 | 7 | 2 |
Answer: (1) 48.5
$N = 39$, $N/2 = 19.5$; cumulative frequencies 4, 10, 18, 30, so the median class is 48–52. Median $= 48 + \dfrac{19.5 - 18}{12} \times 4 = 48.5$. (The classes are unequal; the formula uses the median class’s own width.)
Study this: Descriptive Statistics Unit 3 — Measures of Central Tendency
The geometric mean of five numbers is 8 and the geometric mean of the first three numbers is 4. The geometric mean of the last two numbers is:
Answer: (2) $16\sqrt{2}$
Product of all five $= 8^5$, of the first three $= 4^3$, so of the last two $= 8^5/4^3 = 512$, and their GM $= \sqrt{512} = 16\sqrt{2}$.
Study this: Descriptive Statistics Unit 3 — Measures of Central Tendency
If the geometric mean of 2, 4, 8, 16, 32 is 8, then the geometric mean of 24, 192, 1536, 12288, 98304 is:
Answer: (3) 1536
The new numbers are the old ones times 12, 48, 192, 768, 3072 — that is, $12 \times 4^k$ with GM $12 \times 4^2 = 192$. The GM of a product is the product of the GMs: $8 \times 192 = 1536$.
Study this: Descriptive Statistics Unit 3 — Measures of Central Tendency
If $g(x) = \log x$, then the arithmetic mean of $g\left(\frac{x}{y}\right)$ and $g(xy)$ is:
Answer: (1) $\log x$
$\tfrac{1}{2}\big(\log\tfrac{x}{y} + \log xy\big) = \tfrac{1}{2}(\log x - \log y + \log x + \log y) = \log x$.
Study this: Descriptive Statistics Unit 3 — Measures of Central Tendency
Which of the following is not a measure of location?
Answer: (3) Range
Midrange, quartiles and the maximum all locate a point of the distribution. The range is a spread — a measure of dispersion.
Study this: Descriptive Statistics Unit 4 — Measures of Dispersion
The midrange of the following data is:
9, 1, 0, 1, 5, 1, 9, 0, 10, 9
Answer: (1) 5
Midrange $= \tfrac{1}{2}(\text{smallest} + \text{largest}) = \tfrac{1}{2}(0 + 10) = 5$.
Not taught on this site yet — see where this site is thinnest.
Interquartile range of corona incubation in days for the following data is:
29, 31, 24, 29, 30, 25
Answer: (3) 5.5 days
In order: 24, 25, 29, 29, 30, 31, so $n = 6$. $Q_1$ is the $\tfrac{n+1}{4} = 1.75$th value, $24 + 0.75 \times (25 - 24) = 24.75$, and $Q_3$ is the $\tfrac{3(n+1)}{4} = 5.25$th value, $30 + 0.25 \times (31 - 30) = 30.25$. IQR $= 30.25 - 24.75 = 5.5$ days.
Study this: Descriptive Statistics Unit 3 — Measures of Central Tendency
The median of the data set 26, 23, 28, 22, 29, 21 is:
Answer: (1) 24.5
In order: 21, 22, 23, 26, 28, 29. With six values the median is the mean of the third and fourth: $(23 + 26)/2 = 24.5$.
Study this: Descriptive Statistics Unit 3 — Measures of Central Tendency
For the arbitrary data set, the mean and mode are 14 and 20 respectively. The median by empirical relation is:
Answer: (4) 16
Empirically, mode $= 3\,$median $- 2\,$mean, so $20 = 3M - 28$ and $M = 16$.
Study this: Descriptive Statistics Unit 3 — Measures of Central Tendency
The mode of marks obtained by the students of Mathematics class given in the following data is:
| Marks | 50-56 | 56-62 | 62-68 | 68-74 | 74-80 | 80-86 | 86-92 |
|---|---|---|---|---|---|---|---|
| Frequency | 6 | 11 | 25 | 35 | 18 | 12 | 6 |
Answer: (3) 70.22
Modal class 68–74 ($f_1 = 35$, $f_0 = 25$, $f_2 = 18$, $h = 6$). Mode $= 68 + \dfrac{35 - 25}{2(35) - 25 - 18} \times 6 = 68 + \dfrac{10}{27} \times 6 = 70.22$.
