A Well-stirred Sample

Why do this problem?

This problem offers students an opportunity to pull together and revise what they have learnt about random variables, probability distributions, sampling and surveying in order to understand the reasoning behind a key decision made by polling companies: how big a sample should they survey?

Possible approach

You could find the report of an online survey, for example on the Ipsos-MORI news page: their poll results state how many people were polled.  Then ask the class to think about how many people they would want to poll to get a reliable result for this question before showing them the poll results and stating how large the sample actually was.  They are likely to be surprised by this, and have questions such as "Surely that's not big enough?", "Won't the results be inaccurate/unreliable?"  Then explain that you will be addressing these questions in this lesson.

You may want to give out the whole problem in one go, and have students working on it at their own pace and getting ready to present their thinking in a plenary.  Alternatively, you may choose to ask the questions one at a time so that it is easier to check that everyone is following.  You could skip the question "What question should we ask in our survey?" as it is not critical for the rest of the problem.

Key questions

• What are the key factors which need to be considered when choosing the sample size for a survey?
• How accurate are the results of a survey?

Possible extension

Occasionally, groups say that they are going to do a "massive survey" to find out what people "really think" about an important issue.  Why might they do this, when the improved accuracy will be so small?