Sampling methods

The idea

A sample is chosen to learn about a population. Simple random, systematic and stratified samples are random methods; quota and opportunity samples are not, so they risk bias. A stratified sample takes each group in proportion to its size.

Say what the population and the sampling frame are.
For a stratified sample, each group gets $\frac{\text{group size}}{\text{population}} \times \text{sample size}$ .
For a systematic sample, take every $k$ th item, where $k = \frac{\text{population}}{\text{sample size}}$ , from a random start.

Watch out Describe how the sample is actually chosen before you judge its bias or cost.

See it worked

Worked example

A club has $90$ juniors and $60$ seniors. Describe how to take a stratified sample of $20$ members.

Juniors: $\frac{90}{150} \times 20 = 12$ . Seniors: $\frac{60}{150} \times 20 = 8$ .
Number the juniors $1$ to $90$ and pick $12$ with random numbers.
Do the same for the seniors and pick $8$ .

Answer $12$ juniors and $8$ seniors, each chosen at random within their group

Your turn

Question 1Non-calculator3 marks

A school has $240$ students in Year 12 and $360$ in Year 13. A stratified sample of $50$ students is taken. How many should be from Year 12?

Question 2Non-calculator3 marks

A list of $500$ customers is used to take a systematic sample of $25$ . What is the gap $k$ between chosen customers?

Question 3Non-calculator3 marks

A researcher stands outside a gym at 7 am and asks the first $30$ people who pass. Name the sampling method and give one reason the sample may be biased.

Write your answer, then show the working

People are chosen because they are available, so it is opportunity sampling.
Only people at a gym at 7 am can be chosen.
They are likely to be fitter or keener than the population, so the sample is biased.

Answer An opportunity sample; early gym-goers are unlikely to represent the whole population

In past papers

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