Study this: Descriptive Statistics Unit 3 — Measures of Central Tendency
The median, mode, and mean of 19, 15, 18, 19, 19, 17, 18, 19, 18, respectively, are:
Answer: (3) 18, 19, 18
In order: 15, 17, 18, 18, 18, 19, 19, 19, 19. The median is the 5th value, 18; the mode is 19 (four times); the mean is $162/9 = 18$.
Study this: Descriptive Statistics Unit 3 — Measures of Central Tendency
If the coefficient of variation of 1, 2, 4, 5 is $\sqrt{\frac{5}{18}} \times 100$, then the coefficient of 2, 3, 5, 6 is:
Answer: (1) $\sqrt{\frac{5}{32}} \times 100$
2, 3, 5, 6 are 1, 2, 4, 5 plus 1: the SD stays $\sqrt{2.5}$ but the mean rises from 3 to 4. CV $= \dfrac{\sqrt{2.5}}{4} \times 100 = \sqrt{\tfrac{5}{32}} \times 100$.
Study this: Descriptive Statistics Unit 4 — Measures of Dispersion
If the mean and coefficient of variation of $X$ are 20 and 20, respectively, then the variance of $Y = 20 - 3X$ is:
Answer: (4) 144
CV 20% with mean 20 gives $\sigma_X = 4$. $\text{Var}(20 - 3X) = 9\,\text{Var}(X) = 9 \times 16 = 144$.
Study this: Descriptive Statistics Unit 4 — Measures of Dispersion
If the first four moments about the origin are $-2.5, 18, -32, 110$ , then the third moment about the mean is:
Answer: (2) 71.75
$\mu_3 = \mu_3' - 3\mu_2'\mu_1' + 2\mu_1'^3 = -32 - 3(18)(-2.5) + 2(-2.5)^3 = -32 + 135 - 31.25 = 71.75$.
Study this: Descriptive Statistics Unit 5 — Moments, Skewness & Kurtosis
The second and fourth moment about mean for a distribution are 5 and 20, respectively. The value of Pearson’s coefficient of kurtosis $\beta_2$ is:
Answer: (4) 0.8
$\beta_2 = \mu_4/\mu_2^2 = 20/25 = 0.8$.
Study this: Descriptive Statistics Unit 5 — Moments, Skewness & Kurtosis
For the unequal class intervals, the first, second, and third quartiles are 20.5, 23, and 25.5, respectively. The Bowley’s coefficient of skewness is:
Answer: (3) 0
Bowley’s coefficient $= \dfrac{Q_3 + Q_1 - 2Q_2}{Q_3 - Q_1} = \dfrac{25.5 + 20.5 - 46}{5} = 0$.
Study this: Descriptive Statistics Unit 5 — Moments, Skewness & Kurtosis
The standard deviation of the data set 9, 11, 14, 12, 17, 15 is:
Answer: (3) $\sqrt{7}$
Mean 13; deviations $-4, -2, 1, -1, 4, 2$; squares sum to 42. $\sigma = \sqrt{42/6} = \sqrt{7}$.
Study this: Descriptive Statistics Unit 4 — Measures of Dispersion
If the mean and standard deviation of 5, $a, b$ are 4 and $\sqrt{\frac{2}{3}}$ respectively, then the values of $a$ and $b$ respectively are:
Answer: (1) (4, 3)
Mean 4 gives $a + b = 7$; variance $\tfrac{2}{3}$ gives $\tfrac{25 + a^2 + b^2}{3} - 16 = \tfrac{2}{3}$, so $a^2 + b^2 = 25$. Hence 4 and 3.
Study this: Descriptive Statistics Unit 4 — Measures of Dispersion
If the standard deviation of $p, q, r$ is $t$ , then the standard deviation of $\alpha p + \beta, \alpha q + \beta, \alpha r + \beta$ is:
Answer: (1) $\alpha t$
Adding $\beta$ to every value moves them all equally and leaves the spread unchanged; multiplying every value by $\alpha$ multiplies the spread by $|\alpha|$. So the SD is $|\alpha|\,t$, which is $\alpha t$ for a positive $\alpha$, as here.
