‘What’s the difference between mathematics and statistics?’ Many school students put this question to their teacher, aware that these subjects are related but not clear on what it is, exactly, that distinguishes them. Unravelling this puzzle is generally not made any easier for students by the fact that, in most schools around the world, it is the mathematics department that normally teaches statistics. To these curious but bewildered students, ‘maths’ seems to be defined by the topics that the teacher and the textbook say are maths, and similarly for ‘stats’. So, algebra, calculus, geometry and trigonometry are ‘maths’, while frequency distributions, averages, sampling, the normal distribution, and estimation are ‘stats’. That doesn’t go very far towards providing a convincing answer to our opening question. Anyway, what about probability? Is that ‘maths’ or ‘stats’?

A thoughtful teacher will want to supply a better answer. Surprisingly, in our experience, a better answer is rarely found either in curriculum documents or in textbooks. So let’s see if we can formulate a better answer in a straightforward way.

A constructive start is to ask in what ways statistics problems differ from mathematics problems.

Here is something fairly obvious: statistics problems have a lot to do with getting a view of the variability in data collected from the real world. For example, a statistical problem may present 100 measurements (by different ...

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