Stratified sampling GCSE maths means splitting a population into groups (strata), then taking a sample from each group in the same proportion as the whole population. The formula is: sample from stratum = (number in stratum ÷ total population) × overall sample size. It keeps every subgroup fairly represented.
What is stratified sampling?
Stratified sampling is a method of choosing a sample so that different groups within a population — for example, year groups in a school, or age bands in a town — are represented in the sample in roughly the same proportions as they appear in the whole population. Each group is called a stratum (plural: strata).
The alternative would be a simple random sample, where every member of the population has an equal chance of being picked with no attention paid to group sizes. A simple random sample could easily under-represent a smaller stratum by chance. Stratified sampling removes that risk by fixing the proportions in advance.
What is the stratified sample formula?
The number to sample from each stratum is found using:
$$\text{sample from stratum} = \frac{\text{number in stratum}}{\text{total population}} \times \text{overall sample size}$$
This formula is applied separately to every stratum in the population. Because each stratum uses the same fraction (sample size ÷ population), the proportions in the sample always match the proportions in the population.
How do you calculate a stratified sample step by step?
Follow these steps whenever a GCSE question gives you group sizes and asks for a stratified sample:
- Find the total population by adding up the number of people (or items) in every stratum.
- Work out the sampling fraction: overall sample size ÷ total population.
- Multiply the sampling fraction by the size of each stratum to get the number to sample from that group.
- Round each answer to the nearest whole number (you cannot survey a fraction of a person), checking your rounded totals still sum sensibly to the overall sample size.
- State your final answer for each stratum clearly, showing the calculation used.
Worked example: sampling students by year group
A secondary school has 900 students, made up of 320 in Year 10 and 580 in Year 11. A researcher wants a stratified sample of 90 students, split by year group. How many students should be sampled from each year?
Step 1 — total population. 320 + 580 = 900. This matches the number given, so it checks out.
Step 2 — sampling fraction. 90 ÷ 900 = 0.1 (one-tenth of the population is being sampled).
Step 3 — apply the fraction to each stratum.
- Year 10: 320 × 0.1 = 32 students
- Year 11: 580 × 0.1 = 58 students
Step 4 — check. 32 + 58 = 90, which matches the required overall sample size exactly.
The table below summarises the calculation:
| Stratum | Number in stratum | Sampling fraction | Number to sample |
|---|---|---|---|
| Year 10 | 320 | 90/900 = 0.1 | 32 |
| Year 11 | 580 | 90/900 = 0.1 | 58 |
| Total | 900 | — | 90 |
What happens when the numbers do not divide exactly?
Sometimes multiplying the stratum size by the sampling fraction gives a decimal, such as 27.4. GCSE mark schemes expect you to round to the nearest whole number — in this case, 27. Occasionally rounding every stratum independently means the rounded totals do not add up to exactly the overall sample size requested. Examiners generally accept sensible rounding here, but it is worth double-checking your rounded figures against the target total and noting any small discrepancy in your working, since showing your method clearly is usually worth marks even if the final total is one out.
How is stratified sampling different from other sampling methods GCSE statistics covers?
GCSE statistics introduces several sampling methods, and exam questions often ask you to compare them or justify why stratified sampling was chosen.
| Method | How it works | Main advantage |
|---|---|---|
| Simple random sampling | Every member of the population has an equal chance of selection, e.g. numbers drawn from a hat | Free from selection bias |
| Systematic sampling | Every nth member of an ordered list is chosen | Quick and easy to carry out |
| Stratified sampling | Population split into groups; each group sampled in proportion to its size | Ensures every subgroup is fairly represented |
| Quota sampling | Interviewer fills fixed quotas for each group, but chooses who fills them | Fast, but not random within each quota |
Stratified sampling is preferred over simple random sampling whenever a population has clearly defined subgroups of very different sizes, because it guarantees the sample reflects the structure of the population rather than leaving proportions to chance.
Why does stratified sampling matter for real data?
Stratified sampling is used well beyond the classroom — market researchers use it to make sure a survey reflects the age or income mix of a population, and public health studies use it to make sure results are not skewed by over-sampling one demographic. Understanding the method at GCSE also builds the foundation for later statistical work, since the same logic of proportional representation appears in more advanced sampling theory at A-level and beyond.
When answering exam questions, always show the sampling fraction as a clear step in your working, even if you could do the multiplication mentally. Examiners award method marks for showing the fraction, the multiplication for each stratum, and the final rounded answer — so setting your work out exactly as in the worked example above protects your marks even if you make a small arithmetic slip.
Frequently asked questions
What is a stratum in stratified sampling?
A stratum is one of the distinct groups a population is divided into before sampling, such as a year group, age band, or gender category. The plural is strata. Every member of the population must belong to exactly one stratum, and the strata together must cover the whole population with no overlap.
Why use stratified sampling instead of simple random sampling?
Stratified sampling guarantees that every subgroup appears in the sample in proportion to its size in the population, which simple random sampling cannot guarantee — a random sample could by chance include very few people from a small but important group. This makes stratified sampling more reliable when a population has clearly defined subgroups of different sizes that all need fair representation.
Do you always round to the nearest whole number in a stratified sample?
Yes, in GCSE questions you round each stratum's calculated sample size to the nearest whole number, since you cannot sample a fractional person or item. If the rounded values do not sum exactly to the target sample size, show your working clearly — examiners mark the method, and a one-off rounding difference is normal and expected.
Can stratified sampling use more than one characteristic at once?
Yes — a population can be stratified by more than one characteristic simultaneously, for example by year group and gender together, creating smaller sub-strata such as "Year 10 girls" and "Year 10 boys." The same formula applies to each sub-stratum, though GCSE questions usually keep it to a single characteristic to keep the calculation manageable.
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