The economic problem — Scarcity means that available resources cannot satisfy every competing want. It applies to affluent economies as well as poorer ones: skilled labour, time, land and productive capacity still have alternative uses. Distinguish this general constraint from a temporary shortage of one product at a particular price. Economics investigates how choices allocate resources and what consequences follow for different agents.
Wants, resources and priorities — A want is something people would like to obtain; resources are the inputs and capacities available to meet wants. Priorities differ between people and change over time. Calling something a need can express an important social judgement, but it does not remove the resource cost of providing it. Explain the actual constraint and decision rather than assuming every desirable service can expand without a trade-off.
Opportunity cost — Opportunity cost is the value of the next best alternative forgone when a choice is made. It is not the sum of every rejected possibility. If a student chooses an hour of paid work instead of the most valued available revision session, the opportunity cost concerns that forgone session. The wage received is a benefit of the chosen action, not automatically its opportunity cost.
Money and non-money costs — Money prices can help compare alternatives, but time, enjoyment, access, risk and effects on others can also matter. A free-entry event still uses travel time and a place that another activity could use. Identify whose cost is being discussed and what alternative was realistically available. A payment transferred between people is not necessarily the same as a net resource cost to society.
Trade-offs for consumers — A consumer with a limited budget chooses among combinations of goods and services. In an original example, £30 can buy three £10 meals or two meals and a £10 travel pass. Choosing the pass sacrifices one meal in that simplified choice. The example assumes the prices, available combinations and budget stated; it does not describe every real consumer's priorities or access.
Trade-offs for producers — A firm uses limited workers, equipment and managerial time across possible outputs. Assigning a machine to one order can delay another even if no extra cash payment occurs. Compare the next best contribution or other benefit forgone, including relevant constraints. The highest selling price need not identify the best use if the products have different input requirements and variable costs.
Trade-offs for government — A government faces choices over spending, taxation, borrowing and the use of real resources. Additional funding can expand one service but has financing and capacity implications elsewhere. Borrowing shifts financial obligations over time rather than making labour or materials unlimited. Evaluate the relevant benefits, opportunity costs and distributional effects instead of assuming all public spending is either costless or automatically wasteful.
Production possibility reasoning — A production possibility boundary represents combinations of two outputs achievable with stated resources and technology. A point on it is productively efficient in that simplified model; a point inside indicates unused or inefficiently used capacity. Moving along the boundary reallocates resources and creates an opportunity cost. The model does not by itself establish which combination society should prefer.Schematic two-output model with X on the horizontal axis and Y vertically. The red point is inside available productive potential; the blue point lies on the boundary. Moving along the boundary reallocates resources and creates opportunity cost. The drawing is not measured national data or a claim about the socially preferred mix.
Changing productive potential — More or better resources and improved technology can expand feasible output, while lost capacity can reduce it. A movement from inside a boundary towards it uses existing potential more fully; an outward shift changes potential itself. Distinguish the two when explaining growth. A two-output diagram simplifies an economy and does not prove every sector benefits equally from a particular change.
Positive and normative reasoning — A positive statement makes a claim that can in principle be investigated using evidence; a normative statement includes a value judgement about what ought to happen. The claim that a tax reduces sales is different from the judgement that the tax is fair. A positive claim can be false or uncertain; it is not automatically a true fact. Evaluation often needs both evidence and explicit criteria.
Models and assumptions — A model simplifies selected relationships to help explain a question. Ceteris paribus means other relevant influences are held constant for the comparison. State what the model assumes and what could change in practice. A useful model can identify a mechanism without predicting an exact outcome when several influences move together or agents respond differently from the assumptions.
Evidence, causation and evaluation — Compare the claim, measure, time period and alternative explanations before judging an economic argument. Two variables moving together do not establish that one caused the other. An observed sales increase after advertising may also reflect income, season or a competitor's closure. Use context to assess the likely mechanism and limits rather than treating a diagram or correlation as independent causal proof.
Business objectives and stakeholder conflicts
Profit maximisation — Profit is revenue minus the relevant costs over a period; profit maximisation seeks the greatest difference rather than the greatest sales total. A higher price or more output need not increase profit if it reduces demand or raises costs sufficiently. The later marginal analysis develops this decision more precisely. Do not assume that the most profitable feasible choice is automatically the fairest or the one every owner chooses.
