Mathematics • Year 8 • Unit 4 • Lesson 1
Collecting Data in the Real World
Apply stratified sampling, fair survey design, and bias spotting to real situations: school polls, government surveys, sports clubs, news headlines, and online opinion polls.
1. Word problems
Each problem uses ideas from Lesson 1 — populations, samples, sampling methods, bias, or stratified counts. Show your working — a single answer with no working only earns half marks.
1.1 — School uniform vote. A school of 800 students has 250 in Year 7, 220 in Year 8, 180 in Year 9, and 150 in Year 10. The principal wants a stratified sample of 80 students to vote on a new uniform.
(a) Calculate the sampling fraction.
(b) Calculate how many students should be selected from each year group.
(c) Verify the four numbers add to 80. 4 marks
1.2 — Online news poll. A news website asks readers to click Yes or No on "Should the school day start later?" After 24 hours, 5,000 readers have voted and 78% say Yes.
(a) Name the sampling method used.
(b) Identify ONE source of bias and explain how it affects the result.
(c) Should the government use this result to change school hours? Justify in one sentence. 3 marks
1.3 — Sports club survey. A junior sports club has 360 members: 180 in soccer, 90 in netball, 60 in athletics, 30 in cricket. The committee wants a stratified sample of 60 members to review training times.
(a) Find the sampling fraction.
(b) How many members from each sport? 3 marks
1.4 — Census vs sample. The Australian Bureau of Statistics runs the national Census every 5 years, counting every person in Australia. It costs around $500 million. A private polling company asks 1,200 randomly chosen Australians about their voting intentions every month.
(a) Which uses a census, and which uses a sample?
(b) Give ONE reason why the ABS prefers a census for population counts.
(c) Give ONE reason why polling companies use samples instead of a census. 3 marks
1.5 — Survey question rewrite. A student writes this question for a school screen-time survey: "Most experts agree too much screen time is harmful. How many hours of screens do you waste each day? 0–2 2–4 4 or more"
(a) Identify TWO problems with this question.
(b) Rewrite it as a fair version with non-overlapping options. 3 marks
2. Explain your thinking
This question is about communication, not just answers. Use full sentences. 4 marks
2.1 A classmate says: "If a survey has 5,000 responses it must be more accurate than a survey of only 100 responses." In your own words, explain (i) why this claim is not always true, (ii) what matters more than sample size, and (iii) give one example where a small well-chosen sample beats a large biased sample. Use the term sampling bias somewhere in your answer.
How did this worksheet feel?
What I'll revisit before next class:
1.1 — School uniform vote
(a) Sampling fraction = 80 ÷ 800 = 1/10.
(b) Year 7: 250 × 1/10 = 25. Year 8: 220 × 1/10 = 22. Year 9: 180 × 1/10 = 18. Year 10: 150 × 1/10 = 15.
(c) Check: 25 + 22 + 18 + 15 = 80 ✓
1.2 — Online news poll
(a) Convenience sampling combined with self-selection (also called voluntary-response sampling).
(b) Self-selection bias: only people who feel strongly about school start times bother to vote, so the 78% Yes likely overstates support in the wider population. People who don't read this news site, or don't have internet access, are excluded entirely.
(c) No — the poll is not a random sample of the population, so it should not be used as evidence for a policy change without a properly designed survey.
1.3 — Sports club survey
(a) Sampling fraction = 60 ÷ 360 = 1/6.
(b) Soccer: 180 × 1/6 = 30. Netball: 90 × 1/6 = 15. Athletics: 60 × 1/6 = 10. Cricket: 30 × 1/6 = 5. Check: 30 + 15 + 10 + 5 = 60 ✓
1.4 — Census vs sample
(a) ABS = census. Polling company = sample.
(b) A census gives an accurate count of every person, with no sampling error — essential for funding decisions, electorate boundaries, and service planning.
(c) A sample is much cheaper, faster, and can be repeated monthly to track changes; a census would be impossible to run that often.
1.5 — Survey question rewrite
(a) Problem 1 — leading wording: "Most experts agree too much screen time is harmful" pushes respondents toward saying they use less than they actually do, and "waste" is emotive. Problem 2 — overlapping intervals: 2 appears in both "0–2" and "2–4", so respondents don't know which to tick.
(b) Sample rewrite: "How many hours per day do you use a screen (phone, tablet, computer, TV) for personal use? Less than 1 / 1 to less than 2 / 2 to less than 4 / 4 or more." Neutral wording, non-overlapping intervals, exhaustive options.
2.1 — Explain your thinking (sample response)
The claim is wrong because sample quality matters more than sample size. A large sample collected with sampling bias — for example, 5,000 gym members asked whether they exercise daily — will give a misleading result, because the people surveyed are not representative of the wider community. In contrast, a smaller sample of 100 people chosen randomly from the whole community will give a much fairer estimate, because every member of the population had an equal chance of selection. So before trusting any statistic, you should always ask "How was the sample selected?" not just "How big was it?"
Marking: 1 mark for identifying the flaw; 1 mark for naming what matters more (random/representative selection); 1 mark for a concrete example; 1 mark for clear, full-sentence explanation that uses "sampling bias".