Stratified Sampling
Stratified sampling is a method of choosing a sample so that different groups, or strata, within a population, such as year groups or genders, are represented in the sample in the same proportion as they appear in the whole population. It is used to make sure a sample reflects the structure of the population rather than over-representing or under-representing any one group.
Before you start
Make sure you're comfortable with these topics first:
Method
- Find the total size of the population and the size of each stratum (group) within it.
- Decide on the total sample size required.
- For each stratum, calculate the number to sample using: (stratum size divided by population size) x total sample size.
- Round each calculated number to the nearest whole number, since you cannot select a fraction of a person.
- Within each stratum, choose the actual individuals using simple random sampling.
- Check the numbers sampled from each stratum add up to the required total sample size.
Worked example
A school has 280 Year 10 students and 220 Year 11 students. A stratified sample of 50 students is to be taken, split between the two year groups in proportion to their sizes. Find the number of Year 10 students that should be sampled.
- Find the total number of students: 280 + 220 = 500.
- Find the fraction of the total that are in Year 10: 280/500.
- Multiply this fraction by the sample size: (280/500) x 50 = 28.
- So the final answer is 28 Year 10 students should be sampled (leaving 50 - 28 = 22 Year 11 students).
Practice questions
Try each question, then tap to reveal the answer.
Exam-style questions
Written in the style of a GCSE Statistics exam paper, with a full mark scheme.
A gym has 350 members: 210 women and 140 men. A stratified sample of 25 members is to be taken based on gender. Calculate the number of women that should be included in the sample.
A survey of a school's 900 students is to use a stratified sample of 60 students by year group. The school has 300 students in Key Stage 3, 360 in Key Stage 4 and 240 in Key Stage 5. (a) Calculate the number of Key Stage 4 students that should be sampled. (b) State one reason why stratified sampling might give more reliable results than simple random sampling for this survey.
A company wants a stratified sample of 20 employees from 3 departments: Sales (45 employees), Warehouse (75 employees) and Admin (30 employees), 150 employees in total. Find the number to sample from the Warehouse department.
Free printable worksheet
Want more practice on paper? Download the stratified sampling worksheet pack - 15 pages of exam-style questions with a full mark scheme. No sign-up, no email wall - just the PDF, free for personal and classroom use.
Build a full practice pack.
This topic is one of hundreds in the library - pick the ones a student needs and generate a printable PDF in minutes.