Stratified Sampling
Understand Stratified Sampling for GCSE Statistics with this free worksheet and full mark scheme — Foundation and Higher exam-style questions with worked answers for AQA and Edexcel. Stratified sampling splits the population into groups (strata) and samples each in proportion to its size.
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Topic overview
Stratified sampling divides the population into groups called strata, then samples from each in proportion to its size.
The number to take from each stratum is calculated as \(\frac{\text{stratum size}}{\text{population size}} \times \text{sample size}\). Within each stratum, members are then selected using simple random sampling.
For a school with 300 boys and 200 girls taking a sample of 50, the boys contribute \(\frac{300}{500} \times 50 = 30\) and the girls \(\frac{200}{500} \times 50 = 20\). The advantage is that every subgroup is represented in proportion, giving a more representative sample. The disadvantage is that the strata must be known and clearly defined.
Revision notes
The calculation
Number from each stratum \(= \frac{\text{stratum size}}{\text{population size}} \times \text{sample size}\).
Calculate this for each stratum separately. The results should add up to the total sample size, which provides a useful check.
Rounding
Results are usually rounded to the nearest whole number, since you cannot sample part of a person.
If rounding makes the total differ from the required sample size, adjust the largest stratum by one. Always check the totals add up.
Advantages and disadvantages
Advantage: every subgroup is represented in proportion to its size, giving a more representative sample than simple random sampling.
Disadvantage: the strata must be known and clearly defined, and the calculation takes more time. A sampling frame for each stratum is needed.
Key points
- Stratified sampling divides the population into strata.
- Each stratum is sampled in proportion to its size.
- Number = (stratum ÷ population) × sample size.
- Simple random sampling is used within each stratum.
- The stratum results should total the sample size.
- Every subgroup is represented proportionally.
Worked examples
Example 1
A club has 240 adults and 160 children. A stratified sample of 50 is taken. Work out how many adults should be in the sample. [3 marks]
Working
Example 2
Explain one advantage of stratified sampling over simple random sampling. [2 marks]
Working
Example 3
A stratified sample gives 12.4 people from one stratum. State what should be done. [1 mark]
Working
Common mistakes
Forgetting to find the population total first.
The proportion needs the total, not just the stratum sizes.
Using the stratum size as the answer.
It must be multiplied by the fraction of the sample.
Not checking the strata totals add up.
They should sum to the required sample size.
Leaving a decimal answer.
Round to a whole number, since people cannot be sampled in parts.
Exam tips
- Find the population total as your first step.
- Show the fraction clearly before multiplying.
- Check the strata add to the sample size.
- Round to whole numbers and state that you have done so.
Key terms
- Stratified sampling
- Sampling each subgroup in proportion to its size.
- Stratum
- A group within the population, such as a year group.
- Proportion
- The fraction of the population in each stratum.
- Representative
- Reflecting the composition of the population.
Related topics
Written and reviewed against the current AQA and Edexcel specifications. Spotted an error? Let us know.