Mathematics • Year 8 • Unit 4 • Lesson 5
Bar and Pie Charts — Mixed Challenge
Pull together everything from Lesson 5: sector angle calculation, reverse calculation, chart choice, bar-chart rules, and identifying misleading charts.
1. Mixed problems — choose the right move
Each question uses a different idea from Lesson 5. Show your working. 3 marks each
1.1 Calculate the pie-chart sector angle for a category with 15 responses out of 60 total.
1.2 A pie chart sector measures 108° in a sample of 200 people. How many people are in that sector? What percentage?
1.3 Calculate all sector angles for: A 16, B 12, C 8, D 4 (total 40). Verify the sum is 360°.
1.4 A bar chart has these required features. Tick the THREE that are correct and write a brief correction for the THREE that are wrong:
(a) Bars must be the same width.
(b) Bars should always touch — no gaps allowed.
(c) The y-axis must start at 0.
(d) The title should describe what the data shows.
(e) Both axes can use any scale that fits.
(f) The y-axis must have a label including units where relevant.
1.5 Decide which chart is better — bar chart or pie chart — and give a one-sentence reason:
(a) Comparing monthly rainfall across 12 months in your suburb.
(b) Showing what proportion of household income is spent on rent, food, transport, savings.
(c) Comparing test scores of 40 students.
1.6 A pie chart has 3 sectors with angles 135°, 90° and one missing angle. (a) Find the missing angle. (b) If n = 120, how many people does the missing sector represent?
2. Find the mistake
Another student attempted this pie-chart problem. Their working is shown below. Exactly one line contains a mistake. Spot it, explain why it's wrong, then re-do the working correctly. 3 marks
Problem: 80 students chose a sport. Soccer 40, Tennis 24, Hockey 16. Calculate the pie-chart sector angles.
Line 1: Total n = 40 + 24 + 16 = 80 ✓
Line 2: Soccer: (40 ÷ 80) × 360 = 0.5 × 360 = 180°.
Line 3: Tennis: (24 ÷ 80) × 360 = 0.3 × 360 = 108°.
Line 4: Hockey: (16 ÷ 80) × 360 = 0.2 × 180 = 36°.
Line 5: Check: 180 + 108 + 36 = 324° ✓
(a) Which line contains the mistake?
(b) Explain in one or two sentences why that line is wrong (consider both the answer AND the check).
(c) Write the corrected working and the correct sum check.
Stuck? In Line 4, the student wrote × 180 instead of × 360. Recompute. Then check the sum — does it now equal 360°?3. Open-ended challenge — design your own pie chart
This question has many valid answers. 4 marks
3.1 Your job: design a pie chart for a Year 8 class survey of EXACTLY n = 120 students. You must invent a topic and category breakdown that produces SECTOR ANGLES THAT ARE ALL WHOLE NUMBERS.
Write up your design with the following:
(i) State your topic (e.g. "favourite weekend activity", "main transport to school", "type of pet at home").
(ii) Choose 4–5 categories with whole-number frequencies that sum to 120.
(iii) Calculate each sector angle. Show working.
(iv) Verify all angles sum to 360°.
(v) State the modal category.
(vi) Justify in ONE sentence why a pie chart suits this data better than a bar chart (or vice versa).
How did this worksheet feel?
What I'll revisit before next class:
1.1 — Single angle
(15 ÷ 60) × 360 = (1/4) × 360 = 90°.
1.2 — Reverse pie chart
Proportion = 108 ÷ 360 = 0.3. Count = 0.3 × 200 = 60 people. Percentage = 30%.
1.3 — All angles
A (16÷40) × 360 = 144°; B (12÷40) × 360 = 108°; C (8÷40) × 360 = 72°; D (4÷40) × 360 = 36°. Check: 144 + 108 + 72 + 36 = 360° ✓.
1.4 — Bar chart features
Correct: (a) ✓ equal widths; (c) ✓ y-axis starts at 0; (d) ✓ descriptive title; (f) ✓ axis labels with units.
Wrong: (b) ✗ bars must have GAPS between them, not touch (touching is a histogram); (e) ✗ the y-axis MUST start at 0, you can't pick any scale you like.
1.5 — Choose the chart
(a) Bar chart — 12 categories is too many for a pie chart; bar chart shows monthly comparison cleanly.
(b) Pie chart — parts of a whole (the four categories together make 100% of income).
(c) Bar chart (or stem-and-leaf) — discrete values like test scores compare best as bar heights, and 40 students is too many distinct values for a pie chart.
1.6 — Missing angle
(a) Missing angle = 360 − 135 − 90 = 135°.
(b) Count = (135 ÷ 360) × 120 = 0.375 × 120 = 45 people.
2 — Find the mistake
(a) The mistake is on Line 4.
(b) The student wrote "× 180" instead of "× 360" — they accidentally halved the 360. The Line 5 check sum (324°) also flags this: the sum should be exactly 360°, so the 36° figure for Hockey is wrong.
(c) Corrected: Hockey = (16 ÷ 80) × 360 = 0.2 × 360 = 72°. Check: 180 + 108 + 72 = 360° ✓.
3 — Open-ended (sample solution — Favourite weekend activity, n = 120)
(i) Topic: Favourite weekend activity of 120 Year 8 students.
(ii) Categories & frequencies (sum = 120): Sports 40, Gaming 30, Hanging out with friends 20, Reading 15, Other 15.
(iii) Sector angles: Sports (40÷120) × 360 = 120°; Gaming (30÷120) × 360 = 90°; Friends (20÷120) × 360 = 60°; Reading (15÷120) × 360 = 45°; Other (15÷120) × 360 = 45°.
(iv) Check: 120 + 90 + 60 + 45 + 45 = 360° ✓.
(v) Modal category: Sports (highest frequency = 40).
(vi) Justification: A pie chart suits this data because we are showing parts of a whole (the 5 categories together account for all 120 students), and 5 categories is within the readable limit.
Marking: 1 mark for plausible whole-number frequencies summing to 120; 1 mark for correct angle calculations; 1 mark for the 360° check + modal category; 1 mark for a clear chart-choice justification.