Stratified sampling

Objective. Calculate proportional sample sizes and handle rounding.

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Learn: the key idea

Stratified sampling chooses a sample so each subgroup (stratum) of a population is represented in proportion to its size within the whole population. To find how many to sample from a group, use (group size ÷ total population) × total sample size, then round sensibly to a whole number. This keeps the sample's structure matching the population's structure, improving reliability of any conclusions drawn. For a school of 400 students with 100 in Year 11 and a sample of size 40 needed overall, Year 11's share is (100/400) × 40 = 10. Rounding issues should be checked so the stratified amounts still sum close to the required total.

Worked example

A college has 250 students, of whom 90 study science. A stratified sample of 50 students is taken. How many science students should be sampled?

1 $Use (group size \div total) \times sample size$
2 $Fraction studying science = 90/250$
3 $Number sampled = (90/250) \times 50$
4 $Number sampled = 18$

Answer: 18 students

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Common mistake. A common mistake is sampling equal numbers from every stratum regardless of its size, which overrepresents small groups and underrepresents large ones, breaking the proportional structure stratified sampling requires.

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