Question bank · 28 min read
Economics: Unit-wise Group A and Group B Question Bank
This chapter drills the Economics paper unit by unit. Each section opens with a facts line — the numbers, names and formulae that the one-mark questions keep returning to — then gives twelve questions for Group A and four for Group B, with keys and answer outlines. The two units that carry the most marks are unit 2 (microeconomics, 24 marks) and unit 6 (quantitative methods, 15 marks); if you have limited time, drill those two twice. Every question is an original practice question written to the official pattern; none is claimed to have appeared in any year's paper.
6.1 Basic Concepts of Economics and Allocation of Resources
Facts. Economy = the system that produces, distributes and consumes. Scarcity → choice → opportunity cost (the next best alternative forgone, not the money paid). Factors of production: land/rent, labour/wages, capital/interest, enterprise/profit. Three central problems: what, how, for whom. Y = C + S; equilibrium when S = I. Nepal is a mixed economy.
Group A — Very short answer (1 mark each)
- What is an economy? [1]
- Define scarcity. [1]
- What is opportunity cost? [1]
- Write the rewards of land and capital. [1]
- Write any two features of a capitalist economy. [1]
- What is a mixed economy? [1]
- What is allocation of resources? [1]
- Write any two central problems of an economy. [1]
- Write any two macroeconomic variables. [1]
- What is per capita income? [1]
- What is meant by the circular flow of income? [1]
- What is a leak in the circular flow? [1]
Answers
1. The organised system by which the people of a country produce goods and services, distribute them and consume them to satisfy their wants with limited resources.
2. Scarcity means that the resources available to satisfy human wants are limited in supply relative to the wants for them.
3. The value of the next best alternative forgone when a choice is made.
4. Land — rent; capital — interest.
5. Any two of: private ownership; freedom of enterprise; profit motive; consumer sovereignty; price mechanism; competition; limited government.
6. An economy in which the private sector and the public sector exist side by side, with the market taking many decisions and the state taking others and regulating the rest. Nepal is a mixed economy.
7. The process of deciding how much of each factor of production shall be used, and where, to produce the goods and services the society wants.
8. Any two of: what to produce and how much; how to produce; for whom to produce.
9. Any two of: national income, per capita income, consumption, saving, investment, inflation, unemployment, money supply, balance of payments, population.
10. National income divided by population — the average income of one person in a year.
11. The continuous movement of factor services and goods from households to firms and back, and of income and expenditure from firms to households and back.
12. Saving, which leaves the circular flow of spending; investment is the corresponding injection.
Group B — Short answer (5 marks each)
- Distinguish between a capitalist, a socialist and a mixed economy. [5]
- What is scarcity? Explain the relation between scarcity, choice and opportunity cost with an example. [5]
- Explain the three central problems of an economy. [5]
- Explain the circular flow of income in a two-sector economy and show the condition of equilibrium. [5]
Answer outlines
1. Capitalist: private ownership; decisions by the market and prices; distribution by ability to pay; efficient but unequal. Socialist: state ownership; decisions by the central plan; distribution by need or work; equal but often inefficient. Mixed: both sectors; decisions shared; distribution by wages tempered by social policy; the aim is to keep the market's efficiency while curing its inequality and instability. Nepal is a mixed economy with a socialist orientation.
2. Scarcity means resources are limited relative to wants. It forces a choice between alternative uses, and a choice means something is given up — the opportunity cost, which is the value of the next best alternative alone, not the money paid and not the sum of all the alternatives. Example: a student with Rs. 30,000 ranks a computer, a coaching class and a smartphone; if he buys the computer, the opportunity cost is the value of the coaching class.
3. (i) What to produce and how much — which goods and services and in what quantities; answered by prices in a capitalist economy. (ii) How to produce — the technique, labour-intensive or capital-intensive; the method that produces a given output at the lowest cost is technically efficient. (iii) For whom to produce — distribution by ability to pay, by need or by work. Modern writers add the full utilisation of resources and growth over time.
