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A teacher wants to know what share of the 900 students in her school eat breakfast…

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Try it on paper first. A hint, the key idea and the worked solution are here when you need them.

A teacher wants to know what share of the 900 students in her school eat breakfast. Five pupils each take their own random sample of 60 students. They find these percentages: $42\%$ , $35\%$ , $47\%$ , $38\%$ and $45\%$ . Find the mean of the five statistics and their range. One pupil says that four of the five samples must be wrong, because only one answer can be true. Explain why the pupil is mistaken.

Need a reminder? The key ideaShow

A parameter describes the whole population and is usually unknown. A statistic is worked out from a sample and is used as its estimate. If a fair sample of $n$ has $k$ with a property, $\hat p = \dfrac{k}{n}$ , and the estimate for a population of $N$ is $N \times \dfrac{k}{n}$ .

The worked solution

Have you tried it?

Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.

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