Study this: Descriptive Statistics Unit 4 — Measures of Dispersion
The third decile $D_3$ for the following frequency table is:
| Range | 10-20 | 20-30 | 30-40 | 40-50 | 50-60 | 60-70 | 70-80 |
|---|---|---|---|---|---|---|---|
| Frequency | 8 | 12 | 14 | 10 | 6 | 16 | 4 |
Answer: (4) 30.71
$N = 70$, $3N/10 = 21$; cumulative frequencies 8, 20, 34, so $D_3$ is in 30–40. $D_3 = 30 + \dfrac{21 - 20}{14} \times 10 = 30.71$.
Study this: Descriptive Statistics Unit 3 — Measures of Central Tendency
For the frequency table of marks obtained by the students, the ninetieth percentile $P_{90}$ is:
| Marks | 0-10 | 10-20 | 20-40 | 40-60 | 60-80 | 80-100 |
|---|---|---|---|---|---|---|
| Frequency | 8 | 10 | 22 | 25 | 10 | 5 |
Answer: (3) 74.0
$N = 80$, $0.9N = 72$; cumulative frequencies 8, 18, 40, 65, 75, so $P_{90}$ is in 60–80. $P_{90} = 60 + \dfrac{72 - 65}{10} \times 20 = 74.0$.
Study this: Descriptive Statistics Unit 3 — Measures of Central Tendency
A fire in a production unit delaying manufacturing for some time is a/an:
Answer: (2) irregular trend
A fire is a one-off, unpredictable event: an irregular (random) variation. Trend, seasonal and cyclical movements are systematic.
Study this: Applied Statistics Unit 1 — Time Series
Which of the following is NOT a component of the time series?
Answer: (4) Periodic movements
A time series has four components: secular trend, seasonal variations, cyclical variations and irregular variations. “Periodic movements” is not a component of its own; it is a group name for the seasonal and cyclical variations together.
Study this: Applied Statistics Unit 1 — Time Series
The STL decomposition is an acronym for:
Answer: (1) Seasonal and Trend decomposition using Loess
STL is Seasonal and Trend decomposition using Loess (locally weighted regression), the method of Cleveland and others (1990).
Not taught on this site yet — see where this site is thinnest.
Deseasonalisation is a statistical method for removing the ______ of a time series.
Answer: (4) seasonal component
Deseasonalising removes the seasonal component (dividing each value by its seasonal index, or subtracting the seasonal effect), leaving trend, cycle and irregular.
Study this: Applied Statistics Unit 2 — Seasonal Component
To remove an underlying trend in the time series data, the method of detrend are:
(I) Detrend by differencing
(II) Detrend by model fitting
Which option is correct?
Answer: (3) Both (I) and (II) are correct.
A trend can be removed either by differencing ($y_t - y_{t-1}$) or by fitting a trend model and keeping the residuals; both are standard.
Study this: Applied Statistics II Unit 1 — Growth Curves
The moving average method is used with time-series data to smooth out:
(I) Short term fluctuations
(II) Long term trends
Which option is correct?
Answer: (1) Only (I) is correct.
A moving average replaces each value by the mean of the values around it, which smooths out short-term fluctuations, so (I) is correct. In doing so it brings out the long-term trend rather than smoothing it away, so (II) is not correct. Only (I).
Study this: Applied Statistics Unit 1 — Time Series
By method of semi-average, the linear trend is observed from the plot between which points for the following time series data?
| Year | 2011 | 2012 | 2013 | 2014 | 2015 | 2016 | 2017 | 2018 |
|---|---|---|---|---|---|---|---|---|
| Production | 20 | 22 | 20 | 21 | 23 | 26 | 28 | 30 |
Answer: (3) (2012.5, 20.75) and (2016.5, 26.75)
Split the eight years into halves: $\bar{y}_1 = (20 + 22 + 20 + 21)/4 = 20.75$ centred at 2012.5 and $\bar{y}_2 = (23 + 26 + 28 + 30)/4 = 26.75$ centred at 2016.5. The trend line joins these two points.