4. In a two-sector economy households supply factor services and receive factor income (rent, wages, interest, profit); they spend that income on the firms' output, and the firms receive sales revenue with which they pay the factors again. The real flow and the money flow run in opposite directions, and the value of output equals income equals expenditure. With saving and investment, Y = C + S and Y = C + I, so equilibrium requires S = I; if investment exceeds saving, income and employment tend to rise.
6.2 Microeconomics
Facts. TR = P \times Q; AR = \frac{TR}{Q} = Price; MR = \frac{\Delta TR}{\Delta Q}. Under perfect competition AR = MR = P; under monopoly MR falls twice as fast as AR. TC = TFC + TVC; MC = \frac{\Delta TC}{\Delta Q}; MC cuts AC at AC's minimum. Law of variable proportions: MP then AP then stages. Equilibrium of the firm: MC = MR, with MC rising. VMP = MP \times Price.
Group A — Very short answer (1 mark each)
- Define total revenue. [1]
- How is average revenue related to price? [1]
- What is marginal revenue? [1]
- Under which market structure is AR equal to MR? [1]
- State the law of demand. [1]
- What is price elasticity of demand? [1]
- Define marginal cost. [1]
- How is total cost found? [1]
- At which point does the marginal cost curve cut the average cost curve? [1]
- What is the law of variable proportions? [1]
- What is a monopoly? [1]
- Write any two features of perfect competition. [1]
- State the condition for a firm's equilibrium. [1]
- What is rent? [1]
- State the marginal productivity theory of distribution. [1]
Answers
1. The whole amount a firm receives from the sale of a given quantity: TR = Price \times Quantity.
2. Average revenue equals the price: AR = \frac{TR}{Q} = Price.
3. The addition to total revenue from selling one more unit: MR = \frac{\Delta TR}{\Delta Q}.
4. Under perfect competition.
5. Other things remaining the same, when the price of a good rises the quantity demanded falls, and when the price falls the quantity demanded rises.
6. The ratio of the percentage change in quantity demanded to the percentage change in price.
7. The addition to total cost from producing one more unit: MC = \frac{\Delta TC}{\Delta Q}.
8. Total cost = total fixed cost + total variable cost.
9. At the minimum point of the average cost curve.
10. As more and more units of a variable factor are applied to a fixed factor, total product first increases at an increasing rate, then at a diminishing rate, and finally declines.
11. A market with a single seller of a good that has no close substitute and blocked entry, giving the seller considerable control over price.
12. Any two of: very many buyers and sellers; homogeneous product; free entry and exit; perfect knowledge; perfect mobility of factors; no transport cost; the firm is a price taker.
13. MC = MR, with MC rising (cutting MR from below).
14. The reward for the use of land and other natural resources whose supply is fixed; a surplus over the minimum needed to bring the factor into use.
15. Under perfect competition each factor is paid a reward equal to the value of its marginal product, VMP = MP \times Price.
Group B — Short answer (5 marks each)
- Complete the following table and comment on the behaviour of TR and MR. [5]
| Price (Rs.) | Quantity | TR | AR | MR |
|---|---|---|---|---|
| 20 | 1 | … | … | … |
| 18 | 2 | … | … | … |
| 16 | 3 | … | … | … |
| 14 | 4 | … | … | … |
| 12 | 5 | … | … | … |
- Explain the relation between AR and MR under perfect competition and under monopoly. [5]
- Explain the relation between marginal cost and average cost, and between ATC and AVC. [5]
- Explain the law of variable proportions with a table showing the three stages. [5]
- Compare perfect competition with monopoly on any five points. [5]
Answer outlines
1.
