Mathematics • Year 7 • Unit 4 • Lesson 2
Collecting Data — Mixed Challenge
Bring together collection methods, census vs sample, sample size, biased wording and biased samples. Then spot a study-design error and propose your own fair data plan.
1. Mixed problems
Each question mixes collection method, sampling and bias. Justify briefly. 2 marks each
1.1 A national TV ratings agency wants to know which shows the country watched on Saturday night. Census or sample? Why?
1.2 A bushwalking app records how many steps each user takes each day automatically through the phone's sensor. Survey, observation or experiment? Explain.
1.3 Rewrite this leading question fairly: "Do you think the bullying problem at our school is getting worse?"
1.4 A maths teacher wants to test whether quiet background music helps students concentrate in maths quizzes. Briefly describe the experiment, including the variable they would CHANGE and the variable they would MEASURE.
1.5 A national election uses a census of all enrolled voters. Why does it make sense for elections to be a census, even though they cost millions of dollars?
1.6 Identify TWO ways the following sample is biased: "A reporter stands outside a vegan café at 1 pm on Sunday and asks shoppers how often they eat meat."
2. Find the mistake
A Year 7 student has designed a survey to find out students' attitudes to homework. Their plan is shown below. Exactly one step contains a serious error. Spot it, explain why it's wrong, and rewrite it. 3 marks
Student's survey plan:
Step 1: Population — every Year 7 student in our school (180 students).
Step 2: Sample — randomly choose 30 students from the school roll.
Step 3: Question — "Don't you agree that we get too much homework? YES / NO."
Step 4: Report the percentage of YES answers from the 30 students.
(a) Which step contains the mistake?
(b) Explain in one or two sentences why that step is wrong.
(c) Rewrite that step correctly.
Stuck? Look at Step 3 carefully — "don't you agree" and only two answer options.3. Open-ended challenge — design your own data plan
This question has many correct answers. Show your work clearly. 4 marks
3.1 The school wants to find out how Year 7 students get to school. Design a full data-collection plan with at least five clear steps:
- State the population.
- Decide and JUSTIFY census or sample (and if sample, the size).
- Describe HOW you would select the sample fairly.
- State the collection method (survey / observation / experiment) and why.
- Write your fair question, with balanced answer options that cover every realistic way of getting to school.
Bonus: identify one potential source of bias in your plan and how you would reduce it.
How did this worksheet feel?
What I'll revisit before next class:
1.1 — TV ratings
Sample. A national census of every household is impractical and expensive. Ratings agencies use a representative sample (typically a few thousand households fitted with meters) to estimate national viewing.
1.2 — Bushwalking app step counter
Observation. The data is recorded automatically by the phone's sensor — no one is asked, no variable is deliberately changed.
1.3 — Rewrite "bullying problem is getting worse"
The phrase "the bullying problem" assumes a problem exists, and "getting worse" pushes the responder toward YES. Fair version: "Compared to last year, how do you feel bullying at our school has changed? Better / About the same / Worse / Not sure."
1.4 — Quiet music experiment
Experiment. The teacher CHANGES the music (on for one class, off for another class — or two halves of the same class on different days), and MEASURES the quiz score. Keep the difficulty of the quiz, the time allowed, and the seating arrangement the same in both conditions, so the only difference is the music.
1.5 — Why elections use a census
Elections must be a census because they directly DECIDE the result, not estimate it. A sample of voters cannot legitimately choose a government — every eligible vote must count. The cost is justified by the fact that the outcome is binding.
1.6 — Vegan café reporter
Bias 1 — Place bias: shoppers at a vegan café are far more likely to be vegetarian or vegan than the general public, so meat-eating rates will appear MUCH lower than they really are.
Bias 2 — Time bias: Sunday at 1 pm captures one specific demographic (people with weekend free time who chose to shop at this café), not a cross-section of all meat-eaters.
2 — Find the mistake
(a) The mistake is in Step 3.
(b) The question "Don't you agree that we get too much homework?" is a leading question — the wording pressures students toward YES. Two answer options (YES / NO) also hide students who have no strong opinion.
(c) Corrected Step 3: "In your opinion, how is the amount of homework? Too little / About right / Too much / Not sure."
3 — Sample data plan ("how do Year 7s get to school?")
Population: all 180 Year 7 students in the school.
Census or sample: Sample of 50 students — large enough to be representative, small enough to collect in a single morning roll call.
Sample selection: use the school roll alphabetically and pick every 4th name (180 ÷ 50 ≈ 3.6, round to 4). Avoid choosing only one class, which might be biased (e.g. a class of students who all live in one suburb).
Method: survey — we have to ASK; transport choice can't be observed without following students.
Fair question: "How do you usually travel to school? Walk / Cycle / Bus / Train / Car (driven by family) / Other ____."
Bias bonus: students who walk to school may arrive first, so if we only ask the morning roll the sample could over-represent walkers. Reduce by surveying during lesson 1 when all students are present, regardless of how they arrived.
Marking: 1 mark each for population, justified sample size, fair selection method and fair question (all five required). Award bonus for any reasonable bias-reduction comment.