Sales volume and sales revenue objectives — Sales volume is the quantity sold, while sales revenue is the money received or earned from sales under the stated accounting basis. A sales-maximising objective may emphasise volume or revenue, so specify which is meant in a case. A lower price can increase volume without increasing revenue. Revenue equals price multiplied by quantity for one product sold at a uniform price.
Satisficing and competing aims — Satisficing means seeking an acceptable outcome rather than the maximum possible result on one measure. An owner may accept sufficient profit to preserve independence, manageable hours or a social purpose. This is not necessarily poor decision-making: the relevant objective may include several valued outcomes. Explain the threshold and trade-off rather than defining satisficing as making no profit or having no objectives.
Survival and the stage of development — A new or financially stressed firm may prioritise meeting payments and retaining customers, while an established firm may pursue growth or efficiency. Objectives can change with ownership, competition, resources and the economic environment. Survival is not identical to profit maximisation in every period. A temporarily profitable firm can still face a cash shortage, developed further in the business-performance chapter.
Market share — Market share is a firm's sales as a proportion of the total defined market, measured consistently by value or volume. In an original value example, £2 million sales in a £10 million market gives 2 ÷ 10 × 100 = 20%. A rise in the firm's sales can coincide with a fall in share if the whole market grows faster. State the market boundary, period and measure.
Cost efficiency and return — A cost-efficiency objective seeks to use resources effectively for the intended output and quality, rather than merely cutting every payment. Return on investment relates an identified return to the investment committed, normally expressed as a percentage over a stated period. Define the numerator and denominator before comparing cases; a cash distribution to investors alone is not a general definition of return on investment. For an original one-year example defining the return as £500 profit on £5,000 invested, the ratio is 500 ÷ 5,000 × 100 = 10%. State that definition and period; it is not a promise of an investment return.
Employee welfare and customer satisfaction — A firm can pursue working conditions, development, job stability and customer experience alongside financial outcomes. These aims may improve retention, reputation and productivity, but benefits are not guaranteed or always immediate. Explain the mechanism and relevant evidence. A stated welfare policy does not establish how workers experience it, and customer ratings may not represent every purchaser or non-customer.
Social objectives and responsibility — A social objective aims at an outcome beyond private financial return, such as improving access or reducing environmental harm. Corporate social responsibility concerns how a firm takes account of its effects on people and the environment. Compare stated commitments, actual practices and outcomes. Donations do not automatically offset harmful core activity, and responsible practice need not mean abandoning every commercial objective.
Economic agents and stakeholders — Economic agents include households, firms, workers and government making decisions that affect the economy. A stakeholder is a person or group affected by or able to affect a firm's activity, such as owners, employees, customers, suppliers, creditors, communities and government. A person can occupy several roles. Shareholders are owners; they are one stakeholder group, not a synonym for everyone affected.
Conflicting objectives — A price rise might support margins but reduce customer access, while higher wages benefit workers but may raise costs or stimulate productivity. The outcome depends on demand, market power, costs and time. Identify a specific mechanism and the distribution of gains and losses. Stakeholders are not internally uniform: a local worker can benefit from employment while also experiencing pollution as a resident.
Power, influence and stakeholder response — Ownership rights, legal duties, bargaining power, information and the ability to switch affect whose objectives influence decisions. Workers may bargain, customers may change supplier and communities may organise pressure, with different constraints and costs. Do not assume every stakeholder has equal influence or that the most visible campaign represents everyone. Evaluate actual channels and evidence of response.
Judging an objective in context — Identify the objective, possible measures, constraints, likely consequences and alternatives before reaching a judgement. A proposal to maximise market share may help future bargaining power but weaken current cash flow if prices are cut heavily. Use the case evidence and distinguish short from long run. A recommendation is an argued conclusion, not the repeated assertion that all firms should choose the same aim.
Enterprise, resources and the wider environment
Entrepreneurial role — An entrepreneur brings resources together, identifies or creates an opportunity and makes decisions under uncertainty. Starting, operating, expanding and changing an enterprise require judgement, coordination and adaptation. Entrepreneurship is not confined to inventing a physical product or to a particular personality stereotype. Some ventures succeed and others fail; a convincing story of one success does not prove a universal formula.
Creative destruction — Innovation can introduce new products, processes or business models while displacing established activities. This process can raise productivity and consumer choice but also impose adjustment costs on workers, owners and communities. Explain what changes and who gains or loses rather than assuming every new firm is more efficient or every closure is evidence of economic decline.
