Populations and sampling · GCSE Statistics

Populations, censuses and samples

The population is everything or everyone you want to find out about. A census collects data from the whole population; a sample collects data from part of it.
A census is accurate and complete, but slow and expensive, and impossible if items are destroyed by testing. A sample is quicker and cheaper, but may not represent the population.
A sampling frame is a list of everyone in the population, such as a school register. Each member is a sampling unit.
Bias means the results lean one way and don't fairly represent the population. Larger, well-chosen samples reduce the effect of chance.

Simple random sampling: every member has an equal chance. Number the sampling frame and use a random number generator, ignoring repeats.
Systematic sampling: choose every kth member from a list, after a random start. k = population size ÷ sample size. For 500 people and a sample of 25, k = 20.
Stratified sampling: split the population into groups (strata), such as year groups, and sample each in proportion to its size. Number from a stratum = stratum size ÷ population size × sample size. Then choose randomly within each stratum.
Cluster sampling: split the population into clusters (such as schools), randomly choose some clusters and sample within them. It is cheaper but may be less representative.

Quota sampling: the interviewer chooses a set number of people from each group, such as 20 men and 20 women. It is quick but not random, so it can be biased.
Convenience (opportunity) sampling: using whoever is easiest to reach. It is quick but very likely to be biased.
Judgement sampling: the researcher picks people they think are representative.

The Petersen method estimates the size of an animal population. Catch and mark a sample (M), release them, then catch a second sample (C) and count how many are marked (R).
Estimate N = M × C ÷ R. If 40 fish are marked, and a later catch of 50 has 10 marked, N = 40 × 50 ÷ 10 = 200.
It assumes the population doesn't change, marks aren't lost, marked animals mix back in and every animal is equally likely to be caught.

Population: Everyone or everything you want to find out about.
Census: Collecting data from the whole population.
Sampling frame: A list of every member of the population.
Simple random sample: A sample where every member has an equal chance of being chosen.
Systematic sample: Choosing every kth member from a list after a random start.
Stratified sample: Sampling each group in proportion to its size.
Quota sample: Choosing a set number from each group, not randomly.
Bias: When results don't fairly represent the population.