The problem of averages

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Yesterday’s Western Mail led with a story about how Wales is getting wealthier and Cardiff is booming.  Superficially, it looked like a good news story, but for me it highlighted the problem with measuring averages. 

I have no reason to doubt the accuracy of the report, although I’ll admit that I’ve not pored over the figures in detail.  But I’m prepared to believe that the headline figure – that average wealth in Wales has increased by 3% - is accurate.  But I also suspect that most people in Wales don’t feel 3% better off.  But then, why should they?  The one conclusion doesn’t flow from the other. 

Mathematically speaking, if wealth is evenly spread and 30% of any population become 10% richer while 70% see no increase at all, the average for the whole population is a 3% increase in wealth.  If 10% of the population own 30% of the total wealth, and if that 10% become 10% richer, the average again increases by 3%, although on this basis, 90% of the population see no difference.  And if 1% own 30% of the wealth and that 1% become 10% richer…

Those examples highlight the way in which simply measuring an average can be a very crude approach; it only tells us the overall increase, it tells us nothing about how that increase is shared.

Does it matter?  At one level, no; it’s just an interesting set of figures.  At another level, it’s extremely important.  If governments fall into a mindset of believing that ‘success’ is measured by an overall average, they can end up pursuing policies which enrich a tiny minority and either make no difference to – or even impoverish – the rest. 

That has been part of the problem of the approach of successive UK Governments over many years; and it’s led to a geographical concentration of wealth rather than improvements for all.  But my biggest concern is that the Welsh Government often seems to be falling into the same mindset.  There is no doubt that growth in Cardiff improves the overall Welsh average, but it doesn’t necessarily do anything for the rest of us.  Averages can sometimes be positively dangerous measures.