Core quantitative skills assessed within the 20% minimum
- Syllabus
- 2018
- Topic
- —
- Level
- AS
Learning objectives
—QS1—Ratios and fractionsCalculate, use and understand ratios and fractions.—QS2—Percentages and percentage-point changesCalculate, use and understand percentages, percentage changes and percentage-point changes.—QS3—Means, medians and quantilesUnderstand and use the mean and median at AS; at A2, also understand and use relevant percentiles, deciles, quintiles and quartiles.—QS4—Standard graphical formsConstruct and interpret a range of standard graphical forms.—QS5—Index numbersCalculate and interpret index numbers.—QS6—Revenue, cost and profit calculationsCalculate total revenue at AS; at A2, calculate marginal, average and total cost, revenue and profit.—QS8—Elasticity calculationsCalculate elasticity and interpret the result.—QS9—Analysing economic informationInterpret, apply and analyse information in written, graphical, tabular and numerical forms.
Reading ratios and fractions in economic data
A ratio compares two quantities in a stated order; a fraction shows one quantity divided by another. Both are relative measures, so they reveal scale or composition more clearly than two isolated totals.
\text{ratio of }A\text{ to }B=A:B=\frac{A}{B}
Put both quantities in the same units, keep the requested order, divide both sides by a common factor if a simplified ratio is useful, and interpret the quotient. A part-to-whole fraction uses the whole as its denominator; a part-to-part ratio does not.
If output is 90billionandoutputperpersonis3,000, population is 90billion/3,000 = 30 million. This rearranges the ratio 'output per person = output / population' while preserving compatible units.
The order changes the meaning: 90:30 is not the same comparison as 30:90. A ratio also has no percentage sign unless the fraction is multiplied by 100, and units cancel only when numerator and denominator use compatible units.
Percent changes and percentage-point changes
A percentage describes a share of a base; a percentage change compares a change with the original value; a percentage-point change is the arithmetic difference between two percentages.
\text{percentage}=\frac{\text{part}}{\text{whole}}\times100\qquad %\Delta=\frac{\text{new}-\text{old}}{\text{old}}\times100
| Change from 4% to 5% | Calculation | Result |
|---|---|---|
| percentage-point change | 5−4 | +1 percentage point |
| percentage change | (5−4)/4×100 | +25% |
To find a value from a percentage, write the percentage as a decimal and multiply by the base: 18% of 250millionis45 million. To recover the base, divide the part by its decimal share: if 45millionis1845 million / 0.18 = $250 million.
Always identify the denominator. Percentage change uses the original value, while percentage points compare rates directly. A fall from 8% to 6% is -2 percentage points but a -25% change; writing -2% answers a different question.
Choosing a centre and locating quantiles
The mean and median summarise the centre of a distribution. Quantiles locate positions in ordered data, helping economists describe how values are distributed rather than relying on one average.
| Measure | How it is found | What it reveals |
|---|---|---|
| mean | sum all values and divide by the number of values | the arithmetic average; every value affects it |
| median | order the values and take the middle position | the central observation; resistant to extreme values |
| percentile | divides ordered data into 100 ranked parts | the value at a stated percentage position |
| decile / quintile / quartile | divides ordered data into 10 / 5 / 4 parts | ranked sections of 10% / 20% / 25% |
For incomes 2, 3, 3, 4 and 18, the mean is 30/5=6, while the median is 3. The unusually high value raises the mean but does not move the middle position, so the median better represents the typical value in this small skewed set.
At IAS the required terms are mean and median. At IA2 the same reasoning extends to relevant percentiles, deciles, quintiles and quartiles; the median is the 50th percentile and separates the lower and upper halves.
A quantile names a ranked boundary, not the share of total income owned by that group. Exact interpolation rules can differ for finite datasets, so use the method supplied with the data when a precise boundary must be calculated.
Constructing and interpreting economic graphs
A graph converts data into a spatial pattern. Construct it so position, height or slope has one unambiguous meaning, then interpret the measured pattern before attaching an economic explanation.
| Standard form | Best used for | Main reading move |
|---|---|---|
| time-series line | a variable changing through time | level, direction, turning points and rate of change |
| bar chart | comparing discrete categories | compare bar heights from a common zero where appropriate |
| scatter graph | association between two variables | direction, strength, clusters and outliers |
| pie chart | shares of one whole | compare sector proportions that sum to the whole |
| economic model diagram | relationships such as demand and supply | axes, curves, shifts, equilibrium and resulting changes |
Choose the form to match the data; label both axes and units; use a consistent, readable scale; plot values accurately; add a title, key and source where needed. When interpreting, quote the relevant values and time period, calculate a change if useful, then state what the pattern shows.
A steeper-looking line may reflect a compressed axis, and two series moving together do not prove that one caused the other. Distinguish a movement along a curve from a shift of the curve, and never infer values outside the displayed scale without justification.
Calculating and reading index numbers
An index number expresses each value relative to a chosen base value set equal to 100. It makes proportional movement comparable even when the original series uses different units or magnitudes.
