Mathematics • Year 10 • Unit 4 • Lesson 2
Collecting Data in the Real World
Apply sampling methods to real Australian scenarios — election polling, school SRC surveys, market research and online questionnaires. Spot bias, choose the best method, and design a stratified sample with proportional numbers.
1. Word problems
Each problem uses ideas from Lesson 2: population vs sample, the four sampling methods, and bias. Show your working — naming a method with no reason only earns half marks.
1.1 — School SRC referendum. The SRC of a 900-student school wants to know if students support a longer recess. They put a Google Form link on the senior-school noticeboard for one week. 220 students respond, 78% in favour.
(a) Name the sampling method.
(b) Give two distinct reasons the 78% figure may not represent the whole student body. 3 marks
1.2 — Stratified sample of a year level. A Year 10 cohort of 180 students has 60 in Class A, 70 in Class B and 50 in Class C. A teacher wants to interview a stratified random sample of 36 students.
(a) Calculate how many students should be selected from each class so the sample is proportional.
(b) Briefly describe one practical way to randomly choose those students from each class. 3 marks
1.3 — Election exit poll. On election day, a polling firm interviews every 25th voter as they leave one polling booth in inner-Sydney. 600 people are interviewed. The firm reports the result as "Sydney's voting intention".
(a) Name the sampling method used at that booth.
(b) Identify a serious source of bias when this one booth's result is reported as Sydney-wide.
(c) Suggest a better sampling design. 3 marks
1.4 — Coles customer survey. A Coles store of 4,200 weekly customers wants to know average spend per visit. They survey 200 customers on Saturday morning at one store.
(a) Identify the population and the sample.
(b) Name the sampling method.
(c) Give one reason the estimate of "average spend per visit" is likely biased upward (too high). 3 marks
1.5 — Health study with strata. A health researcher wants to study average daily steps for adults in NSW. The adult population is roughly 30% aged 18-34, 40% aged 35-54, and 30% aged 55+. The researcher wants a sample of 500.
(a) How many participants should come from each age stratum to keep the sample proportional?
(b) Explain in one sentence why a stratified sample reduces bias compared to a simple random sample of 500 NSW adults. 3 marks
2. Explain your thinking
This question is about communication, not just method-naming. Use full sentences. 4 marks
2.1 An online influencer posts a poll on Instagram Stories asking their 500,000 followers: "Should Year 12 exams be replaced by coursework?" 320,000 vote and 89% say yes. They then claim "Australia's Year 12 students overwhelmingly want exams replaced." Using Lesson 2's vocabulary, explain in 4 to 6 sentences (i) what is technically correct about the poll, (ii) why the 89% figure is misleading when generalised to all Year 12 students, (iii) what kind of bias is present, and (iv) what a less-biased method would look like. Use at least two of: population, sample, voluntary response, random, stratified, bias.
How did this worksheet feel?
What I'll revisit before next class:
1.1 — SRC Google Form
(a) Voluntary response (a self-selected convenience) sampling.
(b) Two distinct reasons: (i) the link was only on the senior noticeboard, so juniors are systematically excluded; (ii) students with strong feelings about recess are more likely to bother filling it in, so the 78% over-represents the keen yes-voters. The true population proportion is unknown.
1.2 — Proportional stratified sample of 36
(a) Sample fraction = 36 ÷ 180 = 1/5. So Class A: 60 × 1/5 = 12; Class B: 70 × 1/5 = 14; Class C: 50 × 1/5 = 10. Check: 12 + 14 + 10 = 36 ✓.
(b) For each class, put every student's name in a hat and draw the required number, or use the roll-number list with a random-number generator (e.g. =RANDBETWEEN in a spreadsheet).
1.3 — Election exit poll
(a) At that one booth: systematic sampling (every 25th voter).
(b) One booth in inner-Sydney is not representative of Sydney as a whole — different suburbs have different demographics and different voting patterns, so reporting it as "Sydney's intention" is biased.
(c) Better design: choose multiple booths spread across Sydney (a stratified-by-electorate design), and apply systematic sampling at each booth.
1.4 — Coles store survey
(a) Population = the 4,200 weekly customers of that Coles. Sample = the 200 surveyed.
(b) Convenience sampling (Saturday morning, one location).
(c) Saturday-morning shoppers typically do the big weekly grocery shop, so their average spend is higher than mid-week top-up shoppers — the sample over-represents big spenders, biasing the average upward.
1.5 — NSW step-count study
(a) 18-34: 500 × 30% = 150; 35-54: 500 × 40% = 200; 55+: 500 × 30% = 150. Check: 150 + 200 + 150 = 500 ✓.
(b) Stratification guarantees each age group is represented in proportion, whereas a simple random sample of 500 could (by chance) miss younger or older adults entirely, biasing the average daily step count.
2.1 — Instagram poll (sample response)
(i) The poll did collect 320,000 responses from a real sample, and reporting "89% of those who answered" would be technically correct. (ii) However, the population the influencer is generalising to — all Year 12 students in Australia — is not the same as the influencer's followers, and the people who chose to vote are not a random or stratified slice of all Year 12s. (iii) This is voluntary response bias: only followers with strong opinions click "vote", so the 89% over-represents one side. (iv) A less-biased method would be a stratified random sample of Year 12 students across NSW, Vic, Qld, WA, SA, Tas, ACT and NT, with sample sizes proportional to each state's Year 12 enrolment.
Marking: 1 mark for naming "voluntary response", 1 for explaining that followers ≠ all Year 12, 1 for using at least two of the listed terms correctly, 1 for proposing a stratified or random alternative.