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21st May 2013

## GCSE Maths

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# Sampling

"Sampling" basically means selecting people/objects from a "population" in order to test the population for something. For example, we might want to find out how people are going to vote at the next election. Obviously we can't ask everyone in the country, so we ask a sample.

When considering a particular population it is usually advisable to choose a sample in such a way that everyone is represented. This is not easy and requires careful thought about sample size and composition. Often questionnaires are devised to identify the required information. These need to be idiot proof, so questions need to cover all alternatives and give little scope for variation.

#### Example question

A bus company attempted to estimate the number of people who travel on local buses in a certain town. They telephoned 100 people in the town one evening and asked 'Have you travelled by bus in the last week?'
Nineteen people said 'Yes'. The bus company concluded that 19% of the town's population travel on local buses.
Give 3 criticisms of this method of estimation.

In answering this question, there are no 3 correct answers. As long as what you say is plausible and sensible, you should get the marks. For example, you might say:

• 100 people in a large town is not a large enough proportion of the population to give a good sample.

• People who travel on local buses once a fortnight may have said no to the question. They nevertheless travel on local buses.

• On the evening that the sample was carried out, anybody travelling by bus would be out.