Statistical sampling

Section S1

Year 1

1 specification point

Notes and three levels of exam-style practice for each registered specification point in this section.

Checked against Edexcel 9MA0 section S1

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.

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In the exam: Formulae booklet provided · calculator allowed in every paper

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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.

Notes

Worked answers & exam appearances →

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Explanation

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.

Tier 1 · Easy

ORIGINAL

A college wants to estimate the weekly study time of all

1840

students. It records the study time of

75

students. State the population and the sample.

(2)

(Total for Question 1 is 2 marks)

Tier 2 · Standard

ORIGINAL

A student surveys the first

40

people leaving the school cafeteria at lunchtime about the quality of all school meals. Identify the sampling method, give two reasons the sample may be biased, and suggest one improvement.

(4)

(Total for Question 1 is 4 marks)

Tier 3 · Hard

ORIGINAL

To estimate support for extending library opening hours, a researcher asks the first

120

people entering the library after

8

pm. Of these,

96

support the proposal. Critique the sampling method and the inference that about

80\%

of all town residents support the proposal.

(5)

(Total for Question 1 is 5 marks)

Your progress and exam materials

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Answer conventions

Follow the wording on the question and its mark scheme. awrt means an appropriately rounded value is accepted; an exact answer must stay as a fraction, surd, logarithm or multiple of π when required, and a rounded decimal may be disallowed. Include requested units and forms. A cso tag protects that accuracy mark, while earlier method marks follow the question-specific dependencies.

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