Study this: Applied Statistics Unit 1 — Time Series
Which frequency table is correct for the following data set?
76, 51, 68, 83, 74, 61, 42, 72, 51, 64, 53, 70, 45, 63, 47, 75, 67, 58, 54, 59, 52, 79
Answer: (4), the table marked (4)
Tally the 22 values: 41–49: 42, 45, 47 (3); 50–58: 51, 51, 53, 58, 54, 52 (6); 59–67: 61, 64, 63, 67, 59 (5); 68–76: 76, 68, 74, 72, 70, 75 (6); 77–85: 83, 79 (2).
Study this: Descriptive Statistics Unit 2 — Measurement Scales & Data Presentation
Government publications, websites, books, journal articles, internal records etc. are appropriate for:
(I) primary data
(II) secondary data
Which option is correct?
Answer: (2) Only (II) is correct.
Material someone else has already collected and published — government publications, books, websites, records — is secondary data.
Study this: Descriptive Statistics Unit 1 — Statistical Description of Data
Which of the following is NOT a characteristics of frequency curve?
Answer: (3) Frequency polygon
A frequency curve is described by its central tendency, dispersion and shape (skewness, kurtosis). A frequency polygon is another diagram, not a characteristic.
Study this: Descriptive Statistics Unit 2 — Measurement Scales & Data Presentation
The feature of absolute zero is a characteristic of:
Answer: (4) ratio scale
Only the ratio scale has a true (absolute) zero, which is what makes ratios such as “twice as heavy” meaningful.
Study this: Descriptive Statistics Unit 2 — Measurement Scales & Data Presentation
Questions that can be measured on the interval scale is:
(I) Likert scale
(II) Net promoter score
(III) Bipolar matrix table
Which option is correct?
Answer: (4) All (I), (II), and (III) are correct.
All three are question types whose answers are analysed as interval data in survey research: a Likert item (strongly disagree to strongly agree), the 0–10 net promoter score, and a bipolar matrix of rating scales between two opposite adjectives. Each places the answer on equally spaced steps that can be added and averaged. (Strictly a single Likert item is ordinal; treating it as interval is the common convention.)
Study this: Research Methodology Unit 2 — Survey Methodology and Data Collection
‘The number of germs in the patient’s body’ is an example of the:
Answer: (2) infinite population
Germs in a body cannot be counted out one by one; the textbook treats such a population as infinite.
Study this: Sampling Techniques Unit 1 — Sample Survey Concepts
Which of the following is NOT correct?
Answer: (4) Stratified random sampling: population is divided into heterogeneous groups
Stratified sampling divides the population into homogeneous strata (alike within, different between). “Heterogeneous groups” is wrong; the other three describe their methods.
Study this: Sampling Techniques Unit 1 — Sample Survey Concepts
A box contains 5 red and 3 white marbles. Two marbles are chosen at random. What is the probability that both are of the same colour?
Answer: (3) 13/28
$P = \dfrac{\binom{5}{2} + \binom{3}{2}}{\binom{8}{2}} = \dfrac{10 + 3}{28} = \dfrac{13}{28}$.
Study this: Theory of Probability Unit 1 — Elementary Probability
Let $X, Y,$ and $Z$ be mutually exclusive and exhaustive events such that $P(X) = 2P(Y) = 6P(Z)$ . The value of $P(X)$ is:
Answer: (4) 0.6
Let $P(X) = p$; then $P(Y) = p/2$ and $P(Z) = p/6$. Exhaustive and exclusive: $p(1 + \tfrac{1}{2} + \tfrac{1}{6}) = 1$, so $p = 0.6$.
Study this: Theory of Probability Unit 1 — Elementary Probability
Let $A$ and $B$ be exhaustive and equally likely, and independent events. The value of $P(A \cap B)$ is:
Answer: (4) 1
Exhaustive means $P(A \cup B) = 1$. Equally likely gives $P(A) = P(B) = p$, and independence gives $P(A \cap B) = p^2$. So $1 = P(A) + P(B) - P(A \cap B) = 2p - p^2$, that is $(1 - p)^2 = 0$ and $p = 1$. Hence $P(A \cap B) = p^2 = 1$. (Halves, giving 0.25, would need $A$ and $B$ to be mutually exclusive as well, and mutually exclusive events with positive probability cannot be independent.)
