S1 Statistical sampling — notes on one page

Every Edexcel A-level Maths 9MA0 specification point in S1, read straight through: 1 point with definitions, explanations, mark-scheme wording and worked examples. Practice questions are in the printable question pack.

Checked against Edexcel 9MA0 section S1. Review basis: the qualification registry sourced from the Pearson Edexcel Level 3 Advanced GCE in Mathematics (9MA0) specification; registry verification recorded 11 July 2026.

How this checking works

S1.1 · Understand and use the terms 'population' and 'sample'; use samples to make informal inferences about the population; use sampling techniques including simple random and opportunity sampling; select or critique techniques in context.

The population is the complete set about which an inference is required; a sample is the subset from which data are actually collected.
A simple random sample gives every member an equal selection chance; systematic sampling uses a fixed interval after a random start, while stratified sampling preserves chosen population proportions.
Quota sampling fills category targets without random selection, whereas opportunity sampling uses whoever is available; both are quick but vulnerable to selection bias.
When drawing an informal inference, discuss representativeness, sampling frame, non-response and sample size; a large biased sample is not automatically reliable.
A census avoids sampling variation but may be slow, costly or impractical; a sample is faster and cheaper but may be unrepresentative, and different valid samples can lead to different conclusions.

Worked example

A theatre has a numbered list of its $1260$ members. Describe how to select a simple random sample of $60$ members.

1.Use the complete membership list as the sampling frame.
2.Assign each member one unique number, generate numbers uniformly from the full range, and ignore repeats until $60$ different labels have been obtained.
3.This gives each member an equal chance of selection.

Answer: Label the members $1$ to $1260$ .; Use a random-number generator to obtain $60$ distinct integers from $1$ to $1260$ .; Select the members with those labels.

Common mistakes

Don't use an opportunity sample from one class and generalise its result to the whole school.
Don't select numbers with replacement or from the wrong range, so some members are duplicated or impossible.

Exam tip. For a simple random sample, specify the numbered sampling frame, a random generator and rejection of repeats or out-of-range values.