The law of averages

This weekend, we learnt that the average person spends just 11 minutes a day reading fiction, compared with more than three hours watching TV. It's an arresting statistic, but what do these facts really tell us about ourselves, asks Robert Hanks
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The Independent Online

Averages surround us – hemming us in, or swaddling us. Every day the news is peppered with averages: waiting times for an operation on the NHS, waiting times for trains, house prices, the Dow Jones industrial, batting averages, bowling averages, temperature for the time of year. Just this week we learnt that the average adult in Britain spends a mere 77 minutes a week reading fiction, compared with more than 23 hours a week watching television. These averages may or may not matter to us. Less frequently, we hear about other sorts of averages, which play a part in shaping our sense of the world we live in, and how well we measure up or fit in: average earnings, average weight, average duration of marriage, number of children, time spent doing housework or watching TV.

Averages surround us – hemming us in, or swaddling us. Every day the news is peppered with averages: waiting times for an operation on the NHS, waiting times for trains, house prices, the Dow Jones industrial, batting averages, bowling averages, temperature for the time of year. Just this week we learnt that the average adult in Britain spends a mere 77 minutes a week reading fiction, compared with more than 23 hours a week watching television. These averages may or may not matter to us. Less frequently, we hear about other sorts of averages, which play a part in shaping our sense of the world we live in, and how well we measure up or fit in: average earnings, average weight, average duration of marriage, number of children, time spent doing housework or watching TV.

Some averages you will never know about, though you will notice their effects: your insurance company will know how often, on average, a home like yours gets burgled, and will make you pay accordingly. And then there are the more intimate kinds of average that occasionally press in on our lives: the average time it takes for someone of your age to conceive a child; the average life expectancy for someone with your condition...

The Chambers Dictionary is cautious on the etymology of the word "average", suggesting only that the reader should "Cf Fr avarie, avaria duty on goods, from Ar awariyah damaged goods". The derivation seems appropriate, because averages, in the wrong hands, can be dangerous, untrustworthy things.

To begin with, it's important to know that there are different sorts of averages, and which sort you use depends on the situation and what information you're trying to draw from it. The most common sort is the mean, which is what you get if you add up a lot of numbers and then share them out: say you have five children, aged three, five, six, seven and seven; you get the mean age by adding all their ages together (which gives you 28) and dividing by five (which gives you 5.6). The median is the value in the middle: line up the children in order of age, and the one in the middle is the median child – in this case, the median age is six. The other sort of average is the mode, the most common value – in this case, seven.

In general, when you are looking at a large number of values, mean, mode and median will not be too far apart – clumped together somewhere in the middle. But the differences can be significant. Take the average income: a politician who wants to talk up the nation's prosperity would be well advised to talk in terms of the mean rather than the median, because a single multi-millionaire will outweigh hundreds of low earners, bumping up the average considerably. A politician who wants to make out that the nation is going to hell in a hand-basket may pick on the median, because Bill Gates's trillions at the top would be cancelled out by a lone beggar at the bottom. More significant in electoral terms may be the mode – what most people earn, how prosperous they feel.

Averages can be bad in another way: the word "average" is closely associated in our minds with dullness, boredom. If people tell you that you are average looking or averagely intelligent, they may be offering you reassurance, but they are unlikely to be paying you a compliment. If they tell you that you are very average, they probably intend a deliberate insult: to be very average is not merely to be part of the mass; it is to be submerged in it, unexceptional, forgettable, anonymous. The language of averages doesn't help – "median" has echoes of "mediocrity"; "mean" can also mean stingy or base. On the other hand, "mode" isn't so bad – I wouldn't object to being modish.

What we like to believe is that we are better than the average; and much of the time, we kid ourselves that this is so. Remember Garrison Keillor's characterisation of the people of Lake Wobegon: "All the men are handsome, all the women are beautiful, and all the children are above average." How many parents proudly announce that their own children sit bang in the middle? One statistic that crops up frequently – though I have not been able to find any convincing authority for it – is that 95 per cent of drivers regard themselves as better than average. (Actually, this is just possible if driving ability is defined according to some scoring system, and the gulf between the scores of the bottom 5 per cent and the top 95 per cent is wide enough. But it is not very likely.)

