Maths - Investigating inflation
We have had 90 years of the BBC. It is certainly a venerable institution that has done a lot for news and period drama. But what, you might ask, has it ever done for maths?
Any answer would certainly include Radio 4's excellent More or Less, which tackles topical statistical problems with admirable brio and perception. But can the mathematics here be easily transferred to lessons? Most certainly.
More or Less gave us this example: our basket of goods contains a shirt costing #163;20 and a blouse costing #163;25. Over the course of the year, the shirt goes up to #163;25 (a 25% increase), while the blouse drops to #163;20 (a drop of 20%). Using one method of calculating inflation, we can say that inflation overall is the average of these, or (25 + (-20))2 = 2.5%. So far, so good.
Now, suppose that in the next year, the price of the shirt drops back to #163;20, while the price of the blouse rises back to #163;25. What is our inflation percentage for this year? Once again, we have ((-20) + 25)2 = 2.5%, so over the two years inflation would seem to be steady at 2.5%. But the prices of our clothing items, taken over the two years, are unchanged, so surely any sensible measure of inflation must give us 0%.
This looks like a magic trick. The calculations are irrefutable, yet the end result is counter-intuitive. The really scary thing is that we can then reveal that the retail price index (RPI) is calculated in this kind of way. So, as we can see from our example, it is biased upwards, sometimes dramatically so. As More or Less presenter Tim Harford succinctly puts it, "What if the RPI number is tosh?" At various times, benefits and pensions have been based, at least in part, on RPI. Who can guess how much this has cost the nation? The programme has highlighted a simple piece of maths that was underestimated by economists and has had huge financial implications. Hopefully this will leave students gasping - and more ready to question the figures they are handed in their own financial lives.
They could then go on to consider what system might be better. Type "list of price index formulas" into Wikipedia and you get a range of 12 possible measures for inflation, which your students can compare. What about the consumer price index (CPI)? This uses the geometric mean (which for our basket over two years deals with the bias problem). The fact that the geometric mean is guaranteed to be less than the arithmetic mean shows why governments tend to prefer the CPI measure.
Jonny Griffiths teaches maths at a sixth-form college
Introduce students to inflation with a PowerPoint from AFJ88.
Revise inflation terminology using Howdrey's bingo game.