OxfordAQA AS and A-level Economics: Graphs and interpreting information (9640) – Revision Notes

These notes condense quantitative skills QS4 (construct and interpret a range of standard graphical forms) and QS9 (interpret, apply and analyse information in written, graphical and numerical forms) from section 3.5 of the OxfordAQA International AS and A-level Economics (9640) specification, version 1.2. The specification says they could be assessed in any assessment, and it adds no extra A2 requirement for either. Sections 3.1 and 3.2 are International AS content and sections 3.3 and 3.4 are the extra International A2 content. For full explanations read the study guide, then test yourself with the practice set. Track progress on the OxfordAQA Economics hub, the printable checklist and the free diagnostics. All data here are invented.

Forms at a glance

Form	Use it to show	Key rule
Line graph	A variable over time	Time on the horizontal axis
Bar chart	Separate categories	Axis starts at zero
Compound bar	A total and its parts	Label each part
Pie chart	Shares of one total	Angles sum to 360 degrees
Scatter graph	Link between two variables	Do not join the points
Economics diagram	Markets, costs, revenue	Label axes, curves, equilibrium

Constructing a graph in steps

1. Pick the form that fits the question.
2. Put the independent or time variable on the horizontal axis (price goes on the vertical axis in market diagrams).
3. Use an even scale and say where it starts.
4. Label axes with variable and unit.
5. Plot, then join only a continuous series.
6. Title it, label lines directly and give a source for real data.

Core calculations

Task	Method	Example (invented)
Pie angle	item / total x 360	Income tax 20 of 50: 20/50 x 360 = 144 degrees
Share of total	item / total x 100	15 of 50 = 30%
Percentage change	(new - old)/old x 100	250 to 280: 30/250 = 12%
Percentage points	new rate - old rate	6.0% to 7.5% = +1.5 points
Relative change in a rate	change / old rate	1.5/6.0 = 25%
Gradient	change in vertical / change in horizontal	(20, 18) to (60, 10): -8/40 = -0.2
Area on a diagram	height x width	Price 10, quantity 60: 600
Index change	(new index - old index)/old index	120 to 125: 5/120 = 4.2%

Check any pie by adding the angles. For a country’s tax revenue of 50 split into income tax 20, sales tax 15, company tax 10 and other 5, the angles are 144, 108, 72 and 36, which sum to 360.

Method for a scatter graph

1. Plot each pair as a point.
2. Describe the pattern: positive, negative or none, strong or weak, and any outlier.
3. Sketch a trend line by eye near the mean point, with the points spread evenly either side.
4. Find its gradient from two points on the line, not two data points.
5. Use it to predict only inside the range of the data.
6. State that correlation does not prove cause.

Method for a market diagram from equations

1. Equate the two quantity equations and solve for price.
2. Substitute back for quantity.
3. Find axis intercepts by setting one variable to zero.
4. For a tax, shift supply up by the tax; for a subsidy, shift it down.
5. Re-solve, then compare the price consumers pay with the price producers receive.
6. Tax revenue (or subsidy cost) is the per-unit amount times the new quantity.

Must-know distinctions

• Level or rate. A positive growth rate means the level is rising, even if the rate is slowing. A negative rate means the level fell that year.
• Percentage or percentage point. Use points for the difference between two rates.
• Share or amount. A pie or 100% bar shows shares and hides the total.
• Index or amount. An index compares with a base year. Two indices with the same base can be compared for growth but not for size.
• Correlation or cause. A pattern needs a reason, a mechanism and a check on other factors.
• Nominal or real. Check whether a series has been adjusted for price changes before comparing years.

Reading written extracts

Extract the figures, quantify them, connect them to a concept and judge their limits. Always give the unit and year when you quote a number. Note who is speaking, since a firm, a government and a union may present the same figure differently. Separate what the source states from what you infer.