| Price | Quantity | TR | AR | MR |
|---|---|---|---|---|
| 20 | 1 | 20 | 20 | 20 |
| 18 | 2 | 36 | 18 | 16 |
| 16 | 3 | 48 | 16 | 12 |
| 14 | 4 | 56 | 14 | 8 |
| 12 | 5 | 60 | 12 | 4 |
AR equals the price; MR falls faster than AR (by Rs. 2 for each extra unit) because the price cut applies to all units sold; TR rises throughout but by a diminishing amount. 2. Under perfect competition the firm is one of a very large number and can sell any quantity at the market price, so price is constant and AR = MR = Price, drawn as one horizontal line. Under monopoly the firm is the whole market and must lower the price on every unit to sell one more, so AR slopes downwards and MR lies below it, falling twice as fast; MR reaches zero where TR is maximum and turns negative beyond it. 3. ATC = AFC + AVC; AFC falls continuously as output rises. AVC, ATC and MC are U-shaped. MC cuts AVC and ATC at their minimum points, because while MC is below AC the average must fall, and while it is above the average must rise — so MC must cross AC where AC stops falling. The vertical distance between ATC and AVC is AFC, so the two come closer as output grows but never meet. 4. Statement of the law, then the table: labour 1 to 7 with TP 10, 24, 39, 52, 60, 64, 64 and MP 10, 14, 15, 13, 8, 4, 0 and AP 10, 12, 13, 13, 12, 10.67, 9.14. Stage I — increasing returns: MP rising, AP rising and below MP (1st to 3rd worker). Stage II — diminishing returns: MP falling but positive, AP maximum where MP = AP, TP still rising (4th to 6th). Stage III — negative returns: MP negative, TP falling. The causes: under-use of the fixed factor and specialisation in stage I; full use of the fixed factor in stage II; mutual obstruction in stage III. The producer should operate in stage II. 5. Number of sellers — very many against one; product — homogeneous against one with no close substitute; entry — free against blocked; price control — none against considerable; demand curve faced by the firm — perfectly elastic against downward sloping; price and output — lower price and larger output against higher price and smaller output; selling cost — none against some publicity.
6.3 Macroeconomics
Facts. Budget\ deficit = Expenditure - Revenue. Public revenue = tax + non-tax + capital receipts. Direct tax cannot be shifted; indirect can. Absolute advantage (Smith) = fewer resources; comparative advantage (Ricardo) = lower opportunity cost. Terms\ of\ trade = \frac{Export\ price\ index}{Import\ price\ index} \times 100. Balance of trade = goods only; balance of payments = everything. Nepal's rupee is pegged to the Indian rupee.
Group A — Very short answer (1 mark each)
- What is public finance? [1]
- Write any two sources of non-tax revenue. [1]
- What is a budget? [1]
- What is a deficit budget? [1]
- What is fiscal policy? [1]
- Distinguish between direct and indirect tax in one line. [1]
- What is absolute advantage? [1]
- What is comparative advantage? [1]
- What is the terms of trade? [1]
- What is the balance of trade? [1]
- What is the balance of payments? [1]
- What is devaluation? [1]
- Write any two features of Nepal's foreign trade. [1]
- Write any two measures of protection. [1]
- What is a public debt? [1]
Answers
1. The branch of economics that studies the income, expenditure and borrowing of the government and their effect on the economy.
2. Any two of: fees and charges, fines, registration fees, royalties, dividends from public enterprises, interest and rent, foreign grants.
3. The government's annual statement of its estimated revenue and proposed expenditure for the coming financial year, presented to the legislature and authorising collection and spending once approved.
4. A budget in which the estimated expenditure exceeds the estimated revenue.
5. The government's policy on taxation, public expenditure and public borrowing, used deliberately to influence income, employment and prices.
6. A direct tax is borne by the person on whom it is legally imposed and cannot be shifted; an indirect tax is shifted to another, ultimately the final consumer.
7. The ability of a country to produce a good with fewer resources than another country.
8. The ability of a country to produce a good at a lower opportunity cost than another; it is the basis of gainful trade.
9. The ratio of the index of a country's export prices to the index of its import prices, multiplied by 100.
10. The difference between the value of a country's exports of goods and its imports of goods in a year.
11. The complete record of all a country's economic transactions with the rest of the world in a year — goods, services, income, transfers and capital movements.
12. A deliberate official reduction in the value of a country's currency in terms of foreign currencies under a fixed exchange rate.
13. Any two of: concentration on India; a chronic and large trade deficit; exports dominated by a few primary and semi-processed goods; imports of manufactures, fuel and machinery; landlocked and transit-dependent.