Adding value — Added value relates the value of output to the cost of bought-in inputs used to produce it. In an original simplified example, a product sells for £50 and bought-in materials cost £20, giving £30 added value. This is not automatically £30 profit: wages, rent and other relevant costs still need to be met. Distinguish value creation from merely increasing the selling price without considering demand.
Entrepreneurial motives — Profit can reward effort and risk-bearing, while independence, ethical aims, social entrepreneurship and flexible or home-based working can also matter. Motives can coexist and change as a venture develops. Home working does not remove the need for coordination, resources or demand. Evaluate the particular opportunity and constraints instead of assuming all entrepreneurs value the same mix of money and autonomy.
Factors of production — Land covers natural resources, labour human effort and skills, capital produced resources used in production, and enterprise the organisation and judgement combining them. A factory building and a machine are physical capital; money used to buy them is finance rather than the productive equipment itself. Premises can involve both a natural site and produced structures, so explain the relevant distinction.
Labour, management and capital — Employees and managers provide labour, while their training and experience affect its quality. Equipment can complement workers or substitute for particular tasks. A capital-intensive process uses relatively more capital than labour; labour intensity concerns the production method rather than an assumption that one method is always superior. Suitability depends on scale, product variation, available skills and relative costs.
Division of labour — Division of labour splits production into specialised tasks. Repetition can improve dexterity (skill and speed in performing a task), reduce switching time and make specialised equipment worthwhile, raising output per input. The gains depend on coordination, demand and the process. A highly specialised worker or station can become a bottleneck, and narrow repetitive tasks can reduce motivation or opportunities to develop wider skills.
Specialisation and interdependence — Individuals, firms or regions can concentrate on activities and exchange with others, gaining from expertise and scale. This also creates dependency on reliable demand, suppliers and transport. A disruption in one specialised input can affect several firms. Explain both potential gains and vulnerability instead of treating self-sufficiency or maximum specialisation as universally best.
Interest rates and firms — Interest is the cost of borrowing and a return on relevant savings. Higher rates can increase financing costs on variable or newly arranged debt and alter consumption and investment demand. Existing fixed-rate arrangements and cash-rich firms may be affected differently. Trace the actual channel and timing; a rate rise does not instantly increase every firm's loan payment by the same amount.
Exchange rates and firms — An exchange rate is the price of one currency in terms of another. In an original example, if £1 buys €1.20, a €120 input costs £100 before other charges; if £1 buys €1.50, it costs £80 at that new rate. This sterling appreciation can lower that import cost but can make UK exports dearer in foreign currency. Contracts, imported inputs and customer responses qualify the outcome.
Taxation and unemployment — Taxes can affect costs, disposable income, incentives and spending, depending on the tax and its incidence, meaning who ultimately bears its burden. Unemployment can reduce household spending and affect recruitment, skills and local demand. A larger number of jobseekers does not guarantee that every firm's vacancy can be filled because skills and location matter. Distinguish the direct channel from possible indirect and longer-term effects.
Inflation and economic conditions — Inflation is a sustained increase in a general price level, not simply one product becoming dearer. It can raise input costs, change real purchasing power and increase uncertainty, while effects depend on contracts, pricing power and relative price changes. A firm's nominal sales can rise while the volume sold falls. Later chapters develop measurement, real values, causes and policy rather than assuming every price change has the same effect.
Demand, supply and market equilibrium
Markets and defined scope — A market connects potential buyers and sellers of a good, service or resource; it need not be a physical location. Define the product, geography, period and units when analysing it. A national market for all transport and a local market for one bus route have different substitutes and constraints. A precise market definition improves diagrams, research and evaluation.
Effective demand — Demand is the quantity consumers are willing and able to buy at different prices over a stated period, other relevant conditions held constant. Desire without purchasing ability is not effective market demand, although it can matter to social need. A demand curve summarises a relationship, not a claim that every consumer buys the same quantity or that their preferences never change.
The demand curve — For many goods, a lower own price increases quantity demanded, other things equal. Represent price on the vertical axis and quantity per period on the horizontal axis, with a downward-sloping demand curve for that model. Explain the relevant incentives and available substitutes. The slope is not the same as a calculated elasticity, and the simplified relationship needs qualification in particular cases.
Movement along demand — An own-price change produces a movement along a given demand curve when other influences remain unchanged. A fall in price leads to an extension of quantity demanded; a rise leads to a contraction. Do not label this a shift of demand. If a firm cuts price at the same time as income changes, separate the two mechanisms before interpreting the observed sales result.An original schematic demand curve D has price vertically and quantity per period horizontally. The movement down the same curve follows a lower own price, other relevant influences unchanged. Quantity demanded increases; the curve itself does not shift.
