Sampling Methods –

Sampling methods is a topic that bridges Foundation and Higher GCSE Maths and appears across AQA, Edexcel and OCR exam papers. In real life, it is rarely possible to survey every member of a population, so you take a sample instead. The way you choose that sample matters — a biased sample gives misleading results, while a well-chosen sample reflects the population accurately. You need to know the main types of sampling, their advantages and disadvantages, and how to calculate sample sizes for stratified sampling. This guide covers all of this, with clear worked examples, common mistakes to avoid, and practice questions. For a full list of everything you need to revise, see our complete GCSE Maths topics list.

What Is Sampling?

A population is the entire group you want to find information about. A sample is a smaller group selected from the population to collect data from. The goal is for the sample to be representative of the population — meaning the conclusions you draw from the sample also apply to the population.

Why Sample?

• Surveying the entire population is often too expensive, too time-consuming or impractical.
• A well-chosen sample gives reliable results more quickly.
• Results from the sample can be used to make estimates about the whole population.

Bias

A sample is biased if it does not fairly represent the population. For example, surveying only people outside a gym about exercise habits would over-represent active people. To reduce bias:

• Use a random method to select participants.
• Ensure every member of the population has a chance of being selected.
• Use a large enough sample size.

Types of Sampling

Random Sampling

Every member of the population has an equal chance of being selected. You can use:

• Numbered lists and a random number generator.
• Names drawn from a hat.

Advantages: Eliminates selection bias; every member has an equal chance.

Disadvantages: Needs a complete list of the population (a sampling frame); may not represent subgroups proportionally by chance, especially with small samples.

Systematic Sampling

You select every k-th member from an ordered list. For example, every 10th person on a register.

Advantages: Simple to carry out; spreads the sample evenly across the list.

Disadvantages: Requires a sampling frame; can be biased if there is a pattern in the list that matches the sampling interval.

Stratified Sampling

The population is divided into strata (subgroups) — for example, by year group, gender or age range. A proportional number of individuals is then randomly selected from each stratum.

Advantages: Guarantees proportional representation of each subgroup; more accurate than simple random sampling when the population has distinct strata.

Disadvantages: Requires knowledge of the population structure; more complex to organise.

Other Methods (Awareness)

• Convenience (opportunity) sampling — selecting whoever is easiest to reach. Quick but highly biased.
• Quota sampling — interviewers choose set numbers from each category. No need for a sampling frame, but interviewer bias can occur.

Step-by-Step Method

Performing Stratified Sampling

1. Identify the strata (subgroups) in the population.
2. Find the total population size.
3. Decide on the overall sample size.
4. For each stratum, calculate: (stratum size ÷ population size) × sample size.
5. Round to the nearest whole number if necessary (check the total still equals the sample size).
6. Randomly select the required number from each stratum.

Worked Example 1 — Foundation Level

Question: A school has 600 pupils and wants to survey a sample of 60. The table shows the number of pupils in each year group.

Using stratified sampling, how many pupils should be sampled from each year group?

Working:

Sample fraction = 60/600 = 1/10.

• Year 7: 140 × (1/10) = 14
• Year 8: 130 × (1/10) = 13
• Year 9: 120 × (1/10) = 12
• Year 10: 110 × (1/10) = 11
• Year 11: 100 × (1/10) = 10

Check: 14 + 13 + 12 + 11 + 10 = 60 ✓

Worked Example 2 — Higher Level

Question: A factory has 250 workers: 80 in the assembly department, 120 in packaging, and 50 in administration. A stratified sample of 40 is to be taken. (a) Calculate how many workers should be selected from each department. (b) Explain why stratified sampling is more appropriate than random sampling here. (c) The factory manager instead decides to survey the first 40 workers to arrive on Monday morning. Explain why this could be biased.

Working:

(a) Sample fraction = 40/250 = 4/25.

• Assembly: 80 × (4/25) = 320/25 = 12.8 → 13
• Packaging: 120 × (4/25) = 480/25 = 19.2 → 19
• Administration: 50 × (4/25) = 200/25 = 8

Check: 13 + 19 + 8 = 40 ✓

(b) Stratified sampling ensures each department is represented in proportion to its size. Random sampling might, by chance, over-represent one department and under-represent another, especially in a sample of only 40.

(c) The first 40 workers to arrive may have different characteristics to later arrivals — for example, they may live closer to the factory, work in a particular shift pattern, or have different roles. This means the sample would not be representative of all workers, introducing bias.

Common Mistakes

• Confusing sample and population — the population is everyone; the sample is the subset you actually survey.
• Forgetting to round stratified sampling numbers — you cannot sample 12.8 people. Round sensibly and check the total still matches.
• Applying the wrong formula — for stratified sampling, use (stratum ÷ total) × sample size. Do not divide the sample size equally across strata.
• Not explaining bias clearly — saying a sample "might not be fair" is vague. Explain which groups could be over- or under-represented and why.
• Thinking random = haphazard — random sampling requires a systematic method (e.g. random number generator), not just picking people casually.

Exam Tips

1. Know the three main types — random, systematic and stratified. Be ready to describe each and give an advantage and disadvantage.
2. Stratified sampling calculations are very common — learn the formula and practise with different strata sizes. This is straightforward arithmetic that earns guaranteed marks.
3. Bias questions require specific explanations — always say which group is over- or under-represented and link it to the sampling method used.
4. Large samples are more reliable — if asked how to improve a survey, suggest increasing the sample size. This reduces the effect of random variation.
5. Link to data representation — once data is collected, you will likely need to display it using charts or calculate averages. See frequency tables and grouped data and bar charts, pie charts and pictograms.
6. For revision strategies, see our guide on how to revise GCSE Maths.

Practice Questions

Question 1 (Foundation): A company has 200 employees. They want a sample of 50. Describe how they could use random sampling.

Question 2 (Foundation): Explain one advantage and one disadvantage of systematic sampling.

Question 3 (Higher): A club has 60 adults and 40 juniors. A stratified sample of 25 is needed. How many of each should be selected?

Question 4 (Higher): A student surveys her friends about screen time and concludes that the average teenager watches 5 hours of TV per day. Give two reasons why her conclusion may be unreliable.

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Related Topics

• Frequency Tables and Grouped Data
• Mean, Median, Mode and Range
• Bar Charts, Pie Charts and Pictograms
• Scatter Graphs and Correlation

Summary

Sampling methods determine how you select a subset of a population to collect data from. Random sampling gives every member an equal chance of selection. Systematic sampling selects every k-th member from a list. Stratified sampling divides the population into subgroups and selects proportionally from each — use the formula (stratum size ÷ population size) × sample size. To avoid bias, use a proper random method, ensure every member of the population has a chance of being selected, and use a sufficiently large sample. In the exam, be ready to calculate stratified sample sizes, describe sampling methods, and explain why certain approaches may introduce bias. These skills support all data collection and analysis topics across the statistics strand.