14. Any two of: tariff (customs duty), quota, embargo, subsidy to domestic producers, administrative barriers.
15. The total amount the government has borrowed and not yet repaid, whether internally or from abroad.
Group B — Short answer (5 marks each)
- What is public finance? Explain the sources of public revenue and the kinds of public expenditure. [5]
- What is a budget? Explain the balanced, surplus and deficit budgets and when each is appropriate. [5]
- Explain the theory of comparative advantage with an example and state the gains from international trade. [5]
- Distinguish between the balance of trade and the balance of payments, and explain them with the Nepali case. [5]
Answer outlines
1. Public finance studies the government's income, expenditure and debt. Revenue: tax revenue (income tax, VAT, excise, customs, land and house tax); non-tax revenue (fees, fines, registration fees, royalties, dividends, interest, rent, foreign grants); capital receipts (internal and external borrowing). Expenditure: by nature, recurrent (salaries, goods and services, interest) and capital (roads, buildings, machinery); by purpose, developmental (education, health, agriculture, infrastructure) and non-developmental (defence, general administration, debt service).
2. Definition, then: balanced — revenue equals expenditure; prudent and non-inflationary, appropriate in normal times. Surplus — revenue exceeds expenditure; used to check inflation, retire debt and build reserves. Deficit — expenditure exceeds revenue; used to raise demand and employment in a slump and to finance development, but continued year after year it causes inflation, growing debt and loss of confidence. Give Deficit = Expenditure - Revenue.
3. Ricardo's theory: trade benefits a country even when it is absolutely less efficient in both goods, provided relative efficiencies differ; specialise where the opportunity cost is lower. Example (100 units of labour each): Nepal 40 cloth or 80 rice; India 60 cloth or 100 rice. Opportunity cost of one cloth = 2 rice in Nepal and 1.67 in India, so India specialises in cloth and Nepal in rice; both gain. Gains: larger total output through the international division of labour, lower prices, wider variety, transfer of technology, competition, larger markets.
4. Balance of trade — goods only: merchandise exports minus merchandise imports; the visible part of the current account. Balance of payments — every transaction: goods, services, income, transfers and capital movements; a complete account that always balances through a change in reserves or borrowing. Nepali case: a chronic and large trade deficit, a very large remittance inflow in transfers, and therefore a manageable overall balance of payments; heavy dependence on India; a landlocked, transit-dependent economy.
6.4 Development Economics
Facts. Growth = quantitative (national income or real per capita income); development = quantitative and qualitative (health, education, equality, freedom). Indicators: per capita income, HDI (life expectancy, schooling, GNI per capita, UNDP), PQLI, poverty rate, Gini. Capital formation stages: saving → mobilisation → investment. Nepal's socialist-oriented economy rests on three sectors — public, private and cooperative.
Group A — Very short answer (1 mark each)
- What is economic growth? [1]
- What is economic development? [1]
- Write any two indicators of economic development. [1]
- What is the Human Development Index? [1]
- What is capital formation? [1]
- Write any two stages of capital formation. [1]
- What is meant by the demographic dividend? [1]
- Name the three sectors of Nepal's socialist-oriented economy. [1]
- Write any two features of the Nepali economy. [1]
- Write any two problems of the Nepali economy. [1]
- What is Rostow's take-off? [1]
- What is meant by balanced growth? [1]
Answers
1. A quantitative increase in a country's output of goods and services over time — a rise in national income or real per capita income.
2. Growth in income together with a qualitative improvement in the whole life of the people — health, education, nutrition, housing, employment, equality and freedom.
3. Any two of: per capita income, Human Development Index, poverty rate, Gini coefficient, literacy rate, life expectancy.
4. A composite measure prepared by the UNDP combining life expectancy at birth, years of schooling and gross national income per capita into a figure between 0 and 1.
5. The process by which a country adds to its stock of capital goods so that future output is larger.
6. Any two of: saving; mobilisation of savings through financial institutions; investment.
7. The growth opportunity that arises when a fall in the birth rate gives a country a large working-age population and a small dependent population.
8. The public, private and cooperative sectors.
9. Any two of: an agrarian economy; low per capita income and productivity; a growing service sector and dependence on remittance; a low rate of capital formation; a mixed economy with a socialist orientation; landlocked and transit-dependent; uneven development.
