Mathematics • Year 7 • Unit 4 • Lesson 2
Collecting Data — Real World
Apply the survey/observation/experiment choice, census vs sample reasoning, and bias spotting to five real settings: a council traffic study, a mango quality check, a fertiliser trial, an online poll, and a school cafeteria review.
1. Word problems
For each scenario, choose the right method, decide census vs sample, and watch for bias. Show your reasoning.
1.1 — Council traffic study. Hornsby Council wants to know how many cars use the corner of Pacific Hwy and Edgeworth David Ave between 7 am and 9 am on weekdays so they can plan a roundabout upgrade.
(a) Which data collection method should they use, and why?
(b) Is this a census or a sample of "all cars that use this intersection"? Justify briefly. 3 marks
1.2 — Mango quality check. A food company receives a shipment of 50,000 mangoes. To check the percentage that are bruised, they have to cut each mango open, which destroys it.
(a) Should they use a census or a sample? Justify in one sentence.
(b) Suggest a fair way to choose 200 mangoes from the shipment so the sample is representative. 3 marks
1.3 — Fertiliser trial. A farmer wants to know whether a new fertiliser makes wheat grow taller. They have one field.
(a) Which collection method is appropriate, and why?
(b) Describe one variable the farmer must keep the same in both groups for the test to be fair. 3 marks
1.4 — Online poll bias. A radio station posts a poll on its website: "Should the speed limit on city roads be reduced from 50 km/h to 40 km/h to save lives?"
(a) Identify TWO sources of bias — one in the wording, one in the way the sample is collected.
(b) Rewrite the question fairly, AND suggest a better way to collect the sample. 4 marks
1.5 — Cafeteria review. Your school cafeteria wants to know which menu items Year 7 students like best. There are 180 Year 7 students. The cafeteria has 30 minutes during one lunch break to collect data.
(a) Census or sample? Justify briefly.
(b) Suggest one fair way to choose a sample of 30 students.
(c) Write a fair survey question with at least four answer options. 3 marks
2. Explain your thinking
Communication matters. Use full sentences. 4 marks
2.1 A student says: "I asked 5 of my friends what they think about the new bell times. 4 out of 5 said they hate it. That's 80% — so 80% of the school hates the new bell times." In your own words, explain (i) why the SAMPLE here is biased, (ii) why 5 friends is too small to draw conclusions about the whole school, and (iii) describe a fairer way to collect data on this question.
How did this worksheet feel?
What I'll revisit before next class:
1.1 — Council traffic study
(a) Observation. Counting cars doesn't require asking anyone or changing anything — just watch and record.
(b) It's a sample of "all cars that ever use this intersection". The 7–9 am weekday window is only one slice of all possible times. (It would be a census if the population was redefined as "all cars at this intersection between 7 and 9 am on the chosen day".)
1.2 — Mango quality
(a) Sample. The test destroys each mango, so a census would leave nothing to sell.
(b) Pick mangoes randomly from many different crates and from different layers (top, middle, bottom). Avoid picking only one crate or only the visible top layer, which might be the freshest. A random-number approach (e.g. every 250th mango) is fairer.
1.3 — Fertiliser trial
(a) Experiment. The farmer is deliberately changing one variable (fertiliser used or not) and measuring the effect on wheat height.
(b) The farmer must keep variables like amount of water, soil type, sunlight exposure and wheat variety the SAME in both groups. Only fertiliser type should differ. This is the principle of a "fair test" — change one thing at a time.
1.4 — Online poll bias
(a) Wording bias — "to save lives" is a loaded add-on that pressures responders toward YES. Sample bias — only listeners who visit the radio station's website and choose to vote answer, so the sample is self-selected (often the most opinionated people).
(b) Fair question: "What is your opinion on changing the city speed limit from 50 km/h to 40 km/h? Support / Neutral / Oppose."
Better sample: randomly mail-survey a balanced selection of drivers from across the city (or use a properly-designed telephone poll with random number dialling), so participation isn't self-selecting.
1.5 — Cafeteria review
(a) Sample. With only 30 minutes there is not enough time to ask every one of the 180 Year 7 students.
(b) Approach random students in the playground rather than the food line — for example, ask every 6th Year 7 student you see, regardless of where they are. This avoids only sampling students already at one counter.
(c) Fair question: "Which canteen item would you most often choose? Pasta / Wrap / Sushi / Sandwich / Pie / Other ____."
2.1 — Explain your thinking (sample response)
The student's sample is biased because friends are not chosen at random — they usually share similar opinions to the student, so the result will tend to look like the student's own view. The sample is also too small: 5 students is a tiny fraction of a school of (say) several hundred, so the 80% number swings wildly with just one extra response. A fairer approach would be to choose a much larger sample (say 30–60 students) spread across all classes, perhaps by randomly selecting names from the school roll, and to use a neutrally-worded question with balanced options such as: "What is your opinion of the new bell times? Better / About the same / Worse." Only then can a percentage actually represent the whole school.
Marking: 1 for explaining friend-group bias; 1 for sample-size point; 1 for a fairer sampling method; 1 for clear full-sentence communication.