Guide8 patterns

Charts & Graphs

Reading bar, pie and line charts and combining values off them.

Weighted sum

The method

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

The method

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

The method

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

The method

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

The method

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

The method

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

The method

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

The method

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.