Shifts in demand — A change in a non-own-price influence can alter quantity demanded at each price and shift the demand curve. Relevant influences include income, related-goods prices, tastes, advertising and population size or age distribution. State the direction, mechanism and assumptions. A rightward shift means more demanded at each price in the diagram, not a movement caused by the good's own price falling.An original schematic change from D₀ to D₁ shows more demanded at each unchanged price, with price vertical and quantity per period horizontal. A non-own-price influence causes the shift; the diagram is not a movement caused by a fall in the good’s own price. No observed numerical scale is implied.
Substitutes and complements — Substitutes can satisfy a similar use, so a rise in one price can increase demand for the alternative, other things equal. Complements are used together, so a rise in one price can reduce demand for the other. The strength depends on actual consumer choices and context. Tea and coffee may be substitutes for some consumers without being identical products or universal substitutes for everyone.
Income and demand — For a normal good, higher income increases demand, other things equal; for an inferior good, higher income reduces demand over the relevant range. Inferior describes an income relationship rather than a moral or necessarily physical-quality judgement. A good's own-price effect does not define whether it is normal. Different consumers and income ranges can produce different relationships.
Tastes, branding and population — Fashion, perceived quality, advertising, reputation and changes in the number or composition of consumers can shift demand. An ageing population may alter demand across products, but stereotypes about every older consumer are not evidence. Advertising can fail or inform rather than simply persuade. Explain a specific response and distinguish measured exposure from demonstrated purchases.
Supply decisions — Supply is the quantity producers are willing and able to offer at different prices over a period under stated conditions. A higher price can make extra output worthwhile when additional costs rise, giving the usual upward-sloping model. Capacity, time, stock and objectives affect responses. A supply curve is not the total amount physically present regardless of price or production conditions.
Movement along supply — An own-price change causes movement along a given supply curve, other relevant influences held constant. A higher price can extend quantity supplied and a lower price contract it. Do not draw a new supply curve merely because the market price changes after demand shifts. Distinguish producers' response to the new price from a separate change in their costs or capacity.
Shifts in supply — Changes in input costs, technology, indirect taxes, subsidies, firm numbers and external shocks can change supply at each price. Lower relevant production costs can shift supply right, while disrupted inputs can shift it left. Specify the time period and what remains constant. A tax's final burden or a subsidy's full effect cannot be inferred from its legal recipient alone.Original schematic supply increase: lower relevant costs can shift S₀ right/down to S₁. More is supplied at each price. With the same downward demand curve, the new equilibrium has a lower price and larger quantity. The horizontal arrow illustrates a shift at a given price; movement along demand follows the changed equilibrium price.
Equilibrium price and quantity — Equilibrium occurs where planned quantity demanded equals planned quantity supplied at a price, within the model and stated period. The intersection identifies an equilibrium price and quantity. It does not imply everyone can afford the product, all costs are socially accounted for or the outcome is fair. Market efficiency and distribution require additional analysis.An original schematic standard model: the upward supply curve S and downward demand curve D intersect at equilibrium price Pe and quantity Qe. Planned quantities match under the stated conditions. No numerical scale, observed market estimate or claim of fairness or complete social efficiency is implied.
Excess demand and adjustment — At a price below the model's equilibrium, quantity demanded exceeds quantity supplied: there is excess demand. Competition for available output or sellers' responses can put upward pressure on price, encouraging supply and reducing quantity demanded. The adjustment is not guaranteed to be instant or complete; contracts, queues, controls and information can affect the process.Original schematic price Pl below equilibrium. At that price the supplied quantity Qs is below demanded quantity Qd; the highlighted horizontal gap is excess demand Qd−Qs. The same curves describe the equilibrium model, while actual price adjustment depends on contracts, information, rationing and other conditions.
Excess supply and adjustment — At a price above equilibrium, quantity supplied exceeds quantity demanded. Unsold stocks and competitive pressure can encourage price cuts, which raise quantity demanded and reduce planned supply. Firms may also change output, marketing or quality. Avoid assuming every product can be stored indefinitely or every seller can adjust price without contractual or practical constraints.Original schematic price Ph above equilibrium. At that price demanded quantity Qd is below supplied quantity Qs; the highlighted horizontal gap is excess supply Qs−Qd. Unsold output and competitive responses can put downward pressure on price, with practical constraints and timing affecting adjustment.
