Populations, sampling frames, census versus sample, random, systematic, stratified, quota and cluster sampling.

What this dot point is asking

AQA wants you to define a population and a sampling frame, contrast a census with a sample, and describe and apply the main sampling methods: random, systematic, stratified, quota and cluster. You must also be able to calculate a stratified sample, which is one of the most common calculation questions in this module.

Population, sampling frame, census and sample

A census is the most accurate way to learn about a population, but it is expensive, slow and sometimes impossible (you cannot test every light bulb to destruction). A sample is faster and cheaper, and if chosen well it represents the population closely, but it introduces sampling error and the risk of bias. The quality of any sample depends on having a good sampling frame: if the frame misses part of the population, no sampling method can fix the resulting bias.

Random sampling

Random sampling is fair and free of selection bias, which makes it the benchmark other methods are judged against. Its drawbacks are that it needs a complete sampling frame and that, by chance, a random sample can still under-represent a group (it might pick mostly boys from a mixed school).

Systematic sampling

In systematic sampling you choose a starting point at random and then take every $n$th member of the list. If a population of $200$ needs a sample of $20$, the interval is $\frac{200}{20} = 10$, so you pick a random start between $1$ and $10$ and take every $10$th person after it. It is quick and spreads the sample evenly through the list, but it can go wrong if the list has a repeating pattern that matches the interval.

Stratified sampling

Stratified sampling guarantees that each group is represented in proportion to its size, which is why examiners favour it for populations split into obvious groups (year groups, age bands, departments). Within each group the members are then chosen at random.

Quota and cluster sampling

Quota sampling sets a target number to survey in each group (for example $10$ men and $10$ women) and the interviewer fills the quotas; it needs no sampling frame but can be biased by who the interviewer chooses to approach. Cluster sampling divides the population into clusters (for example schools or towns), selects some clusters at random, and surveys everyone in the chosen clusters; it is convenient and cheap when the population is spread out, but the chosen clusters may not represent the whole population.