If you are by now thoroughly confused, you are not alone. The average historic return on the volatile equity market is central to calculations of the cost of capital and provision for future pension liabilities. But the figure has been debated for decades. The dispute is less about the underlying data than about the way you make the calculation. The question is often framed as the choice between arithmetic and geometric means. But there is no right or wrong answer. In all problems of this kind, the relevant measure is specific to the particular purpose you have in mind.

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If you can only sell an old computer at a discount to a new model, economists say the new computer is better - that is how statisticians measure the rising quality of computers. Yet it seems absurd to say that a black skirt is of better quality than a burgundy skirt, and to conclude that skirts are getting better every year because new skirts always sell at a premium to the old. But what is the difference between a skirt and a computer?

Only an economist, or a statistician, could ask that question. And yet these arcane details of index number construction make a substantial difference to our estimates of inflation and market returns. Adjustments to pensions and tax allowances and repayment of index-linked debt - issues involving billions of pounds - are affected by their resolution. Who would have thought the difference between arithmetic and geometric means could matter so much?