An investigation in which every member of the population is observed or measured.

Give two reasons for using a sample rather than a census.

Cheaper and quicker; and essential if testing destroys the item or the population is infinite.

What is a sampling frame?

A list of all the sampling units in the population.

What is a simple random sample of size n?

One in which every possible sample of n units is equally likely to be chosen.

Describe how to use random numbers to take a simple random sample.

Number the units, generate random numbers of the right length, ignore numbers outside the range and repeats, and continue until n different units are chosen.

Why are repeated random numbers ignored?

Sampling is without replacement: a unit cannot be chosen twice, or the sample would contain fewer than n different units.

How is the sampling interval found in a systematic sample?

k=\frac{N}{n}, the population size divided by the sample size.

How is the first unit chosen in a systematic sample?

At random from the first k units; then every kth unit is taken.

State a disadvantage of systematic sampling.

It is not a simple random sample, and a regular pattern in the list can cause bias.

How many are taken from each stratum in a stratified sample?

\frac{stratum size}{population size}\times n, chosen by simple random sampling.

State one advantage of stratified sampling.

Each stratum is represented in proportion, so the sample is more representative of the population.

State one disadvantage of stratified sampling.

The population must be split into strata with a list for each, which takes time and effort.

What is a quota sample?

A non-random sample in which an interviewer selects people until fixed quotas for each group are filled.

Give one advantage and one disadvantage of quota sampling.

Advantage: no sampling frame needed, quick and cheap. Disadvantage: not random, so there is interviewer or selection bias.

Methods of samplingEdexcel International A Level Further Maths: Flashcards

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What is a census?

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What is a census?: An investigation in which every member of the population is observed or measured.
Give two reasons for using a sample rather than a census.: Cheaper and quicker; and essential if testing destroys the item or the population is infinite.
What is a sampling frame?: A list of all the sampling units in the population.
What is a simple random sample of size $n$ ?: One in which every possible sample of $n$ units is equally likely to be chosen.
Describe how to use random numbers to take a simple random sample.: Number the units, generate random numbers of the right length, ignore numbers outside the range and repeats, and continue until $n$ different units are chosen.
Why are repeated random numbers ignored?: Sampling is without replacement: a unit cannot be chosen twice, or the sample would contain fewer than $n$ different units.
How is the sampling interval found in a systematic sample?: $k=\frac{N}{n}$ , the population size divided by the sample size.
How is the first unit chosen in a systematic sample?: At random from the first $k$ units; then every $k$ th unit is taken.
State a disadvantage of systematic sampling.: It is not a simple random sample, and a regular pattern in the list can cause bias.
How many are taken from each stratum in a stratified sample?: $\frac{\text{stratum size}}{\text{population size}}\times n$ , chosen by simple random sampling.
State one advantage of stratified sampling.: Each stratum is represented in proportion, so the sample is more representative of the population.
State one disadvantage of stratified sampling.: The population must be split into strata with a list for each, which takes time and effort.
What is a quota sample?: A non-random sample in which an interviewer selects people until fixed quotas for each group are filled.
Give one advantage and one disadvantage of quota sampling.: Advantage: no sampling frame needed, quick and cheap. Disadvantage: not random, so there is interviewer or selection bias.

Exam questions on Methods of sampling

A college has 840 students, listed alphabetically on a register. The principal wants the views of 60 of them on a proposed new timetable.
Describe how the principal could select the systematic sample of 60 students from the register.2 marks
A council has 500 houses, numbered 001 to 500. A researcher uses a calculator to generate three-digit random numbers, in this order: 417, 862, 093, 417, 250, 501, 338, and so on. She wants to choose a simple random sample of 40 houses.
Explain why the numbers 862 and 501 are ignored, and why the second 417 is also ignored.2 marks
A company has 480 employees: 192 work in production, 168 in sales and 120 in administration. The managers expect views on a new working-hours policy to differ between the departments. A stratified sample of 40 employees is to be taken.
Calculate the number of employees that should be sampled from each department.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).