Give one advantage and one disadvantage of a census.

Advantage: gives the true population value. Disadvantage: time-consuming and expensive (or impossible, if testing destroys items).

Give one advantage and one disadvantage of a sample.

Advantage: cheaper and quicker. Disadvantage: only an estimate and may not be representative.

How do you select a simple random sample?

Number the members 1 to N, generate random numbers in that range, ignore repeats and select those members.

Interval for a systematic sample of size n from N items?

k=\frac{N}{n}, with a random start in the first interval.

Formula for the number from a stratum?

\frac{stratum size}{population size}\timessample size

Why can systematic sampling be biased?

A pattern in the list that matches the interval can cause the sample to include all or none of a type.

What is quota sampling?

An interviewer fills fixed quotas from each group, choosing individuals non-randomly.

What is opportunity sampling?

Taking whoever is available and willing; quick but likely biased.

Why can different samples lead to different conclusions?

They contain different members, so estimates vary (sampling variability).

Population, sample and sampling techniquesEdexcel A-Level Maths: Flashcards

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Define a population in statistics.

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Define a population in statistics.: The whole set of items or people about which information is wanted.
Define a sample.: A selection of members taken from the population.
Define a census.: An observation of every member of the population.
Give one advantage and one disadvantage of a census.: Advantage: gives the true population value. Disadvantage: time-consuming and expensive (or impossible, if testing destroys items).
Give one advantage and one disadvantage of a sample.: Advantage: cheaper and quicker. Disadvantage: only an estimate and may not be representative.
How do you select a simple random sample?: Number the members $1$ to $N$ , generate random numbers in that range, ignore repeats and select those members.
Interval for a systematic sample of size $n$ from $N$ items?: $k=\frac{N}{n}$ , with a random start in the first interval.
Formula for the number from a stratum?: $\frac{\text{stratum size}}{\text{population size}}\times\text{sample size}$
Why can systematic sampling be biased?: A pattern in the list that matches the interval can cause the sample to include all or none of a type.
What is quota sampling?: An interviewer fills fixed quotas from each group, choosing individuals non-randomly.
What is opportunity sampling?: Taking whoever is available and willing; quick but likely biased.
Why can different samples lead to different conclusions?: They contain different members, so estimates vary (sampling variability).

Exam questions on Population, sample and sampling techniques

A college has 900 students: 540 in Year 12 and 360 in Year 13. The principal wants to find out opinion on a new timetable by asking a sample of 60 students.
State one advantage and one disadvantage of using a sample rather than a census in this investigation.2 marks
A factory produces 2000 bottles each day, numbered 1 to 2000 in order of production. A quality controller takes a systematic sample of 80 bottles, choosing the starting bottle at random from the first interval.
The bottling machine has 25 filling nozzles used in turn, and the 7th nozzle is faulty. Explain why the controller's sample may give a misleading picture of the proportion of faulty bottles.2 marks
A market researcher wants to find out how adults in a town feel about a new bus service. She stands outside the railway station on a Monday morning and interviews the first 20 men and the first 20 women who pass and agree to answer.
Name the sampling method used and give two reasons why the sample may not be representative of adults in the town.3 marks

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Written by the Exaim team, led by Shaun Daswani (Head of Upper Secondary, Improve ME Institute; MSc Financial Mathematics, Imperial College London; BSc, UCL) and Jason Daswani (operational lead, Improve ME Institute; LSE).