Study this: Theory of Probability Unit 1 — Elementary Probability
Assuming the marks in Statistics are normally distributed with a standard deviation = 5. The minimum size required to construct a 95% confidence interval for mean with a maximum error = 0.5 is:
Answer: (4) 385
$n = \left(\dfrac{z\sigma}{E}\right)^2 = \left(\dfrac{1.96 \times 5}{0.5}\right)^2 = 19.6^2 = 384.16$, rounded up to 385.
Study this: Sampling Techniques Unit 2 — Simple Random Sampling
An officer conducts an ethnographic investigation into the complications confronted by extremely-backwards employees. Which method of sampling will be the most appropriate?
Answer: (3) Cluster sampling
An ethnographic study observes people where they live and work. The investigator goes to the places where these employees are found together, chooses some of those groups, and studies everyone in each: cluster sampling, in which the cluster, not the individual, is the unit chosen. Random, stratified and systematic sampling would all need a list of the employees to draw individuals from, and would scatter them.
Study this: Sampling Techniques Unit 1 — Sample Survey Concepts
Suppose bag A consists of 4 red and 5 white marbles and bag B consists of 6 red and 3 white marbles. A marble is selected at random from bag A and kept in bag B. Finally, a marble is selected at random from bag B. What is the probability that white marble was kept from bag A to bag B given that the marble chosen from bag B is red?
Answer: (4) 15/29
$P(W) = \tfrac{5}{9}$ and then B has 6 red in 10: $P(R \mid W) = \tfrac{6}{10}$. $P(R) = \tfrac{4}{9}$ and then 7 red in 10. $P(W \mid \text{red}) = \dfrac{\frac{5}{9} \cdot \frac{6}{10}}{\frac{5}{9} \cdot \frac{6}{10} + \frac{4}{9} \cdot \frac{7}{10}} = \dfrac{30}{58} = \dfrac{15}{29}$.
Study this: Theory of Probability Unit 1 — Elementary Probability
The number of men, women, and children in society is 30, 70, and 50, respectively. The angle corresponding to men, if the distribution is represented in a pie chart, is:
Answer: (2) 72°
Angle $= \dfrac{30}{150} \times 360° = 72°$.
Study this: Descriptive Statistics Unit 2 — Measurement Scales & Data Presentation
The $x$ -coordinate of the point of intersection of the ‘less than ogive’ and ‘more than ogive’ represents which central tendency among the following options.
Answer: (2) Median
The less-than and more-than ogives cross where half the frequency lies on each side: at the median.
Study this: Descriptive Statistics Unit 2 — Measurement Scales & Data Presentation
The arithmetic mean, geometric mean, and harmonic mean of data set 3, 4, 9, 12, respectively, are:
Answer: (3) $(7, 6, 5.14)$
AM $= 28/4 = 7$; GM $= (3 \cdot 4 \cdot 9 \cdot 12)^{1/4} = 1296^{1/4} = 6$; HM $= 4 \big/ \left(\tfrac{1}{3} + \tfrac{1}{4} + \tfrac{1}{9} + \tfrac{1}{12}\right) = \dfrac{144}{28} = 5.14$.
Study this: Descriptive Statistics Unit 3 — Measures of Central Tendency
The coefficient of quartile deviation for data set 8, 9, 7, 10, 8 is:
Answer: (2) $\frac{2}{17}$
In order: 7, 8, 8, 9, 10. $Q_1$ is the 1.5th value, 7.5, and $Q_3$ the 4.5th, 9.5. Coefficient $= \dfrac{9.5 - 7.5}{9.5 + 7.5} = \dfrac{2}{17}$.
Study this: Descriptive Statistics Unit 4 — Measures of Dispersion
The population skewness from the following data is:
3, 5, 2, 6, 4
Answer: (1) 0
2, 3, 4, 5, 6 are symmetric about their mean 4, so every odd central moment is zero and the skewness is 0.