Evaluation prompts for data answers

• Is the sample or time period long enough?
• Is the figure nominal or real, and an average or a total?
• Could a third factor explain the pattern?
• Does the graph truncate an axis or use two scales?
• Would a different measure, such as a share instead of an amount, change the message?
• What information is missing, such as costs, other years or other countries?

Worked reminders

Rates to levels. Country G (illustrative) has real output of 150. Growth is 2% in year 1, -3% in year 2 and 1% in year 3.

Year 1: 150 x 1.02 = 153.00
Year 2: 153.00 x 0.97 = 148.41
Year 3: 148.41 x 1.01 = 149.89

Year 3 growth is positive, yet output is still below the original 150. A line graph of the growth rate would hide this, so draw or compute the level when the question asks about recovery.

A tax on a market diagram. With Qd = 76 - 2P and Qs = 4P - 20, the equilibrium is P = 16 and Q = 44. A per-unit tax of 3 on sellers moves supply to Qs = 4(P - 3) - 20 = 4P - 32. Then 76 - 2P = 4P - 32 gives 108 = 6P, so P = 18 and Q = 40. Consumers pay 2 more, producers receive 18 - 3 = 15, which is 1 less, and tax revenue is 3 x 40 = 120. Describe the new equilibrium in words: supply shifts left, the price rises and the quantity falls.

A rate of change on a line graph. The steeper the line, the faster the change, and a horizontal stretch means no change. A line that bends downward but stays above the axis still shows a rising series.

Reading a table of data

1. Read the title, the units and the years before any numbers.
2. Find the row and column you need, and note whether the figures are totals, averages, shares or indices.
3. Calculate change, share or ratio rather than saying “it went up”.
4. Compare like with like: same base year, same unit, same period.
5. Write one sentence of meaning for each calculation.

Quick self-test

1. Country F spends 36 on health out of a total of 120. What pie angle is health, and what percentage share?
2. A column grows from 40 to 50. By what percentage?
3. The unemployment rate moves from 4.0% to 5.0%. State the change in two ways.
4. A line passes through (10, 40) and (30, 20). What is its gradient?
5. A price index rises from 120 to 126. What is the percentage rise?
6. Growth falls from 5% to 2%. Is output still rising?
7. On a market diagram the price is 8 and the quantity is 50. What does the rectangle represent, and what is its value?
8. A graph’s vertical axis starts at 90, and two bars show 100 and 110. By how much does the second look taller than the first, and what is the true rise?
9. Why should you not join the points on a scatter graph?
10. Demand is Qd = 100 - 5P and supply is Qs = 3P + 20. Find the equilibrium.

Answers

1. 36/120 x 360 = 108 degrees; 36/120 = 30%.
2. 10/40 = 25%.
3. +1.0 percentage point, or a 25% rise in relative terms (1.0/4.0).
4. (20 - 40)/(30 - 10) = -20/20 = -1.
5. 6/120 = 5%.
6. Yes. A positive growth rate means the level is still rising, only more slowly.
7. It is total revenue or consumer expenditure: 8 x 50 = 400.
8. The bars are 10 and 20 tall from the axis start, so the second looks twice as tall. The true rise is 10/100 = 10%.
9. The points are separate observations, not a continuous series. A line of best fit summarises the pattern instead.
10. 100 - 5P = 3P + 20 gives 80 = 8P, so P = 10; Q = 100 - 50 = 50.

Where marks are usually lost

• Describing the level when the question gives a rate, or the reverse.
• Writing “5%” when the answer is 5 percentage points.
• Quoting a number from a graph without units or year.
• Drawing a bar chart or axis with an uneven scale.
• Forgetting to label axes or the equilibrium.
• Extending a trend line well beyond the plotted data.
• Claiming that one variable causes another from a scatter graph alone.
• Copying a sentence from the extract without using its figures in a calculation.
• Offering an evaluation point with no link to the figures given.

Official syllabus

OxfordAQA International AS and A-level Economics (9640) specification, version 1.2, section 3.5 Quantitative skills, items QS4 and QS9. Published by OxfordAQA.