How do you choose a sample that fairly represents a population, and how does each sampling method avoid or introduce bias?
Understand sampling frames and choose between random, systematic, stratified, quota, cluster and convenience sampling, including how each is carried out and the bias each can introduce.
A CCEA GCSE Statistics answer on sampling methods: sampling frames, simple random, systematic, stratified, quota, cluster and convenience sampling, how each is carried out, and the bias each method can introduce.
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What this dot point is asking
A sample must fairly represent the population, or the conclusions of an enquiry are worthless. CCEA expects you to know the main sampling methods, how each is carried out step by step, and the bias each can introduce. The headline calculation is the stratified sample, which appears almost every year, but you must also be able to describe simple random, systematic, quota, cluster and convenience sampling and judge which is suitable in a given situation.
Sampling frames and random sampling
Before sampling, you usually need a sampling frame.
Simple random sampling gives every member of the population an equal chance of selection. You number every member in the sampling frame and use random numbers (from a calculator, a table or a computer) to choose the sample. It is fair and free of bias, but it needs a full sampling frame and can be slow for a large population.
Systematic sampling
Systematic sampling takes members at regular intervals from the sampling frame after a random start.
Stratified sampling
Stratified sampling is the method CCEA tests most. The population is divided into groups (strata) such as year groups or genders, and a sample is taken from each group in proportion to its size.
Within each stratum, members are then chosen by simple random sampling. Stratified sampling makes the sample representative of the structure of the population, so it is more accurate than a simple random sample when the strata differ. Always round sensibly so the parts add to the total sample size.
Quota, cluster and convenience sampling
These methods are quicker but carry more risk of bias.
- Quota sampling: the interviewer fills set quotas (for example, 10 men and 10 women) but chooses who to ask within each quota. It needs no sampling frame and is fast, but the interviewer's choice can introduce bias.
- Cluster sampling: the population is split into clusters (for example, schools or streets), some clusters are chosen at random, and everyone in those clusters is studied. It is cheap for spread-out populations but less representative if clusters differ.
- Convenience (opportunity) sampling: the easiest-to-reach people are used, such as the first people you meet. It is the quickest but the most biased, because it is rarely representative.
Why this matters
Sampling is the bridge between the planning and collecting stages of the enquiry cycle. The stratified calculation is one of the most reliable sources of marks in the whole course, and the ability to name a method and explain its bias appears in both units. Real surveys, opinion polls and quality control all depend on choosing a fair, practical sampling method, and recognising bias in someone else's sample is a key analytical skill the exam rewards.
Exam-style practice questions
Practice questions written in the style of CCEA exam questions on this dot point, with worked answer explainers. The year tag is the paper they imitate, not the source.
CCEA-style4 marksA school has 600 pupils: 360 girls and 240 boys. A stratified sample of 50 is taken by gender. How many girls and boys should be sampled, and explain how you would then select the girls.Show worked answer →
The sampling fraction is .
Girls: . Boys: . Two marks for the two correct numbers (or for and ).
To select the 30 girls, list all 360 girls (the sampling frame), number them to , and use random numbers (from a calculator or table) to pick 30 different girls. One mark for naming a random method, one for applying it within the stratum. Picking the first 30 on the register is not random and loses the mark.
CCEA-style3 marksA researcher stands outside a gym at 9am and interviews the first 20 people who arrive. State the sampling method used and give two reasons why the sample may be biased.Show worked answer →
The method is convenience (opportunity) sampling: the easiest-to-reach people are chosen. One mark.
Two reasons (one mark each): people at a gym are not representative of the wider population (they are likely fitter or more health-conscious); the 9am timing excludes people who work or exercise at other times; and only those willing to stop and talk are included, which adds volunteer bias. Any two distinct, relevant reasons score.
Related dot points
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Sources & how we know this
- CCEA GCSE Statistics (2017) specification (2260) — CCEA (2017)