10. Any two of: poverty and inequality; unemployment and under-employment; low agricultural productivity; capital deficiency; a weak industrial base; poor infrastructure; a chronic trade deficit; brain drain; instability and corruption.
11. The short critical stage of growth in which the rate of investment rises above about 10 per cent of national income and a leading sector pulls the economy forward.
12. The approach that argues a poor country should invest simultaneously in a range of industries, because the workers in one industry are the customers of another.
Group B — Short answer (5 marks each)
- Distinguish between economic growth and economic development. [5]
- Explain the indicators of economic development. [5]
- What is capital formation? Explain its stages and sources of finance. [5]
- Explain the bases of the socialist-oriented economy provided for in the Constitution of Nepal. [5]
Answer outlines
1. Growth is quantitative — a rise in national income or real per capita income, measured by the GDP growth rate. Development is qualitative as well as quantitative — growth plus better health, education, nutrition, housing, employment, equality and freedom, measured by the HDI and social indicators. Growth is necessary but not sufficient for development. Example: a country whose income rises by 6 % while poverty and schooling do not change has grown but has not developed. Give the comparison table.
2. Per capita income — simple but only an average, ignoring distribution and welfare. Human Development Index — life expectancy, schooling and GNI per capita, giving a figure between 0 and 1. PQLI — literacy, infant mortality, life expectancy. Poverty rate and Gini coefficient — the extent of poverty and inequality. Others — literacy, life expectancy, infant and maternal mortality, access to drinking water, energy consumption, road density, the structure of output and employment.
3. Definition as in Group A answer 5. Stages: saving — forgoing present consumption, depending on ability to save, willingness to save and the institutions available; mobilisation of savings — banks, cooperatives, insurance and the capital market collecting small savings into large funds; investment — putting the funds into capital goods, which needs entrepreneurship, technology, skilled labour, infrastructure and stability. Sources: domestic saving, foreign aid and grants, foreign loans, foreign direct investment.
4. The Constitution declares Nepal's economic system a socialist-oriented economy resting on three sectors — public, private and cooperative. Bases: the three-pillar structure with private property protected and cooperatives promoted; social justice and equality, the state being directed to end exploitation and reduce inequality; a welfare role for the state in basic education, basic health and social security; public welfare given priority over private profit, with ceilings permitted on land and productive assets; lawful private enterprise carrying social responsibility; a planned, self-reliant and independent economy guided by periodic plans; and cooperative-friendly development.
6.5 Nepal's Economy
Facts. Agriculture: about 24 % of GDP and 60 % of employment; small fragmented holdings; a third of the area irrigated. Land Reform Act, 2021 B.S. (1964); Birta abolished 2019 B.S. Industry: cottage and small need little capital. Tourism: foreign exchange without a port; seasonal and concentrated. Foreign employment: remittance about a quarter of GDP, the largest source of foreign exchange; destinations Malaysia and the Gulf.
Group A — Very short answer (1 mark each)
- What is the contribution of agriculture to Nepal's GDP? [1]
- Write any two features of Nepali agriculture. [1]
- What is a cottage industry? [1]
- Write any two problems of the industrial sector in Nepal. [1]
- Write any two importance of tourism in Nepal. [1]
- Write any two problems of tourism in Nepal. [1]
- What is meant by foreign employment? [1]
- Write any two destinations of Nepali migrant workers. [1]
- What is remittance? [1]
- Write any two uses of remittance by a Nepali household. [1]
- What is land reform? [1]
- Write any two importance of agriculture in Nepal. [1]
Answers
1. About a fifth to a quarter of GDP, while it employs about three-fifths of the working population.
2. Any two of: subsistence farming; small and fragmented holdings; heavy dependence on the monsoon; low productivity; traditional technology; unequal ownership of land.
3. A small-scale, usually household or family, industry using local raw material and local skill, needing little capital.
4. Any two of: shortage of capital; old technology; irregular and costly energy; high transport cost; shortage of skilled labour; imported raw material; a small market; competition from imports; labour unrest; weak marketing.
