Charts & Graphs
Data interpretation: reading bar, pie and line charts and combining values off them.
This page is a sequence, not a document: try a question cold, learn the methods, drill until they’re automatic, then prove it under a clock. Skipping straight to reading is the least effective thing you can do here — that’s not opinion, it’s the testing effect.
Try one first
Before any teaching — a real question tells you honestly where you stand.
From the chart, what is the value for Feb?
The methods
Every charts & graphs pattern the tests use — the method in a few lines, then a worked example.
Weighted sum
Multiply each leg's quantity by its own rate, then add the products.
Worked example
Using the chart (kg CO2 per passenger-mile), how much CO2 is produced by a 3.6-mile car journey followed by a 12.8-mile train journey?
Answer: 3.74 kg
Multiply each distance by its rate and add: car 3.6×0.54 = 1.944, train 12.8×0.14 = 1.792, total = 3.74 kg. The 1.94/1.79 foils take one leg only; 0.68 adds the rates and ignores the distances.
Chart read-off
Read values against the gridlines carefully; for stacked segments, subtract the boundary values to get the segment itself.
Worked example
The stacked bars show revenue by product line. What was Product B's revenue in 2023?
Answer: £80m
Product B is the middle segment of the 2023 bar, spanning the 120 and 200 gridlines, so B = 200 − 120 = £80m. The £200m foil reads the cumulative top of B instead of the segment height (the classic stacked-bar error); £120m and £40m read the wrong segments; £240m reads the whole bar.
Dual-axis chart
Read each series against its own axis (bars on one, line on the other) for the same category, then combine the two readings.
Worked example
The chart shows units sold (bars, left axis) and average price (line, right axis). What was the revenue in March (units sold × average price)?
Answer: £4,800
Read both axes for March: 400 units (left) × £12 average price (right) = £4,800. The £400 foil ignores the price line; £4,000 and £6,000 read the price from the wrong month; £5,000 computes February.
Multi-exhibit join
Join the exhibits first (e.g. revenue = price × volume per row), then answer on the derived values.
Worked example
Using the unit prices (Exhibit 1) and units sold (Exhibit 2), what was Product C's revenue as a percentage of total revenue across all four products?
Answer: 23.8%
Compute each revenue = price × volume: A 12×40=480, B 8×70=560, C 15×30=450, D 20×20=400. Total = 1,890. C's share = 450/1890 = 23.8%. Traps: 18.8% uses volume share (30/160); 27.3% uses price share (15/55); 31.3% divides by everything except C; 30.2% forgets Product D in the total.
Pie chart proportion
A slice's share = its angle ÷ 360 (or its percentage of the whole); multiply by the total for the value.
Worked example
The pie chart shows how Brightwell Ltd's £240,000 annual budget is divided. How much is allocated to Operations?
Answer: £84,000
Operations is 35% of the £240,000 total: 0.35 × 240,000 = £84,000. The £72,000 foil reads the adjacent R&D slice (30%); £60,000 reads Marketing (25%); £35,000 reads the percentage as pounds; £156,000 gives the rest of the budget instead.
Series comparison
Identify the correct series first, then compute the change on that series alone: (end − start) ÷ start.
Worked example
The line chart shows monthly sales of two products. By what percentage did Product A's sales grow from January to June?
Answer: 100.0%
Product A rises from 40 (Jan) to 80 (Jun): change = (80 − 40) ÷ 40 = 100.0%. The 20.0% foil reads Product B by mistake (50→60). 50.0% divides by June; 66.7% by the average; 200.0% reports the ratio.
Revenue change
Derive revenue (price × volume) for each period from the exhibits, then compute the change on revenue.
Worked example
A product sold 40,000 units at £12 in 2023, and 44,000 units at £15 in 2024. By what percentage did its revenue change?
Answer: 37.5%
Revenue = price×volume: 2023 = £480k, 2024 = £660k. Change = (660−480)/480 = 37.5%. The 10% and 25% foils give only the volume or price change; 35% adds them (they compound).
Revenue share
Derive each item's revenue (price × volume), total them, then share = item ÷ total.
Worked example
Unit prices (£): A 12, B 8, C 15, D 20. Units sold (000s): A 40, B 70, C 30, D 20. What was Product C's revenue as a percentage of total revenue?
Answer: 23.8%
Revenues = price×volume: A 480, B 560, C 450, D 400; total 1,890. C's share = 450/1890 = 23.8%. The 18.8% foil uses volume share; 27.3% price share — both skip the join.
Drill it
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Prove it under a clock
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