Study this: Descriptive Statistics Unit 5 — Moments, Skewness & Kurtosis
The Pearson correlation coefficient from the following data is:
| $X$ | 2 | 4 | 6 | 8 |
|---|---|---|---|---|
| $Y$ | 1 | 4 | 2 | 3 |
Answer: (3) 0.40
$\bar{x} = 5$, $\bar{y} = 2.5$; $\sum dx\,dy = 4$, $\sum dx^2 = 20$, $\sum dy^2 = 5$. $r = \dfrac{4}{\sqrt{20 \times 5}} = 0.40$.
Study this: Statistical Methods Unit 2 — Correlation
The probable error by Pearson’s product-moment method if the correlation coefficient is 0.8 for 25 pair of samples is:
Answer: (4) 0.0486
PE $= 0.6745\,\dfrac{1 - r^2}{\sqrt{n}} = 0.6745 \times \dfrac{0.36}{5} = 0.0486$.
Study this: Statistical Methods Unit 3 — Concurrent Deviation, Multiple & Partial Correlation
For the particular commodity, the quarter-wise average price for three years is as follows.
| Year | Quarter1 | Quarter2 | Quarter3 | Quarter4 |
|---|---|---|---|---|
| 2020 | 4 | 2 | 5 | 6 |
| 2021 | 4 | 7 | 6 | 3 |
| 2022 | 4 | 5 | 7 | 4 |
The quarterly seasonal index for the second quarter is:
Answer: (2) 98.3%
By simple averages: the quarter means are 4, 4.667, 6 and 4.333, with grand mean 4.75. The second quarter’s index is $4.667/4.75 \times 100 = 98.3\%$.
Study this: Applied Statistics Unit 2 — Seasonal Component
Following is the price table for different fabrics.
| Base Year | Current Year | ||
|---|---|---|---|
| Fabric | Price | Quantity | Price |
| Cotton | 200 | 2 | 150 |
| Silk | 350 | 1 | 400 |
| Woollen | 400 | 3 | 300 |
The Laspeyre’s price index is:
Answer: (2) 82.05%
$\dfrac{\sum p_1q_0}{\sum p_0q_0} \times 100 = \dfrac{300 + 400 + 900}{400 + 350 + 1200} \times 100 = \dfrac{1600}{1950} \times 100 = 82.05\%$.
Study this: Applied Statistics Unit 3 — Index Numbers
Convert $(0.25)_{10}$ to binary.
Answer: (1) $(0.01)_2$
Multiply the fraction by 2 and read off the integer parts: $0.25 \times 2 = 0.5$ (0), $0.5 \times 2 = 1.0$ (1). So $(0.25)_{10} = (0.01)_2$.
Convert the following binary to decimal.
$(1011010)_2 = (?)_{10}$
Answer: (1) $(90)_{10}$
$1011010_2 = 64 + 16 + 8 + 2 = 90$.
Convert the following decimal to hexadecimal.
$(952)_{10} = (?)_{16}$
Answer: (1) $(3B8)_{16}$
$952 = 3 \times 256 + 184$ and $184 = 11 \times 16 + 8$, so the digits are 3, 11 (B), 8: $(3B8)_{16}$.
Convert $(705)_8$ to binary number.
Answer: (1) $(111000101)_2$
Each octal digit is three bits: $7 = 111$, $0 = 000$, $5 = 101$, so $(705)_8 = (111000101)_2$.
Convert the following octal to decimal.
$(3047)_8 = (?)_{10}$
Answer: (1) $(1575)_{10}$
$3 \times 8^3 + 0 \times 8^2 + 4 \times 8 + 7 = 1536 + 0 + 32 + 7 = 1575$.
Convert $(0110101100)_2$ to hexadecimal number.
Answer: (1) $(1AC)_{16}$
Group in fours from the right: $01\;1010\;1100 = 1, A, C$, so $(1AC)_{16}$.
Which of the following options is correct?