\text{index number}=\frac{\text{current value}}{\text{base-period value}}\times100
Suppose output is 216billioninoneyearand240 billion in the base year. The earlier index is 216/240×100=90. Output in that year was therefore 10% below the base-year value.
An index of 100 is the base, 120 is 20% above the base and 85 is 15% below it. To recover a current value, multiply the base value by index/100. To compare two non-base years, calculate their percentage change rather than subtracting each index from 100.
An index is not the original value and 120 does not mean a 120% increase. Comparisons require the same base, definition, weighting and coverage; rebasing changes the index numbers but not the underlying proportional movement.
Calculating revenue, cost and profit
Revenue records receipts from sales, cost records the resources used to produce, and profit is the difference. Total, average and marginal measures answer different questions about the whole, each unit and the next unit.
TR=P\times Q\qquad TC=FC+VC\qquad \pi=TR-TC
AR=\frac{TR}{Q}\qquad AC=\frac{TC}{Q}\qquad MR=\frac{\Delta TR}{\Delta Q}\qquad MC=\frac{\Delta TC}{\Delta Q}
If output rises from 10 to 11 units, total revenue rises from 150to165 and total cost from 100to108. At 11 units, average revenue is 15andaveragecostisabout9.82. The extra unit adds 15ofrevenueand8 of cost, so marginal profit is $7.
IAS requires calculation of total revenue. IA2 extends the skill to marginal, average and total cost, revenue and profit. Average profit is total profit divided by output; marginal profit is the change in total profit per additional unit.
Marginal is a change, not the final total or the average. Profit is not revenue: a firm can have high sales receipts but make a loss when total cost is larger. Keep the same time period, currency and output units throughout.
Converting nominal money into real terms
A nominal money value is measured in current prices; a real value removes the effect of a price-level change so purchasing power or output can be compared on a common-price basis.
\text{real value in base-year prices}=\frac{\text{nominal value}}{\text{price index}}\times100
If nominal income is 540andtherelevantpriceindexis120withbase100,realincomeis540/120\times100=450 in base-year prices. Although the money amount is 540,itbuyswhat450 bought in the base year.
For growth rates, real growth is approximately nominal growth minus inflation; equivalently, nominal growth is approximately real growth plus inflation. The exact conversion uses growth factors: (1+nominal)=(1+real)(1+inflation). A real interest rate is approximately the nominal interest rate minus inflation.
This is an IA2 skill. Deflate with the price index that matches the variable and keep its base year clear. Dividing by the inflation rate is wrong: use the index level, or use growth factors when converting rates.
Calculating and interpreting elasticity
Elasticity measures responsiveness: the percentage change in one variable divided by the percentage change in the economic factor that influences it. Because both changes are percentages, elasticity has no units.
\text{elasticity}=\frac{%\text{ change in the response variable}}{%\text{ change in the causal variable}}
If price rises by 5% and quantity demanded falls by 10%, price elasticity of demand is −10%/5%=−2. Demand is elastic because the absolute value is greater than 1: quantity demanded changes proportionately more than price.
| Magnitude | Interpretation |
|---|---|
| ∣E∣>1 | elastic: response is proportionately larger |
| ∣E∣<1 | inelastic: response is proportionately smaller |
| ∣E∣=1 | unit elastic: proportional changes are equal |
The sign carries economic meaning. PED is usually negative because price and quantity demanded move oppositely; PES is normally positive; positive YED indicates a normal good; XED is positive for substitutes and negative for complements.
Use the correct original base when calculating each percentage change and interpret both sign and magnitude for the elasticity named. A coefficient of -2 does not mean quantity falls by two units; it means a 1% price rise is associated with an approximately 2% quantity-demanded fall over the measured range.
Turning economic information into analysis
Economic analysis begins by extracting an accurate claim from the form in which evidence is presented, applying it to the stated context, and linking it through an economic mechanism to a supported consequence.
| Information form | First checks |
|---|---|
| written | claim, source, date, definition and qualifying language |
| graphical | axes, units, scale, period, trend, turning point and outlier |
| tabular | headings, units, comparable rows or columns and missing values |
| numerical | level versus rate, nominal versus real, total versus per-person, and suitable calculation |
Use a three-stage chain: first state the precise pattern with a relevant value or comparison; next select the economic concept that explains why the variables are connected; finally trace the consequence while keeping other assumptions explicit. Cross-check written claims against the accompanying graph or table before relying on them.
Suppose a dataset shows vehicle sales falling from 5.0 million to 4.5 million while output growth slows. The measured sales fall is 10%. Lower growth may weaken household income expectations, reducing demand for durable goods and therefore vehicle sales. This is a plausible economic explanation, not proof that slower growth was the only cause.
Description reports what the evidence shows; analysis explains a supported link. Do not confuse percentage and percentage-point changes, compare incompatible units or dates, infer causation from association alone, or repeat a contextual number without explaining its relevance.