Of course, averageness has its virtues: there is such a thing as a happy medium. Throughout history, there have been people prepared to stand up for the middle way. Aristotle defined all the virtues in terms of the golden mean, "equidistant from the extremes": Courage sits between Rashness and Cowardice; "Magnificence" involves steering between Vulgarity and Pettiness; Wittiness is halfway from Buffoonery to Boorishness. In the 18th century, the poet David Mallet, in imitation of Horace, offered this prayer:

"O grant me, Heaven, a middle state,
Neither too humble nor too great;
More than enough, for nature's ends,
With something left to treat my friends."

The sentiment might carry more weight if the versification were not so thoroughly average.

There are times when it is a comfort to know that you're average – ordinary, not a freak. When I was at school, they made a point in sex-education lessons of telling us teenage boys in confidence-boosting, soothing tones about average penis size. More recently, Marks & Spencer have tried to make women feel more comfortable with their curves – did you know that in the 1950s the average woman measured 32-20-32, while today she is 36-28-38? This seems important given that Top Santé Health & Beauty magazine says the average woman has tried to diet at least six times.

Bear in mind, though, that such reassurance often has ulterior motives: one recent survey found that the average British male spends £576 annually on cosmetics, which sounds like a lot, especially given that another survey discovered that the average British woman only spends £538.20. If male grooming comes to seem more normal, more acceptable, this may be good news for British women; it is unarguably good news for British cosmetics firms.

And it is almost always a mistake to think that an average is telling you something significant. By itself, it means nothing. In 1998-99, according to the National Office of Statistics, married men had the highest gross weekly individual income (£293); among women, those who were cohabiting had the highest income (£185), whereas those who were married had the lowest (£103). On the face of it, that seems to say that marriage is financially a good deal for men, a bad one for women. But it is entirely possible to put an opposite gloss on the figures: what the figures reflect is married women chucking in their jobs, and their husbands working harder to support them. Conversely, when Barclaycard tells us that men buy reconciliation presents for partners seven times a year, while women do so three times, does that reflect greater male generosity, larger male incomes, or a masculine talent for giving offence?

Over-reliance on averages can have grave effects. Take the case of Professor Geoffrey Sampson, the Tory local councillor who resigned his seat last week after it emerged that his personal website said that there was "nothing wrong" with being racist. Professor Sampson had written: "There is overwhelming scientific evidence that races differ to some extent in their average intelligence levels – yellow-skinned Orientals tend to be rather brighter than whites, Negroes tend to be rather less bright." This statement is unhelpful on several counts: it avoids the complicated questions of how we define "race" or "intelligence"; but it also overlooks the generally agreed fact that variations between racial groups are dwarfed by variations within them – draw all the conclusions you like about the intelligence of Negroes and yellow-skinned Orientals, but remember, it's a mistake to think that your conclusions have any relevance to individual cases.

The most important thing to remember about averages is that they aren't real: the stereotypical household with 2.4 children never existed, for obvious reasons (these days, the stereotypical household only has 1.66 children, which is why we need all the immigrants we can get, if we're going to keep the economy ticking over). But we still tend to regard means and medians as some sort of essence, a Platonic reality underlying ephemeral, mortal things.

The evolutionary biologist Stephen Jay Gould offered a cautionary tale about this tendency, based on his own experience, in an essay called "The Median isn't the Message". In July 1982, he was diagnosed as suffering from abdominal mesothelioma, a rare and almost always fatal form of cancer, usually contracted from exposure to asbestos. Ignoring his doctor's advice not to bother with the literature on his condition, Gould looked it up and found that the median mortality was eight months: that is, eight months after diagnosis, half of all patients had died. Most people would interpret this as meaning: in eight months, I will probably be dead. But Gould, being a trained scientist, reasoned that if this was the median, that meant that half of sufferers would live longer; he set about working out his chances of being in that half. It turned out that his age and the fact that he had been diagnosed early meant that he stood a very good chance. Then he set about finding out how much longer he might go on. It turned out that some – a very few – survived for years.

Gould went on to try an experimental treatment. He died of cancer last Monday, almost 20 years after the initial diagnosis. It's tempting to say the averages caught up with him, and in one sense that's true: on average, you're going to die. But it would be truer to say that Gould beat the averages, comprehensively. In the end, that's the only sensible way to deal with them.

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