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 stratified sampling is used. This guide covers the method in detail with worked examples and practice questions. For an overview of every topic, see our complete GCSE Maths topics list.
What Is Stratified Sampling?
In stratified sampling, the population is divided into distinct subgroups called strata (e.g. year groups, age bands, departments). A proportional number of individuals is then randomly selected from each stratum so that the sample mirrors the population structure.
Key Formulas
This formula ensures each stratum is represented in proportion to its share of the population.
Why Use Stratified Sampling?
- It guarantees proportional representation of each subgroup.
- It reduces bias compared to simple random sampling, especially when the population has distinct groups.
- It produces more reliable estimates for the overall population.
Limitations
- You need to know the size of each stratum before you start.
- It is more complex to organise than simple random sampling.
- Within each stratum, you still need to select randomly.
Step-by-Step Method
- Identify the strata (subgroups) in the population.
- Find the total population size.
- Decide on the overall sample size (or it will be given).
- For each stratum, calculate: (stratum size ÷ population size) x sample size.
- Round to the nearest whole number if needed.
- Check that all rounded values add up to the total sample size — adjust by 1 if necessary.
- Randomly select the calculated number from each stratum.
Worked Example 1 — Foundation Level
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.
Working:
Sample fraction = 50/500 = 1/10.
Year 7: 120 x (1/10) = 12. Year 8: 110 x (1/10) = 11. Year 9: 100 x (1/10) = 10. Year 10: 90 x (1/10) = 9. Year 11: 80 x (1/10) = 8.
Check: 12 + 11 + 10 + 9 + 8 = 50.
Answer: Year 7: 12, Year 8: 11, Year 9: 10, Year 10: 9, Year 11: 8.
Worked Example 2 — Higher Level
Question: A company has 150 full-time, 90 part-time and 60 contract workers. A stratified sample of 40 is to be taken. (a) Calculate the sample from each group. (b) Explain why stratified sampling is appropriate here.
Working:
Total = 150 + 90 + 60 = 300. Sample fraction = 40/300 = 2/15.
(a) Full-time: 150 x (2/15) = 20. Part-time: 90 x (2/15) = 12. Contract: 60 x (2/15) = 8.
Check: 20 + 12 + 8 = 40.
(b) Stratified sampling ensures each employment type is proportionally represented. The three groups may have different views or experiences (e.g. about working conditions), so proportional representation prevents any group being over- or under-represented in the sample.
Answer: (a) Full-time 20, Part-time 12, Contract 8. (b) It ensures proportional representation of groups with potentially different characteristics.
Worked Example 3 — Exam Style
Question: A gym has the following membership breakdown.
| Age group | 16–25 | 26–40 | 41–60 | 61+ |
|---|---|---|---|---|
| Members | 85 | 140 | 95 | 30 |
A stratified sample of 70 is required. Calculate the sample from each age group.
Working:
Total = 85 + 140 + 95 + 30 = 350. Fraction = 70/350 = 1/5.
16–25: 85 x (1/5) = 17. 26–40: 140 x (1/5) = 28. 41–60: 95 x (1/5) = 19. 61+: 30 x (1/5) = 6.
Check: 17 + 28 + 19 + 6 = 70.
Answer: 16–25: 17, 26–40: 28, 41–60: 19, 61+: 6.
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.
Practice Questions
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.
Q3 (Higher): A school has 180 boys and 220 girls. A stratified sample of 50 is required. Calculate how many boys and girls should be sampled. Show that your answer gives the correct total.
Practise stratified sampling calculations free on GCSEMathsAI.
Related Topics
Summary
- Stratified sampling divides a population into subgroups (strata) and samples proportionally from each.
- Use the formula: number from stratum = (stratum size / population size) x total sample size.
- Round to the nearest whole number and check the total matches the required sample size.
- Stratified sampling is more representative than simple random sampling when the population has distinct subgroups.
- Always select randomly within each stratum to avoid bias.
Test your understanding
5 quick MCQs to identify any misconceptions on this topic.
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