Stratified Sampling (Higher)
Stratified sampling is a sampling method in which a population is divided into non-overlapping groups, called strata, based on a shared characteristic such as year group or gender, and a random sample is then taken from each stratum in proportion to its size within the population. It is used so that the final sample reflects the structure of the whole population rather than being skewed towards one group.
Before you start
Make sure you're comfortable with these topics first:
Method
- Identify the strata (groups) within the population and find the size of each stratum, together with the total population size.
- Note the total sample size required, which is usually given in the question.
- For each stratum, calculate the number to sample using: number from stratum = (stratum size / total population size) x total sample size.
- Round each calculated number to the nearest whole number, since you cannot survey part of a person, then check the rounded numbers add up sensibly to the required total sample size.
- Within each stratum, select the required number of individuals using a random sampling method, for example random numbers.
- State the conditions needed for stratified sampling to work: the strata must not overlap, and every member of the population must belong to exactly one stratum.
Worked example
A school has 180 Year 10 students and 220 Year 11 students. A stratified sample of 40 students, stratified by year group, is to be taken. Calculate the number of Year 10 students that should be sampled.
- Total population = 180 + 220 = 400.
- Number from Year 10 = (180/400) x 40 = 18.
- Check: number from Year 11 = (220/400) x 40 = 22, and 18 + 22 = 40, which matches the required sample size.
- Final answer: 18 Year 10 students.
Practice questions
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Q1A population has 100 men and 150 women (250 total). A stratified sample of 25 is required. How many women should be sampled?Show answer
Answer: 15 ((150/250) x 25)
Q2A youth club has 60 juniors and 90 seniors (150 total). A stratified sample of 30 is taken. How many juniors are sampled?Show answer
Answer: 12 ((60/150) x 30)
Q3A factory has 3 departments with 40, 60 and 100 workers (200 total). A stratified sample of 50 workers is taken. How many should come from the department of 60 workers?Show answer
Answer: 15 ((60/200) x 50)
Q4A stratified sample of 45 students is taken from a college with 300 Year 12 and 450 Year 13 students. Find how many Year 13 students are sampled.Show answer
Answer: 27 (total 750; (450/750) x 45)
Q5A stratified sample gives 8 people from a stratum of 80, out of a population of 400. What is the total sample size?Show answer
Answer: 40 (sampling fraction = 8/80 = 0.1; 0.1 x 400 = 40)
Q6A school stratifies by year and gender: Year 7 has 60 boys and 50 girls; Year 8 has 55 boys and 65 girls (230 total). A stratified sample of 46 students is required. How many Year 7 girls should be sampled?Show answer
Answer: 10 ((50/230) x 46)
Exam-style questions
Written in the style of a GCSE Statistics exam paper, with a full mark scheme.
A company has 3 branches with 45, 75 and 30 employees (150 total). A stratified sample of 20 employees, proportional to branch size, is required. Calculate the number of employees that should be sampled from (a) the branch with 75 employees and (b) the branch with 30 employees.
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A survey of 500 residents in a town is to be stratified by age group: 0-17 (120 residents), 18-64 (280 residents), 65+ (100 residents). A stratified sample of 60 residents is required, proportional to age group size. (a) Calculate the number sampled from the 65+ age group. (b) Explain one advantage of stratified sampling over simple random sampling in this context.
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State two conditions that must be true about the strata before a population can be sampled using stratified sampling.
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See real GCSE Statistics past-paper questions, with official mark schemes →
Free printable worksheet
Want more practice on paper? Download the stratified sampling (higher) worksheet pack - 19 pages of exam-style questions with a full mark scheme. One email opens every download in this browser for 14 days - no account, no card. Print it for personal and classroom use.
This topic is chapter 1 of GCSE Statistics Higher Workbook 1, the whole course as one free printable PDF.
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