Mathematics • Year 8 • Unit 4 • Lesson 1
Collecting Data
Build fluency with stratified sampling and identifying sampling methods. One worked example, one guided example with blanks, then eight independent problems from quick recall to bias spotting.
1. I do — fully worked example
Read every line. Each step has a short reason so you can see why we do it, not just what we do.
Problem. A school of 600 students is 40% Year 7, 35% Year 8, and 25% Year 9. A stratified sample of 60 students is required. How many from each year?
Step 1 — Find the number in each year group.
Year 7: 0.40 × 600 = 240 Year 8: 0.35 × 600 = 210 Year 9: 0.25 × 600 = 150
Reason: convert percentages to actual counts first so we know what we are sampling from.
Step 2 — Find the sampling fraction.
sample size ÷ population = 60 ÷ 600 = 1/10
Reason: we want 1 student for every 10 in the school. The same fraction is applied to every group.
Step 3 — Apply the fraction to each group.
Year 7: 240 × 1/10 = 24 Year 8: 210 × 1/10 = 21 Year 9: 150 × 1/10 = 15
Reason: each group sends the same proportion (10%) of itself to the sample.
Step 4 — Check the total matches the required sample.
24 + 21 + 15 = 60 ✓
Answer: 24 from Year 7, 21 from Year 8, 15 from Year 9.
2. We do — fill in the missing steps
Same shape as Section 1, but with the working faded. Fill in each blank. 4 marks
Problem. A town of 2,000 people is 50% adults, 30% teenagers, 20% children. A stratified sample of 100 is needed. How many from each group?
Step 1 — Number in each group:
Adults: 0.50 × 2000 = ______ Teens: 0.30 × 2000 = ______ Children: 0.20 × 2000 = ______
Step 2 — Sampling fraction:
100 ÷ 2000 = 1 / ______
Step 3 — Apply fraction to each group:
Adults: ______ Teens: ______ Children: ______
Step 4 — Check:
______ + ______ + ______ = ______ ✓
3. You do — independent practice
Show your working in the space under each problem. The first four are foundation (single-skill recall). The middle two are standard (two-step). The last two are extension (analyse a scenario).
Foundation — identify the method
3.1 A researcher selects every 8th student on a school roll of 400. Name the sampling method. 1 mark
3.2 A teacher pulls 20 names from a hat (one for each student on the roll). Name the sampling method. 1 mark
3.3 A pollster surveys the first 30 people who walk past the school gate at 8 am. Name the sampling method. 1 mark
3.4 Define bias in one short sentence using the phrase "systematic error". 1 mark
Standard — stratified calculations
3.5 A school of 500 students has 300 in the junior years and 200 in the senior years. A stratified sample of 50 is required. How many from each group? Show the sampling fraction. 2 marks
3.6 A workforce of 1,000 employees is 60% female and 40% male. A stratified sample of 80 is taken. How many of each? 2 marks
Extension — analyse a scenario
3.7 Rewrite this leading question as a fair, neutral one with balanced response options: "Don't you agree that homework is unfair?" 2 marks
3.8 A school surveys 50 students standing outside the canteen at lunchtime and finds 80% prefer pizza. Identify the type of sampling used and explain why the result may not represent the whole school. 2 marks
How did this worksheet feel?
What I'll revisit before next class:
Section 2 — We do (town of 2,000)
Step 1: Adults = 1000, Teens = 600, Children = 400.
Step 2: Sampling fraction = 100 ÷ 2000 = 1/20.
Step 3: Adults = 1000 × 1/20 = 50; Teens = 600 × 1/20 = 30; Children = 400 × 1/20 = 20.
Step 4: 50 + 30 + 20 = 100 ✓
3.1 — Every 8th student
Systematic sampling — every nth person on an ordered list.
3.2 — Names from a hat
Random sampling — every member has an equal chance of being selected.
3.3 — First 30 people at the gate
Convenience sampling — whoever is available is surveyed; the most biased method.
3.4 — Definition of bias
Bias is a systematic error that makes the results of a survey unrepresentative of the population.
3.5 — Junior/senior stratified sample
Sampling fraction = 50 ÷ 500 = 1/10. Junior: 300 × 1/10 = 30. Senior: 200 × 1/10 = 20. Check: 30 + 20 = 50 ✓
3.6 — Workforce stratified sample
Female count = 0.60 × 1000 = 600. Male count = 0.40 × 1000 = 400. Sampling fraction = 80 ÷ 1000 = 2/25 (or 0.08). Female: 600 × 0.08 = 48. Male: 400 × 0.08 = 32. Check: 48 + 32 = 80 ✓
3.7 — Rewrite leading question (sample)
Original is leading: "Don't you agree" pushes respondents toward Yes, and "unfair" assumes a negative view. Fair version: "Do you think the amount of homework you receive is too much, about right, or too little? Too much / About right / Too little / Unsure" — neutral wording, balanced options, non-overlapping responses.
3.8 — Canteen survey
This is convenience sampling. The sample may not represent the whole school because (i) students at the canteen are more likely to be regular canteen users who already prefer canteen food, (ii) students who bring lunch from home are excluded entirely, and (iii) different year groups and times of day are not represented. A stratified random sample across year groups, taken at different times, would be fairer.