Stratified Sampling (Foundation)
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
Type your answer and press Check to be marked straight away, or reveal the answer and mark yourself.
Q1A company has 60 male and 90 female employees (150 total). A stratified sample of 30 employees is taken. How many males should be sampled?Show answer
Answer: 12 (60/150 x 30).
Q2A youth club has 45 members under 13 and 75 members aged 13 to 17 (120 total). A stratified sample of 40 members is needed. How many aged 13 to 17 should be sampled?Show answer
Answer: 25 (75/120 x 40).
Q3A college has 120 Maths students, 80 Science students and 100 English students (300 total). A stratified sample of size 60 is needed. Find the number sampled from each subject.Show answer
Answer: Maths 24, Science 16, English 20 (each group's size divided by 300, then x 60).
Q4A factory has 400 workers: 160 in production, 120 in packing and 120 in admin. A stratified sample of 50 workers is needed. Find how many should be sampled from packing.Show answer
Answer: 15 (120/400 x 50).
Q5A population of 90 people is split into 3 age groups: 30 aged 18 to 30, 40 aged 31 to 50, and 20 aged 51 or over. A stratified sample of 27 is needed. Find how many from the 51-or-over group should be sampled.Show answer
Answer: 6 (20/90 x 27).
Q6A researcher wants a stratified sample of 30 from a population of 300 split into three regions: North (90 people), South (150 people) and East (60 people). She actually samples 9 from the North, 14 from the South and 7 from the East. Show whether her sample is correctly stratified, stating the correct numbers if not.Show answer
Answer: Not correct: North = 9 is right, but South should be 15 (not 14) and East should be 6 (not 7), since each is (region size/300) x 30.
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.
Show mark scheme
Tick each line you got. Your score builds from the marks on the scheme.
Nothing ticked yet - 3 available
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.
Show mark scheme
Tick each line you got. Your score builds from the marks on the scheme.
Nothing ticked yet - 4 available
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.
Show mark scheme
Tick each line you got. Your score builds from the marks on the scheme.
Nothing ticked yet - 2 available
See real GCSE Statistics past-paper questions, with official mark schemes →
Free printable worksheet
Want more practice on paper? Download the stratified sampling (foundation) worksheet pack - 15 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 3 of GCSE Statistics Foundation Workbook 1, the whole course as one free printable PDF.
Next topics
Not quite what you needed?
Tell us what is missing on stratified sampling (foundation), or which topic to write up next. Every request is read, and we reply to every one.
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.