5. Any two of: foreign exchange earnings; employment; income for remote areas; linkage effects; preservation of art and culture; improvement of the balance of payments.
6. Any two of: poor air connectivity; inadequate transport; shortage of hotels and trained staff; poor sanitation; seasonality; weak marketing; dependence on Indian visitors; safety concerns; leakage of earnings; environmental damage.
7. The employment of a country's citizens in a foreign country.
8. Any two of: Malaysia, Qatar, Saudi Arabia, the UAE, Kuwait, Bahrain, Oman, South Korea, Japan.
9. Money sent home by a person working away from home, usually abroad.
10. Any two of: daily consumption; education; health; repayment of the loan taken to go abroad; house construction; purchase of land; small business.
11. The state's intervention to change the ownership and use of agricultural land so that the cultivator obtains security and ownership and inequality is reduced.
12. Any two of: contribution to GDP; employment; food supply; raw material for industry; export earnings; the market it provides to industry.
Group B — Short answer (5 marks each)
- Explain the importance of agriculture in the Nepali economy. [5]
- Explain the problems of Nepali agriculture and state the measures to solve them. [5]
- Explain the role of tourism in the Nepali economy and its problems. [5]
- What is foreign employment? Explain its role and importance in the Nepali economy. [5]
Answer outlines
1. Contribution to GDP (about a quarter) and to employment (about three-fifths); food supply; raw material for agro-processing; export earnings from tea, coffee, ginger, cardamom, lentils and pulses; the market it provides to industry; the labour, saving and food it supplies to other sectors; the culture and settlement pattern it carries; and the sector to which migrant workers return. (Any five.)
2. Problems: low yields; unirrigated and rain-dependent land; small fragmented holdings; costly inputs and scarce credit; poor roads, storage and markets; the middleman; weak extension; low prices; land fragmentation; shortage of farm labour as the young go abroad; loss of fertile Terai land; natural disasters. Measures: assured irrigation; improved seed and balanced fertiliser supplied on time; cooperatives, contract farming, cold storage and market yards; high-value and export crops; agro-processing; crop insurance; land consolidation and cooperative farming; cheap agricultural credit.
3. Role: foreign exchange without needing a port; employment for guides, porters, hotel staff, drivers and artisans, much of it in remote areas; income for the trekking regions; construction of hotels, roads and airports; a market for handicrafts and farm produce; preservation of heritage; improvement of invisible earnings. Problems as in Group A answer 6.
4. Definition as in Group A answer 7. Role: remittance of about a quarter of GDP is the largest source of foreign exchange and keeps the balance of payments in surplus despite the trade deficit; it absorbs the surplus labour the domestic economy cannot employ; it reduces poverty because it reaches households directly; it finances consumption, education, health, housing and small business; it supports the reserves and the exchange rate; workers acquire skills abroad; and it relieves pressure on land and public services.
6.6 Quantitative Methods in Economics
Facts. Mean: \frac{\Sigma X}{N}, \frac{\Sigma fX}{\Sigma f}, \frac{\Sigma fm}{\Sigma f}, or step-deviation A + \frac{\Sigma fd'}{\Sigma f} \times i. Median (continuous): L + \frac{\frac{N}{2} - c.f.}{f} \times i. Quartiles use \frac{N}{4} and \frac{3N}{4}. Mode (continuous): L + \frac{f_1 - f_0}{2f_1 - f_0 - f_2} \times i. Mode = 3 Median − 2 Mean. Pie sector angle = \frac{component}{total} \times 360^\circ. The mid-value of 20–30 is 25.
Group A — Very short answer (1 mark each)
- What is statistics? [1]
- Write any two importance of statistics in economics. [1]
- Distinguish between primary and secondary data in one line. [1]
- What is a frequency distribution? [1]
- What is a discrete series? [1]
- What is the mid-value of the class 20–30? [1]
- Write the formula for the arithmetic mean of an individual series. [1]
- Write the formula for the mean of a continuous series by the step-deviation method. [1]
- What is the median? [1]
- Write the formula for the median of a continuous series. [1]
- What is the mode? [1]
- State the empirical relation between mean, median and mode. [1]
- What is an ogive? [1]
- How is the angle of a sector of a pie chart found? [1]
- Which measure of central tendency is most affected by extreme values? [1]
Answers
1. Statistics is the science of collecting, organising, presenting, analysing and interpreting numerical data; in the plural sense, the numerical facts themselves.