Comparative changes and model limits — A demand increase alone usually raises equilibrium price and quantity in the standard model; a supply increase alone lowers price and raises quantity. If both shift, one outcome may be ambiguous without their relative sizes. Label initial and new curves and trace the causal sequence. Observed outcomes can also depend on market power, adjustment time, expectations, information and assumptions the simple diagram leaves out.
The price mechanism and competitive positioning
Prices as signals — Prices can communicate relative scarcity and changing willingness to pay. An increase may signal an opportunity to producers and encourage changes in supply or resource use. The signal is imperfect when information is missing or prices exclude external costs. A high price can reflect market power as well as a socially desirable opportunity, so the price alone does not establish welfare.
Incentives and resource movement — A prospective increase in returns can encourage firms to enter, invest or expand, while consumers may seek substitutes or economise. Responses depend on capacity, finance, skills, expectations and the time available. A short-term price increase need not justify irreversible expansion if it is expected to reverse. Explain how the incentive connects to an actual feasible decision.
Rationing through willingness and ability to pay — At a market price, those willing and able to pay obtain the available product under the relevant trading arrangements. This rations scarce output through purchasing power, not a direct judgement of need. Evaluate access and distribution as well as incentives. Other arrangements, such as queues or administrative allocation, have their own costs and criteria rather than eliminating scarcity.
Mass and niche markets — A mass market serves a broad group with relatively large potential demand; a niche targets a narrower set of needs or preferences. A niche is not automatically profitable and a mass market does not mean identical consumers. Compare scale, differentiation, rivalry and possible demand. A small firm may specialise successfully, but concentration on one niche can create vulnerability to a changing preference.
Responding to changing demand — A firm can adjust output, price, product, promotion, distribution or capacity when demand changes. The appropriate response depends on whether the shift is temporary, the available capacity and the cost of adjustment. Producing more may be sensible with spare capacity but require expensive expansion near full use. An increase in orders is evidence to assess, not a guarantee of persistent growth.
Market growth and measurement — Market growth measures a change in the defined market's sales value or volume over a period. In an original volume example, sales rise from 20,000 to 23,000 units: the increase is 3,000 ÷ 20,000 × 100 = 15%. Value growth can reflect price increases as well as volume. Keep definitions and periods consistent when using growth to judge an opportunity.
Competitive advantage — Competitive advantage is an attribute or capability enabling a firm to perform more effectively against relevant rivals for a purpose, such as lower delivered costs, trusted service or distinctive features. It must matter to customers or operations and be sustainable enough to influence outcomes. A claimed unique feature does not establish value if consumers do not want it or rivals can quickly replicate it.
Product differentiation and added value — Differentiation makes an offering distinguishable through features, service, design, reputation, convenience or other relevant attributes. It can support willingness to pay or loyalty but can also raise costs. Explain the link to consumer choices and added value rather than assuming every difference justifies a higher price. Branding is one possible means, not the whole of differentiation.
Market positioning and maps — Positioning concerns how an offering is perceived relative to rivals on relevant attributes. A market map plots selected dimensions such as price and perceived convenience; label axes and identify the evidence. An empty area is not proof of profitable unmet demand: consumers may not want that combination, or it may be costly to provide. A two-axis map deliberately omits many influences.Original fictional offers A/B/C placed on perceived price and convenience axes. No measured data or unbuilt market is implied. Research is needed to justify positions and evaluate omitted attributes; empty space is not proof that customers want a profitable product there.
Price and output choices — Price and output decisions depend on demand, costs, rivalry, objectives, capacity and information. A differentiated product may give some pricing discretion without removing substitutes. A firm cannot generally choose an unlimited high price and sell an unlimited quantity. Later chapters develop elasticity, marginal reasoning and market structure to evaluate these choices more fully.
Stable and dynamic markets — A relatively stable market changes more slowly, while a dynamic one experiences substantial changes in technology, consumer preferences, rivalry or business models. The distinction concerns degree and context rather than a guarantee that any market never changes. Dynamic opportunities can reward innovation but increase uncertainty and the risk that research or investment assumptions become outdated.
Researching and evaluating consumer behaviour
Primary and secondary research — Primary research collects new information for the particular question; secondary research uses existing material collected for another or earlier purpose. A firm's own survey can be primary research, while official statistics can be secondary for that firm. Neither category guarantees quality. Assess relevance, definitions, methods, date, representativeness and cost rather than assuming newly collected evidence is always superior.
