Stratified sampling

The method

1. Divide the population into strata (groups that do not overlap, such as year groups or shifts).

2. Work out each stratum's share: sample from stratum = (stratum size ÷ population size) × sample size.

3. Round sensibly so the total is still n.

4. Take a simple random sample of that size from each stratum (using a numbered list for each stratum).

Example

A college has 420 boys and 380 girls and wants a sample of 40. Boys: 420/800 × 40 = 21. Girls: 380/800 × 40 = 19. Then choose 21 boys at random from a numbered list of boys, and 19 girls from a list of girls.

With awkward numbers, round so the total is right: strata of 235, 410, 155, 200 and n = 60 give 14.1, 24.6, 9.3, 12, rounded to 14, 25, 9, 12.

Advantages and disadvantages

• Advantages: the sample reflects the structure of the population; gives estimates for each stratum as well as overall; usually more precise than a simple random sample of the same size.
• Disadvantages: the strata must be clearly defined and non-overlapping; a sampling frame is needed for each stratum; proportions may need rounding.

Worked example

A factory has three shifts with 120, 200 and 80 workers. Describe how to take a stratified sample of 50 workers.

1. Total = 400 workers.
2. Shift sizes: 120/400 × 50 = 15, 200/400 × 50 = 25, 80/400 × 50 = 10.
3. For each shift, number the workers and use random numbers to choose that many.

Answer: 15, 25 and 10 workers, each chosen by simple random sampling within its shift.

Check yourself

1. A college has 420 boys and 380 girls. How many boys should be in a stratified sample of 40?
   Show answer

   21. 420/800 × 40 = 21.

2. A factory has shifts of 120, 200, 80 workers. How many workers from the second shift should be in a stratified sample of 50?
   Show answer

   25. 200/400 × 50 = 25.

3. Four strata have sizes 235, 410, 155, 200. A stratified sample of 60 is taken. How many should come from the second stratum?
   Show answer

   25. 410/1000 × 60 = 24.6, which rounds to 25 (and the four rounded values total 60).

4. A stratified sample of 30 contains 12 people from a stratum of 200. Assuming proportional allocation, find the size of the whole population.
   Show answer

   500. 12/30 = 200/N, so N = 200 × 30/12 = 500.

5. Which is an advantage of stratified sampling over simple random sampling?
   • No sampling frame is needed
   • It is quicker because only one group is sampled
   • The sample reflects the proportions of each group in the population
   • It removes the need for random numbers
   Show answer

   The sample reflects the proportions of each group in the population. Proportional allocation guarantees each group is represented in the right proportion.

6. Which is a disadvantage of stratified sampling?
   • The strata must be clearly defined, with a list of each
   • It gives no information about individual groups
   • It is more biased than quota sampling
   • It cannot be used when strata have different sizes
   Show answer

   The strata must be clearly defined, with a list of each. You must be able to place every member in exactly one stratum and have a frame for each.

7. After working out how many to take from each stratum, how are the individuals in each stratum chosen?
   Show answer

   By simple random sampling within each stratum, for example using random numbers on a numbered list of that stratum.. Within each stratum the members are chosen by simple random sampling.

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Sources

• Pearson Edexcel International Advanced Level in Mathematics specification (issue 3), Unit S3

Last updated 8 November 2026. Spotted a mistake? Tell us.