Flashcards · 9640 · Topic 5

Quantitative skills flashcards

36 cards on Topic 5, subtopics QS1 to QS9. Pick a subtopic or study them all.

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QS1 calculate, use and understand ratios and fractions

Ratio versus fraction: what fraction of the total is the first part of a 3 : 5 ratio?: A 3 : 5 ratio has 8 parts in all, so the first part is 3/8 of the total, not 3/5.
Share 200 in the ratio 1 : 4: Total parts = 5, so one part = 200 ÷ 5 = 40. Shares: 40 and 160 (check: 40 + 160 = 200).
Concentration ratio as a ratio skill: firms hold 30%, 20%, 12% and 8% of a market. Find CR3 and CR4.: CR3 = 30 + 20 + 12 = 62%. CR4 = 62 + 8 = 70%.

QS2 calculate, use and understand percentages and percentage changes

Percentage change: formula and example. A price rises from 50 to 58.: Percentage change = (new − old) ÷ old × 100, with the old value as the base. (58 − 50) ÷ 50 × 100 = +16%.
Percentage points versus per cent: a rate falls from 8% to 6%: It falls by 2 percentage points (the gap between two rates), which is a relative fall of 2 ÷ 8 = 25%.
Successive percentage changes: output rises 10%, falls 5%, then rises 2%: Multiply the multipliers; do not add the rates. 1.10 × 0.95 × 1.02 = 1.0659, so output is about 6.6% higher overall.
Reverse percentage: a price including 20% tax is 120. What was the price before tax?: Original = new value ÷ multiplier = 120 ÷ 1.20 = 100. The tax is 20.

QS3 understand and use the terms mean, median (for A2 assessments, students will also need to understand and use relevant quantiles)

Mean versus median: Mean: sum of values ÷ number of values; uses every value and is pulled by extremes. Median: the middle value of ordered data (average the two middle values if the count is even); robust to a few very high values.
Find the mean and median of 4, 5, 5, 9, 12: Mean = 35 ÷ 5 = 7. Median = the 3rd value = 5.
A region's mean pay is 900 and its median is 700. What does this suggest?: The mean is 29% above the median (900 ÷ 700 = 1.29), so a few high earners are pulling the mean up: pay is unequally spread. The median is the better guide to a typical worker.
Quantiles: quartiles, quintiles, deciles, percentiles and the IQR (A2): Quantiles are cut points that split ordered data into equal groups: quartiles (4), quintiles (5), deciles (10), percentiles (100). Interquartile range = Q3 − Q1, the spread of the middle half.
The 90:10 ratio: 10th percentile income 80, median 240, 90th percentile 720 (A2): 90:10 ratio = 720 ÷ 80 = 9. The 90th percentile to the median is 3, and the median to the 10th percentile is 3. A ratio describes spread without needing every household's income.

QS4 construct and interpret a range of standard graphical forms

Which graphical form suits: a variable over time, shares of one total, a link between two variables?: Over time: a line graph (time on the horizontal axis). Shares of a total: a pie chart (angles sum to 360°) or a 100% bar. Link between two variables: a scatter graph (do not join the points).
Pie chart angle: income tax raises 20 of total tax revenue of 50: Angle = item ÷ total × 360 = 20 ÷ 50 × 360 = 144°.
Gradient of a line from (20, 18) to (60, 10): Gradient = change in vertical ÷ change in horizontal = (10 − 18) ÷ (60 − 20) = −8 ÷ 40 = −0.2.
What must every economics diagram show?: Labelled axes (for example price and quantity), labelled curves (D, S, S1, S2), the original and new equilibrium, and arrows showing the direction of any shift.

QS5 calculate and interpret index numbers

Simple index number: output is 250 in the base year and 275 later: Index = value ÷ base-year value × 100 = 275 ÷ 250 × 100 = 110. Output is 10% above the base year (base = 100).
Index points versus per cent: an index rises from 120 to 138: It rises by 18 index points but by 18 ÷ 120 = 15%. Percent changes are measured against the earlier value, not against 100.
Weighted index: weights 60 and 40, category indices 110 and 95: (60 × 110 + 40 × 95) ÷ 100 = (6,600 + 3,800) ÷ 100 = 104.0. A larger weight means a given price change moves the overall index more.
Inflation from a price index that rises from 96.0 to 100.8: (100.8 − 96.0) ÷ 96.0 × 100 = 5.0%. The index is the price level; inflation is its rate of change.