Quantitative and qualitative evidence — Quantitative evidence is numerical and can describe quantities or patterns; qualitative evidence explores meanings, motives or experiences. A survey can include both closed numerical responses and open explanations. Combine methods where the question requires them. A detailed interview can reveal a possibility without estimating its population frequency, while a numerical total may not explain why customers behave as they do.
Sampling and the target population — A sample is a subset of the relevant population. Define who the firm needs to understand before choosing how to obtain responses. Surveying current customers alone may omit people who avoid the product, and an online sample can miss relevant non-users. A larger sample reduces some random variation but does not automatically remove systematic selection bias.
Question design and response bias — Leading wording, ambiguous categories, recall problems and pressure to give a socially acceptable answer can distort responses. Ask a clear question with appropriate options and pilot it where feasible. A question such as How much did you enjoy our excellent service presupposes approval. A neutral alternative should allow negative, uncertain or not-applicable responses as relevant.
Nonresponse and coverage limits — People who do not respond may differ from respondents in ways relevant to the decision. A high response count is not proof of representativeness if the invitation excludes important groups. Identify the coverage and acknowledge uncertainty rather than treating every percentage as the whole market's preference. Follow appropriate consent and privacy arrangements instead of collecting unnecessary personal data.
Worked survey interpretation — In an original convenience sample, 60 of 100 respondents say they would consider a new service: 60 ÷ 100 × 100 = 60%. This is a reported intention among those respondents, not proof that 60% of the entire population will purchase. Check sample composition, question wording, price, timing and actual behaviour before forecasting demand.
Mean, median and variation — The mean is the total divided by the number of observations; the median is the middle after ordering. In the original spending list £2, £3, £4, £5 and £26, the mean is £40 ÷ 5 = £8, while the median is £4. The large value raises the mean. Choose a relevant summary and examine spread rather than treating one average as a complete consumer profile.
Market segmentation — Segmentation groups consumers using relevant characteristics such as needs, behaviour, location, income or age to inform decisions. A segment is an analytical grouping, not a claim that all its members are identical. Use evidence to connect the grouping to product, price or communication choices. Avoid assuming a demographic category alone determines tastes or willingness to pay.
From research to a decision — Translate findings into a reasoned estimate of likely demand or a testable product decision, with assumptions stated. Compare what consumers report with actual sales or a suitable limited trial where available. A small pilot can reveal practical issues but may not reproduce full-market conditions. Record the uncertainty instead of converting every favourable comment into a guaranteed purchase.
Comparing sources over time — Align product definitions, geographic scope, units, dates and value-versus-volume measures before comparing datasets. An increase in nominal market revenue may partly reflect inflation or a changed boundary. Older research can still inform a trend but may be less relevant in a fast-changing market. Identify what the data can establish and what requires newer or different evidence.
Research cost and proportionality — Research uses money, time and staff capacity, creating an opportunity cost. Select a method proportionate to the decision's scale, reversibility and uncertainty. A low-cost pilot may be appropriate for a small change, while an expensive irreversible expansion needs stronger evidence. More information is not automatically worthwhile if it arrives too late or cannot resolve the key uncertainty.
Building a qualified market judgement — Combine the opportunity, likely consumer response, rivals, costs, capacity, stakeholder consequences and evidence limits before judging a proposal. Explain which assumption matters most and what could change the conclusion. An original fictional exercise supports method practice; it is not an actual firm's data or a personalised financial recommendation. Independent extended reasoning requires more than recalling a term or a short quiz answer.
Quantiles and grouped shares — Quantiles divide an ordered distribution into stated proportions: quartiles into four groups, quintiles into five and deciles into ten. The median is the 50th percentile; lower and upper quartiles are 25th and 75th percentile thresholds. The poorest 20% of people do not necessarily receive 20% of income: population groups and resource shares are different. Check whether a table reports group shares, cumulative shares or thresholds, and use the question's stated convention for sample quantiles.
Original quartile working — For ordered original observations 1, 2, 3, 4, 5, 6, 7, 8, the median is (4+5)/2=4.5. Using the median-of-halves convention, the lower half 1, 2, 3, 4 gives lower quartile 2.5 and the upper half 5, 6, 7, 8 gives upper quartile 6.5. The interquartile range is 6.5−2.5=4. This summarises the middle half without describing the entire distribution. Sample-quantile conventions differ, so follow the method stated in the task rather than silently mixing software definitions.
Test yourself
50 questions · Random sets of 10. These quick checks support revision; practise longer explanations and justified judgements too.
Mr Kidman's Classroom
