ST6: Sampling Techniques
Learn about different sampling techniques including random, systematic, stratified, quota, cluster and opportunity sampling, and when to use each method.
Sampling Techniques
Learn about different sampling techniques including random, systematic, stratified, quota, cluster and opportunity sampling, and when to use each method.
Key Fact: A population is the entire group being studied; a sample is a subset of the population.
Key Fact: Sampling is used when studying the whole population is impractical due to time, cost or access.
Key Fact: A random sample gives every member of the population an equal chance of being selected.
Key Fact: Random sampling can be done using random number tables, calculators or computers.
Key Fact: Systematic sampling selects every kth item from a list after a random start (k = population size ÷ sample size).
Key Fact: Stratified sampling divides the population into subgroups (strata) and samples proportionally from each stratum.
Key Fact: The stratified sample size for a stratum = (stratum size ÷ population size) × total sample size.
Key Fact: Quota sampling selects a predetermined number from each group, but the selection within each group is not random.
Key Fact: Cluster sampling divides the population into clusters (e.g. schools), randomly selects some clusters, and studies all members within them.
Key Fact: Opportunity (convenience) sampling uses whoever is available — it is quick but likely to be biased.
Key Fact: Random, systematic and stratified sampling are probability methods; quota, cluster and opportunity are non-probability methods.
Key Fact: A biased sample does not represent the population fairly, leading to unreliable conclusions.
📋 Key Vocabulary and Concepts
For Sampling Techniques, you must know:
- Population: The entire group of individuals or items that the investigation is about.
- Sample: A subset of the population selected for investigation.
- Random sample: A sample where every member of the population has an equal chance of being selected.
- Stratified sample: A sample where the population is divided into strata and a proportional random sample is taken from each stratum.
- Systematic sample: A sample where every kth member is selected from an ordered list after a random start.
- Opportunity sample: A sample chosen from individuals who are conveniently available at the time.
❓ Practice Questions
Q: What is the advantage of a random sample over an opportunity sample?
Q: How do you calculate the sample size for a stratum in stratified sampling?
Q: A school has 200 Year 10 and 300 Year 11 students. A stratified sample of 50 is needed. How many from each year?
Q: What is systematic sampling?
Q: Why is opportunity sampling likely to be biased?
✅ Answers
- A random sample gives every member an equal chance of selection, reducing bias and making the sample more representative of the population.
- Stratum sample size = (stratum size ÷ population size) × total sample size.
- Year 10: (200/500) × 50 = 20; Year 11: (300/500) × 50 = 30.
- Selecting every kth member from an ordered list after choosing a random starting point, where k = population size ÷ sample size.
- Because it only includes people who happen to be available, who may not be representative of the whole population.
🎯 Exam Tips
- Show your working for stratified sample calculations — the formula is frequently examined.
- Round stratified sample sizes to whole numbers and check they sum to the total sample size.
- When evaluating a sampling method, always comment on whether it is likely to be biased.
- Systematic sampling requires an ordered list (sampling frame) — mention this.
- Cluster sampling studies all members of selected clusters — it is different from stratified sampling.
📝 Exam Technique
GCSE Statistics Exam Tips — Sampling Techniques:
1. For Sampling Techniques questions, show every step of your working clearly — method marks count even if the final answer is wrong
2. Check your answer makes sense in context (estimation, units, reasonableness)
3. Use correct mathematical notation and state formulae before substituting values
4. If a Sampling Techniques question asks you to 'prove' or 'show', write a logical chain of reasoning with a conclusion line
5. For problem-solving, identify the topic first, then recall the relevant method
1. For Sampling Techniques questions, show every step of your working clearly — method marks count even if the final answer is wrong
2. Check your answer makes sense in context (estimation, units, reasonableness)
3. Use correct mathematical notation and state formulae before substituting values
4. If a Sampling Techniques question asks you to 'prove' or 'show', write a logical chain of reasoning with a conclusion line
5. For problem-solving, identify the topic first, then recall the relevant method
⚠️ Common Errors
✗ Using the word 'random' to mean 'any' or 'arbitrary' ✓ Random means every member has an equal chance — it requires a proper random method like random numbers.
✗ Not rounding stratified sample sizes to whole numbers ✓ Sample sizes must be whole numbers — round to the nearest integer and check the total adds up.
✗ Confusing stratified and quota sampling ✓ Stratified sampling selects randomly within each stratum; quota sampling does not use random selection within each group.
✗ Forgetting that systematic sampling needs a random start ✓ The starting point must be chosen randomly between 1 and k; otherwise the sample may be biased.
✍️ Model Answer
Full-Mark Response
A school has 120 boys and 180 girls. A stratified sample of 50 students is required. Calculate how many boys and how many girls should be sampled. Explain why stratified sampling is better than simple random sampling here.
Total students = 120 + 180 = 300. Boys: (120 ÷ 300) × 50 = 0.4 × 50 = 20 boys. Girls: (180 ÷ 300) × 50 = 0.6 × 50 = 30 girls. Stratified sampling is better than simple random sampling because it guarantees the sample reflects the gender balance of the population (40% boys, 60% girls). A simple random sample might by chance include too many or too few of one gender, giving a sample that does not represent the population accurately.
📊 AO Deep Dive
Assessment Objective Analysis
AO1 (Knowledge & Understanding): Demonstrate knowledge and understanding of sampling techniques, including data collection, presentation and calculation techniques relevant to Edexcel 1ST0 & AQA 8382.
AO2 (Application): Apply knowledge and understanding of sampling techniques to interpret data, reason statistically and draw conclusions in context.
AO3 (Evaluation): Evaluate statistical methods and conclusions, assessing appropriateness, reliability, validity and bias through the statistical enquiry cycle.
📝 Exam Questions by Topic
- AQA Past Papers - Topic Questions -- AQA
- Edexcel Past Papers - Topic Questions -- Edexcel
- CCEA Past Papers - Topic Questions -- CCEA
🎬 Video Resources
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