Populations and samples, the advantages and limitations of sampling, simple random sampling, systematic, stratified, quota and opportunity sampling, and the importance of the large data set.

What this dot point is asking

AQA wants you to understand the difference between a population and a sample, judge the advantages and limitations of sampling, describe and apply the main sampling methods, and appreciate why the qualification uses a large data set to ground statistics in real contexts. Sampling questions reward precise vocabulary and clear, replicable descriptions of method.

Populations and samples

A census is fully accurate but expensive, time-consuming and sometimes destructive (you cannot test every match to destruction and still sell them). A sample is cheaper and faster but introduces sampling error. A good sample is representative, large enough to be reliable, and selected by a method that avoids systematic bias.

Random methods

In simple random sampling every member, and indeed every possible sample of the chosen size, has an equal chance of selection. You typically number the population and use random numbers (ignoring repeats). It avoids selection bias but requires a complete, accurate sampling frame, which is not always available.

Systematic sampling lists the population and selects every $k$th member after a random start, where $k$ is the population size divided by the sample size. It is simple to administer but can interact badly with hidden periodic patterns in the list, producing bias if the period matches $k$.

Non-random methods

Quota sampling fills set numbers from each group but lets the interviewer choose who fills the quota, which is fast but open to interviewer bias. Opportunity (convenience) sampling uses whoever or whatever is available, which is the easiest method but typically the least representative.

The large data set

AQA provides a large real data set that you should explore during the course, so you can clean data, spot patterns, compute summary statistics, and answer questions set in its realistic context in the exam. Familiarity with its variables, units and quirks (such as missing values) is examined directly.

Bias and how methods control it

Bias is any systematic tendency for a sample to misrepresent the population. It is not the same as the random sampling error that shrinks as the sample grows; bias does not go away with a larger sample if the method itself is flawed. Selection bias arises when some members are more likely to be chosen (an opportunity sample of shoppers in one street), non-response bias when those who reply differ from those who do not, and the periodicity problem in systematic sampling is another form of bias.

Random methods (simple random and, within strata, stratified) control bias because selection does not depend on any characteristic of the member. Non-random methods (quota, opportunity) trade that protection for speed and low cost. When an exam asks you to "comment on" or "criticise" a sampling method, name the specific source of bias and say which group is likely over- or under-represented, rather than writing "it might be biased".