A Panorama of Statistics

7 Index numbers – time travel for averages

‘Everything seems to be getting dearer. I don’t know how I’m going to be able to make ends meet!’ This customer complaint has been heard for years in supermarkets and shopping centres. Well, how much dearer is everything getting? To answer this, you need to know how statisticians measure the general change in prices over time.

There are many alternative ways of defining such a measure; there is no single ‘correct’ way. Choosing the most informative measure in any particular setting needs an understanding of the strengths and weaknesses of each of the alternatives. This Overview shows how the statistician’s choices mushroom out of what may seem, at first, to be a quite uncomplicated problem.

As the options multiply, it’s good to know that the measures are all never far from that most basic of tools for summarising a set of data – the average. They are all, indeed, averages travelling through time.

Yet, unexpected complications arise when defining these measures. For instance, averaging proportional changes in the values of a variable between two points in time should, you might think, be done in the same way as averaging a set of values of that variable at one point in time. It might surprise you, then, that the average that is most appropriate for the former purpose is often not the one you might think of first … or second!

To explore these matters further, let us specify the context a little more precisely. Since it is retail ...