Sheet № 191 · Higher only · AQA · Edexcel · OCR
Stratified Sampling –
Stratified sampling is a Higher-tier topic that appears regularly on AQA, Edexcel and OCR GCSE Maths papers. It ensures that a sample represents the proportions of different subgroups within a population, making conclusions more reliable. You need to know how to calculate the number of items to sample from each stratum and explain why str
§Key definitions
Question:
A school of 500 pupils wants a stratified sample of 50. Year 7 has 120 pupils, Year 8 has 110, Year 9 has 100, Year 10 has 90 and Year 11 has 80. Calculate how many to sample from each year.
Answer:
Year 7: 12, Year 8: 11, Year 9: 10, Year 10: 9, Year 11: 8.
(a)
Full-time: 150 x (2/15) = 20. Part-time: 90 x (2/15) = 12. Contract: 60 x (2/15) = 8.
Q1 (Foundation):
A population has 200 adults and 100 children. A stratified sample of 30 is needed. How many adults and children should be sampled?
Q2 (Foundation):
Explain one advantage of stratified sampling over random sampling.
§Formulas to memorise
Number from stratum = (Stratum size ÷ Population size) x Total sample size
Sample fraction = 50/500 = 1/10.
Total = 150 + 90 + 60 = 300. Sample fraction = 40/300 = 2/15.
Total = 85 + 140 + 95 + 30 = 350. Fraction = 70/350 = 1/5.
Worked example
A school of 500 pupils wants a stratified sample of 50. Year 7 has 120 pupils, Year 8 has 110, Year 9 has 100, Year 10 has 90 and Year 11 has 80. Calculate how many to sample from each year.
Working:
⚠ Common mistakes
- ✗Dividing the sample equally. Do not split the sample size equally among strata — the whole point is proportional allocation.
- ✗Using the wrong formula. Some students divide the sample by the stratum count instead of multiplying (stratum size ÷ population) by sample size.
- ✗Forgetting to check the total. After rounding, the individual values must add up to the required sample size. Adjust the largest group by 1 if needed.
- ✗Not selecting randomly within strata. After calculating how many from each stratum, you must still use a random method to pick individuals.
✦ Exam tips
- →Show your calculation for every stratum — method marks are awarded for each correct step.
- →Always include a "check" line showing your values sum to the required sample size.
- →If asked to compare stratified sampling with random sampling, highlight that stratified guarantees proportional representation of subgroups, whereas random could over- or under-represent certain groups.
- →For broader sampling context, see sampling methods. For key formulas, visit our GCSE Maths formulas page.