2. Any two of: it presents facts in a definite form; simplifies a mass of data; makes comparison possible; tests theories; guides policy; helps forecasting.
3. Primary data is collected first-hand by the investigator for his own purpose; secondary data has already been collected by somebody else.
4. A table showing how many times each value or class of values occurs.
5. A series in which each value of the variable is given with its frequency, the values being whole numbers not grouped into classes.
6. 25.
7. \bar{X} = \frac{\Sigma X}{N}.
8. \bar{X} = A + \frac{\Sigma fd'}{\Sigma f} \times i, where d' = \frac{m - A}{i}.
9. The value of the middle item when the data is arranged in order of size.
10. Median = L + \frac{\frac{N}{2} - c.f.}{f} \times i.
11. The value that occurs most frequently in a series.
12. Mode = 3\ Median - 2\ Mean.
13. A graph of cumulative frequency, drawn as a "less than" or "more than" curve; the point where the two cross gives the median.
14. Angle = \frac{component}{total} \times 360^\circ.
15. The arithmetic mean.
Group B — Short answer (5 marks each)
- What is statistics? Explain its importance and limitations in economics. [5]
- Distinguish between primary and secondary data and explain any three methods of collecting primary data. [5]
- Explain the histogram, frequency polygon and ogive. [5]
- Find the arithmetic mean of the following discrete series. [5]
| X | 5 | 10 | 15 | 20 | 25 | 30 |
|---|---|---|---|---|---|---|
| f | 4 | 6 | 10 | 12 | 5 | 3 |
- Find the mean, median and mode of the following continuous series. [5]
| Marks | 0–10 | 10–20 | 20–30 | 30–40 | 40–50 | 50–60 |
|---|---|---|---|---|---|---|
| f | 4 | 8 | 14 | 18 | 10 | 6 |
Answer outlines
1. Definition. Importance: definite presentation of facts; simplification; comparison; testing of theories; guidance of policy; forecasting. Limitations: it studies groups and not individuals; deals with quantitative facts only; figures can be manipulated; true only on average; faulty collection ruins the analysis; needs trained people and uniform methods; shows relations and not causes.
2. Primary — collected first-hand for the investigator's own purpose: original and exactly suited, but costly, slow and needing trained staff. Secondary — already collected by another agency: cheap, quick and often the only source, but possibly unsuitable, out of date or inaccurate. Methods of collecting primary data: direct personal investigation; the interview with a schedule; the questionnaire by post or e-mail; the telephone interview; the panel method; observation.
3. Histogram — touching rectangles over the class intervals, height equal to frequency; from it the mode can be read graphically. Frequency polygon — the mid-point frequencies joined by straight lines, closed at both ends to the neighbouring empty classes. Ogive — a cumulative frequency curve; the "less than" ogive plots the upper limits against the cumulative frequencies and rises from left to right, the "more than" ogive plots the lower limits and falls; where the two cross the value on the horizontal axis is the median, and reading at N/4 and 3N/4 gives the quartiles.
4.
| X | f | fX |
|---|---|---|
| 5 | 4 | 20 |
| 10 | 6 | 60 |
| 15 | 10 | 150 |
| 20 | 12 | 240 |
| 25 | 5 | 125 |
| 30 | 3 | 90 |
| Total | 40 | 685 |
\bar{X} = \frac{685}{40} = 17.125. 5. Mean 31.67 marks by the step-deviation method with A = 35 and i = 10: \bar{X} = 35 + \frac{-20}{60} \times 10 = 31.67. Median: N/2 = 30 falls in 30–40, so Median = 30 + \frac{30-26}{18} \times 10 = 32.22. Mode: modal class 30–40 with f_1 = 18, f_0 = 14, f_2 = 10, so Mode = 30 + \frac{4}{36-24} \times 10 = 33.33. Check: 3(32.22) - 2(31.67) = 33.32. ✔