What is a sampling frame?

The list of all members of the population from which the sample is chosen.

Define a simple random sample.

Every member of the population has the same chance of being chosen, and every possible group of the required size is equally likely.

How do you take a simple random sample?

Number the population, generate random numbers, select the matching members, rejecting repeats and out-of-range numbers until the sample is full.

Give one advantage of simple random sampling.

It avoids bias in the selection, because every member has an equal chance.

Give one disadvantage of simple random sampling.

It needs a complete list of the population and may be slow or costly; a random sample can still be unrepresentative by chance.

What is opportunity sampling?

Choosing the members of the population who are conveniently available at the time.

Give one advantage and one disadvantage of opportunity sampling.

Quick, cheap and needs no list; but not every member can be chosen, so it is often biased.

Why do different samples give different estimates?

Sampling variation: each sample contains different members of the population.

Why might a census not be used?

It can be too costly or slow, or the testing may destroy the items.

What does it mean to make an informal inference from a sample?

Use the sample result as an estimate of the population value, not as an exact value.

SamplingAQA A-Level Maths: Flashcards

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What is a population?

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What is a population?: The whole group about which conclusions are to be drawn.
What is a sample?: A selection of members of the population that is actually observed.
What is a census?: An observation of every member of the population.
What is a sampling frame?: The list of all members of the population from which the sample is chosen.
Define a simple random sample.: Every member of the population has the same chance of being chosen, and every possible group of the required size is equally likely.
How do you take a simple random sample?: Number the population, generate random numbers, select the matching members, rejecting repeats and out-of-range numbers until the sample is full.
Give one advantage of simple random sampling.: It avoids bias in the selection, because every member has an equal chance.
Give one disadvantage of simple random sampling.: It needs a complete list of the population and may be slow or costly; a random sample can still be unrepresentative by chance.
What is opportunity sampling?: Choosing the members of the population who are conveniently available at the time.
Give one advantage and one disadvantage of opportunity sampling.: Quick, cheap and needs no list; but not every member can be chosen, so it is often biased.
Why do different samples give different estimates?: Sampling variation: each sample contains different members of the population.
Why might a census not be used?: It can be too costly or slow, or the testing may destroy the items.
What does it mean to make an informal inference from a sample?: Use the sample result as an estimate of the population value, not as an exact value.

Exam questions on Sampling

A researcher wants to estimate the mean time that students at a sixth-form college of 640 students take to travel to college. One morning she stands at the main entrance and asks the first 30 students who arrive.
Explain why the mean travel time of her sample may give a misleading estimate of the mean for the whole college.2 marks
A teacher has an alphabetical list of the 90 students in Year 12. She numbers them 01 to 90 and uses random numbers to choose a sample of 5 students.
Her sample of 5 contains 4 boys. The teacher concludes that most Year 12 students are boys. Explain why this conclusion is not justified.2 marks
A town has 24 000 registered voters. A polling company wants to estimate the proportion who support a new bypass. Method X: phone 200 voters chosen by applying random numbers to the electoral register. Method Y: ask the first 200 people who walk past a shopping centre on a Saturday morning.
Compare the two methods, and state which is more likely to give a representative sample of voters.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).