Mathematics • Year 8 • Unit 4 • Lesson 5
Bar and Pie Charts in the Real World
Apply bar charts, pie charts, sector angles, and reverse calculations to real contexts: school surveys, government data, sports records, and news infographics.
1. Word problems
Each problem uses ideas from Lesson 5. Show your working — a single answer with no working only earns half marks.
1.1 — Class colour survey. 20 students chose a favourite colour: Red 5, Blue 8, Green 4, Yellow 3.
(a) Calculate the pie-chart sector angle for each colour.
(b) Verify the four angles sum to 360°.
(c) Which colour is the modal category? 4 marks
1.2 — Reverse a pie chart. A pie chart of 240 voters has the "Yes" sector at 135°.
(a) What fraction of voters does the Yes sector represent?
(b) How many voters chose Yes?
(c) What percentage of voters chose Yes? 3 marks
1.3 — Sport club enrolments. A school records: Soccer 80, Netball 60, Athletics 40, Cricket 20.
(a) What chart is more appropriate — bar chart or pie chart? Justify.
(b) Find the total enrolment.
(c) Calculate the percentage of students in each sport. 3 marks
1.4 — Misleading news chart. A news website shows a bar chart of survey results where the y-axis starts at 40 instead of 0. The bars for "Brand A" and "Brand B" appear with A's bar visually twice as tall as B's, even though Brand A scored only 50% support and Brand B 45%.
(a) Why does the chart appear so misleading?
(b) What is the actual difference (in percentage points) between the two brands?
(c) Suggest how the chart should be redrawn fairly. 3 marks
1.5 — School subject choices. 200 students were asked their favourite subject across 10 different subjects.
(a) Should the school use a bar chart or a pie chart to display these results? Justify.
(b) Give ONE feature that the chosen chart MUST include to be valid.
(c) What would happen if a pie chart was used here, and there were 10 categories? 3 marks
2. Explain your thinking
This question is about communication, not just answers. Use full sentences. 4 marks
2.1 A classmate calculates pie-chart angles for 4 categories from 60 responses and gets 72°, 90°, 144°, and 60°. In your own words, explain (i) what is wrong with these angles, (ii) what the angles MUST sum to, and (iii) one practical method the classmate could use to fix the error. Use the term sector angle somewhere in your answer.
How did this worksheet feel?
What I'll revisit before next class:
1.1 — Colour survey
(a) Red: (5÷20) × 360 = 90°. Blue: (8÷20) × 360 = 144°. Green: (4÷20) × 360 = 72°. Yellow: (3÷20) × 360 = 54°.
(b) Check: 90 + 144 + 72 + 54 = 360° ✓.
(c) Modal category = Blue (highest f = 8).
1.2 — Reverse a pie chart
(a) Fraction = 135 ÷ 360 = 3/8 (= 0.375).
(b) Count = 0.375 × 240 = 90 voters.
(c) Percentage = 0.375 × 100 = 37.5%.
1.3 — Sport club enrolments
(a) Either works, but pie chart suits showing parts of a whole with only 4 categories (or bar chart if exact comparison is most important).
(b) Total = 80 + 60 + 40 + 20 = 200.
(c) Soccer 40%, Netball 30%, Athletics 20%, Cricket 10% (each = f ÷ 200 × 100).
1.4 — Misleading news chart
(a) The y-axis starting at 40 instead of 0 makes the visible bar heights (10 and 5) appear in a 2:1 ratio, even though the underlying values are 50 and 45 — only a 10% relative difference.
(b) Actual difference = 50 − 45 = 5 percentage points.
(c) Redraw with the y-axis starting at 0, so the bars are 50 and 45 units tall — the visual difference will then accurately reflect the small 5-point gap.
1.5 — Subject choices (10 categories)
(a) Bar chart — pie charts become unreadable with more than ~6 categories; a bar chart handles 10 cleanly and makes exact comparisons easy.
(b) Must include any one of: a descriptive title, labelled axes with units, even scale starting at 0, equal bar widths, or gaps between bars.
(c) With 10 categories the pie slices would be small and crowded — readers couldn't tell which is bigger and the proportions would all look similar.
2.1 — Explain your thinking (sample response)
The angles 72° + 90° + 144° + 60° = 366°, which is impossible because every sector angle in a pie chart shares the same 360° circle — the angles MUST sum to exactly 360°. The 6° excess shows there's a calculation error in at least one of the four angles. A practical fix is to recompute each angle using (f ÷ n) × 360, then add them up again to check; if rounding leaves you 1° over or under, adjust the largest sector by 1° so the total is exactly 360°.
Marking: 1 mark for spotting the sum is wrong; 1 mark for stating sum must = 360°; 1 mark for explaining why; 1 mark for a sensible fix that uses the formula.