# Why averages are not what they used to be

I had a conversation this morning with Jules Birch about the irritating and downright misleading way statistics are often used.

This misuse may be intended or accidental, but the net result is the same. People are fed a distorted picture of reality which influences their view of the world.

More worryingly, the misleading meanings ascribed to these statistics are repeated as facts, because they appear to be supported by hard numbers.

The world becomes more ignorant and more adamant about its ignorance.

What occurred to me as the conversation progressed was that there’s good reason to think abuse of statistics is worse now than for many a year. My thought was not that intentional misuse had necessarily increased. It may have, I don’t know. But, perhaps ironically there are statistical reasons for why statistics are increasingly used inappropriately.

Let’s look at one of the most commonly abused statistical concepts – the “average”.

It’s basically one concept – a measure of central tendency.

The mathematical formulation is easy, isn’t it? You take the total size of a number of objects and divide by the number of objects and there you have it, the average size.

But hang on. That might mean the average UK person is getting taller just because there are more adults than children.

Obviously averages are a bit more complicated and come to think of it we were taught at school that there three averages: mean, median, mode?

Sadly for the mathematically anxious the options don’t end there. Even within the classification of mean, median and mode there are other well-recognised measures of average.

And then, armed with this array of recognised methods of deriving an average we don’t necessarily know (unless we ask) how the data were selected and treated to come up with the average that the statistician or researcher actually thought would best describe the meaning they were looking to convey.

Let’s just accept it. It’s a minefield. I’d suggest by way of example to look at difference in CPI and RPI indexes and the use of arithmetic or geometric means. But that’s too dull for a dinner party.

So consider the recent fuss over the ONS data showing the “average” house price above its peak level when other indexes tell a very different story. Why’s that?

Chris Giles provided a useful service to his FT readers in a recent blog. He highlighted the divergence between mean and median. But as he and Matthew Pointon from Capital Economics agreed in a later twitter chat, it is in fact even more complicated.

If you can get hold of Matthew Pointon’s note on “Why do estimates of the average house price differ?” it is well worth a read.

So averages are tricky.

To my main point. What a particular average, or for that matter any statistical formulation, really means in terms of a policy, to society or to an individual doesn’t necessarily hold over time. However, the meaning people ascribe to a statistic or take from it may hold firm even if it is not appropriate in the circumstances of the time.

The initial point Jules made was sparked by the statement that average rents had fallen in real terms. So let’s look at it quickly.

The newly installed housing minister Kris Hopkins appears to be reacting to data from, I presume, LSL that shows rents rising.

He said: “The latest figures from the Office for National Statistics confirm rents are actually falling in real terms, both in London and across the country.”

Now I don’t want to debate which figures are more accurate or why. That’s not the point I am looking to explore, however fruitful and delightful that exploration might be.

Nor do I wish to dwell on how the new minister last week revealed himself to be poorly equipped in the statistical department when he stated that house building was at a 10-year high.

The issue that struck me here was that he appears to be implying that rents are on average cheaper when we take into account inflation. And an “average” person might quite reasonably take this to imply rents are getting more affordable.

In more normal economic times than today when earnings are going up in line with general inflation, or maybe a bit above, that might be a fairly reasonable thing to suggest and an appropriate measure to use.

But, today, to imply a simple connection between costs in “real terms” and things getting more affordable is just bullshit. Worse still it is dangerous because it appears to be trying to close down important policy discussion.

Anything in “real terms” has a relationship with inflation. Meanwhile, affordability has a very real relationship with how much cash you have. It links to how much one earns, yes, but also to how much other things draw on the purse.

High inflation may mean rising nominal rents are cheaper in “real terms”, but in very real terms for those who see their earnings rise less than inflation, rents can be more expensive and demand a greater proportion of earnings. Meanwhile the call on what cash is available is greater from all those other things that have gone up in price.

So, it is inappropriate to use the notion of “on average in real terms” in this context even though it may have been perfectly reasonable a few years ago.

Now I don’t know the numbers intimately. They don’t particularly matter. Though I suspect he is referring to the ONS experimental data series, which reckons rents have risen 1.2% over the year to August, while, picking at near random a measure of pay growth, the average weekly earnings rose 0.4%.

Not that these figures particularly matter to the argument.

The point I think important is that the meaning we associate with any given and regularly used statistical formulation tends to stick, but the reality of what that statistic actually describes can change quite dramatically.

This is particularly important when we look at growing inequality, short-term and long-term.

Certainly over recent decades people’s incomes and circumstances have become ever more diverse and statistically distributed. We live in a far less equal society.

Ask a statistician and they’ll tell you that means you need to be much more careful in measuring and interpreting changes in central tendencies.

So, whether intentionally of accidentally, it is easier to use an inappropriate measure of average, because averages are not what they used to be.

## 2 thoughts on “Why averages are not what they used to be”

Interesting. The Halifax UK average house price measure stands at close to £170,000, and the ONS average house price measure £247,000. Do you have any thoughts on that, and the implications for price/earnings ratios?

Martin, I think that we have to look at data within ever finer frameworks. It is increasingly difficult to draw sound conclusions from broad data. It is well recognised that we have to treat London differently because it has become so different from the rest of the UK. But I think even within London we have to separate areas to understand what is going on. This is the consequence of increasing heterogeneity and inequality. Previous assumptions do not hold as they once did.