QS6 calculate cost, revenue and profit, including average and totals (for A2 assessments, students will also need to calculate marginal values)

A laundrette has fixed cost 500 a week and variable cost 3 per wash. Find TC and AC at 400 washes.: VC = 3 × 400 = 1,200. TC = 500 + 1,200 = 1,700. AC = 1,700 ÷ 400 = 4.25.
Marginal cost (A2): TC rises from 1,700 at 400 washes to 1,790 at 410 washes: MC = change in TC ÷ change in output = (1,790 − 1,700) ÷ 10 = 9 per wash.
Marginal revenue (A2): TR rises from 4,500 to 4,516 when output goes from 250 to 251: MR = change in TR ÷ change in output = 16 ÷ 1 = 16.
Profit and profit per unit: Profit = TR − TC. Profit per unit = AR − AC. Example: AR 18, AC 15.60, 250 units: profit per unit 2.40, total profit 2.40 × 250 = 600.

QS7 make calculations to convert from money to real terms

Convert money (nominal) to real terms: nominal income 5,250 when the price index is 105: Real value = nominal value ÷ price index × 100 = 5,250 ÷ 105 × 100 = 5,000 in base-year prices.
Real growth: exact and approximate methods: Exact: (1 + nominal growth) ÷ (1 + inflation) − 1. Approximate: nominal growth − inflation. Example: nominal pay +3%, inflation 5%: 1.03 ÷ 1.05 − 1 ≈ −1.9%.
A product costs 6.00 in the base year and 7.50 when the price index is 125. Has its real price changed?: Real price = 7.50 ÷ 125 × 100 = 6.00. The nominal price rose 25% but the real price is unchanged: it kept pace with prices in general.

QS8 make calculations of elasticity and interpret the result

PED: price rises from 8 to 10 and quantity falls from 500 to 420: Price +25%, quantity −16%, so PED = −16 ÷ 25 = −0.64: inelastic. Revenue rises from 4,000 to 4,200, as expected for inelastic demand.
Working back from PED: PED is −1.8 and the firm cuts price by 5%: Quantity rises 1.8 × 5 = 9%. Revenue index = 0.95 × 1.09 = 1.0355, so revenue rises about 3.6%.
Classify: YED −1.0, XED +0.8, PES 0.4: YED −1.0: inferior good. XED +0.8: substitutes. PES 0.4: inelastic supply.
MR and PED (A2): price 24 and PED −3: MR = P × (1 + 1/PED) = 24 × (1 − 1/3) = 16. MR is positive only where demand is elastic.
Watch-out: price rises from 20 to 25 and quantity falls from 300 to 240. PED = −0.8. What happens to revenue?: Revenue is 6,000 before and 25 × 240 = 6,000 after: unchanged, although PED suggests a rise. For large price changes, work out price × quantity directly.

QS9 interpret, apply and analyse information in written, graphical and numerical forms

Level versus rate: output of 150 grows 2%, then −3%, then +1%. Has it recovered?: 150 × 1.02 = 153.00; × 0.97 = 148.41; × 1.01 = 149.89. Growth is positive in year 3, yet output is still below 150. A positive growth rate means the level is rising, not that it has recovered.
Correlation versus causation in data questions: A pattern between two variables needs a reason (a mechanism) and a check on other factors. A third factor may explain both.
Questions to ask when evaluating data: Is it nominal or real? An average or a total? Is the time period long enough? Does the graph truncate an axis or use two scales? Would a share rather than an amount change the message? What is missing?
Interpreting an extract: what should you do with the figures?: Extract the figures, quantify them (with unit and year), connect them to a concept, and judge their limits. Note who is speaking, since a firm, a government and a union may present the same figure differently.