Answer: (2) A kilobyte = $2^{10}$ bytes, a megabyte = $2^{20}$ bytes, and a gigabyte = $2^{30}$ bytes
Each step is a factor of $2^{10} = 1024$: kilobyte $2^{10}$, megabyte $2^{20}$, gigabyte $2^{30}$ bytes (and a terabyte $2^{40}$).
Which of the following statements is/are considered as feature(s) of a spreadsheet?
(i) A spreadsheet is described as a grid that is structured by several rows and column.
(ii) Every column in a spreadsheet is identified by a number assigned sequentially as 1, 2 and 3 and so on.
(iii) Every row in a spreadsheet is assigned a letter or letters for identification.
Answer: (1) (i) only
A spreadsheet is a grid of rows and columns (i). But columns are lettered A, B, C… and rows numbered 1, 2, 3… — (ii) and (iii) have them the wrong way round.
Study this: Data Science Computer Fundamentals and Office Automation Unit 4 — Spreadsheet Basics
Manipulation of a cell in a spreadsheet means which of the following?
(i) Modify or editing cell contents
(ii) Page layout
(iii) Clipboard
Answer: (1) (i) only
Manipulating a cell means working on its contents — entering, editing, deleting. Page layout and the clipboard are features of the program, not operations on a cell.
Study this: Data Science Computer Fundamentals and Office Automation Unit 4 — Spreadsheet Basics
Which of the following statements are true/false?
(i) Formulas are made up of arithmetic operators such as = + − and other functions
(ii) A formula in Excel always has to start with =
Answer: (3) Both statements (i) and (ii) are true
A formula combines values, cell references, operators such as + and −, and functions, so (i) is true in substance (the = that begins a formula is a sign rather than an arithmetic operator). A formula is entered beginning with =, and Excel turns an entry begun with + or − into one that begins with =, so (ii) is true too. Both are true.
Study this: Data Science Computer Fundamentals and Office Automation Unit 4 — Spreadsheet Basics
Find the cell address of the following cells.
(i) $4^{\text{th}}$ row and $15^{\text{th}}$ column
(ii) $10^{\text{th}}$ row and $6^{\text{th}}$ column
Answer: (1) O4 and F10
Column 15 is the 15th letter, O, and column 6 is F; the address is column then row: O4 and F10.
Study this: Data Science Computer Fundamentals and Office Automation Unit 4 — Spreadsheet Basics
Which of the following statements are FALSE?
Answer: (1) The COUNTA function counts the number of cells that are empty in a range.
COUNTA counts the cells that are not empty (COUNTBLANK counts the empty ones), so statement 1 is false. The other three are Excel’s own definitions.
Study this: Data Science Computer Fundamentals and Office Automation Unit 4 — Spreadsheet Basics
Which of the following statements are true/false with regard to Excel functions?
(i) The AVERAGE function returns the average (arithmetic mean) of the arguments.
(ii) The CORREL function returns the correlation coefficient of the array1 and array2 cell ranges.
(iii) The MIN function returns the smallest number in a set of values.
Answer: (1) All statements (i), (ii) and (iii) are true.
All three are Excel’s definitions of AVERAGE, CORREL and MIN.
Study this: Data Science Computer Fundamentals and Office Automation Unit 4 — Spreadsheet Basics
Which of the following statements are true/false?
(i) The IPMT financial function returns the interest payment for a given period based on period, constant payment and a constant interest rate.
(ii) The PPMT financial function returns the payment on the principal for a given period for an investment based on periodic, constant payments and a constant interest rate.
Answer: (2) Both statements (i) and (ii) are true
Both are Excel’s definitions: for a loan repaid in equal instalments, IPMT gives the interest part of a period’s payment and PPMT the principal part.
Not taught on this site yet — see where this site is thinnest.
Which of the following statements are true/false?
(i) The SUMIF function adds all the numbers in a range of cells.
(ii) The OR logical function reverses the value of its argument.
Answer: (3) Both statements (i) and (ii) are false
SUMIF adds only the cells that meet a criterion (SUM adds them all), and it is NOT, not OR, that reverses a logical value. Both are false.
Study this: Data Science Computer Fundamentals and Office Automation Unit 4 — Spreadsheet Basics
15 questions test something no page on this site teaches yet. The working above is all there is for them for now: