Sampling Methods and Stratification
You cannot always ask everyone. Learn to pick a fair sample: random, systematic and stratified methods, plus the proportional maths examiners love.
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Free interactive practice on the steps that lose marks under exam pressure.
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The whole or a part?
The whole group you want to study is the population. Collecting data from every member is a census. Usually that is too slow, too expensive, or impractical. So you study a sample: a smaller subset chosen to stand in for the whole. The risk is bias: if the sample is not representative, its results will not reflect the population fairly.
The key word
What is a census?
- Collecting data from every member of the population
- Studying a small subset of the population
- Picking every tenth person on a list
- Choosing whoever is nearest to hand
Giving a fair chance
Two methods give everyone a fair chance:
Match each method to its description
- Simple random
- Systematic
- Stratified
- Convenience
- Every member has an equal chance of selection
- Pick every nth member from an ordered list
- Sample each group in proportion to its size
- Use whoever is easiest to reach
Name the method
A researcher lists all 500 members and selects every 25th person. Which method is this?
- Systematic sampling
- Simple random sampling
- Stratified sampling
- Quota sampling
Stratified sampling
Split the population into strata, groups that share a feature such as year groups, then sample each stratum in proportion to its size. To find how many to take from a stratum: (stratum size / population size) x sample size.
Stratified calculation
A school has 1200 students. Year 7 has 300 of them. For a stratified sample of 80, how many students should come from Year 7?
One more
A club has 500 members. The junior section has 150. For a stratified sample of 40, how many members should come from the junior section?
True or false
Select the TWO true statements about sampling.
- Stratified sampling keeps each group in proportion
- A biased sample is not representative of the population
- A census always uses fewer resources than a sample
- Convenience sampling is the least likely to be biased
Quick but risky
Some methods trade fairness for speed: - Convenience (opportunity) sampling uses whoever is easiest to reach. It is quick but often biased. - Quota sampling fills fixed numbers for each group, but the members are chosen non-randomly by the researcher.
Pick the method
Match the situation to the right sampling method.
- You want every student to have an equal chance of being picked. Use...
- You need the sample to match the proportion of each year group. Use...
- You only have time to ask people at the school gate as they pass. This is...
Sampling frame
The whole group is the _____; a subset used to represent it is a _____. Simple random sampling gives everyone an equal chance, while _____ sampling takes each group in proportion. A sample that is not representative is _____.
The big picture
Why is stratified sampling often preferred?
- It keeps each group in proportion, so the sample is representative
- It is always the fastest possible method
- It never needs any calculation
- It only ever uses the nearest people