We love averages
They let us know how we are doing, we run our businesses on averages, we judge ourselves against averages, average headlines even sell newspapers:
- £2m: average pay award for JP Morgan’s top staff
- 2013 Weather Summary: Sunnier than average
- Average woman will kiss 15 men and be heartbroken twice before …
(Which link did you click?)
Averages guide us every day.
But they hide as much as they show
If you were born in Switzerland, then on the day of your birth you had an average life expectancy of 83 years. If however you were unlucky enough to be born in Afghanistan the chances were you would only make it to 60. People die younger in Afghanistan… but not 20 years younger. 1 in 5 Afghan children dies before their 5th birthday. If they make it past that, then the Afghans give the Swiss a good run for their money.
According to the Telegraph (the link you didn’t click) the average number of one night stands a UK female has before they find their life partner is 4. The average for a UK Male is 6. I bet that makes your brain hurt a little. Though not as much as mine hurt when I realised that after 45 years I never met one of the women who helped pull my male colleagues average up — on reflection it is worse, I probably have, she just never decided to let me know.
Not all averages are politically acceptable – half of the UK population is below average intelligence (that sounds so much worse when applied to school children). Now the question isn’t are you below average, but how far?
And if the last statistic made you feel uncomfortable the average number of legs a US adult has is about 1.9975. Chances are you outclass the average American — if only in one way.
So never take an average at face value
Look at the variation as well.
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Read another opinion
Image by aboveaverage
Or, another way to illustrate the conundrum . . .
James, the book I’m reading describes the challenge of interpreting averages another way. To paraphrase: a man with his head in a hot oven and feet in the icebox has an average body temperature of 98.6. That still doesn’t yield much information about his condition.
Thanks Andrew, what was the name of the book?
Hi James,
Just refer to the book the flaw of averages by savage. The ideal pocket book for all managers. Likewise, the dangers of frequentists stats so beloved of six sigma and lean sigma so called experts have to be socialised. This coupled with the dangers of reductionist methods such as pdca / dmaic and solution driven approaches so beloved of deminites the instant six sigma gurus
Thanks Geoff, I will have a look. I take it you are not a big fan of “deminites the instant six sigma gurus”?
James
It is a well known fact that the average driver’s skills are above average.
Particularly if they are mine
Thanks for the comment
James
Something’s that count can’t be counted, and something’s that can be counted don’t count. Albert E. —.
When people synergise instead of compromise; 1 and 1, can make 11.
Excellent article. I am trying to find the right way to describe the behaviour. The issue is that people want a single easy to interpret answer to describe something. We do not want to have to understand the nuances of everything, so when someone says the average…
Other easy to misinterpret items. Just about every pie chart out there. A little unfair but comparing pie charts to pie charts is bad. Its related to comparing percentage figures. Comparing percentages are a great way of confounding the situation.
I remember a certain UK politician who loves spouting their percentages. The claim was the percentage trade for the UK to Europe had decreased, something like 38% to 35% cannot remember the exact claim so forgive me for that). So the statement was we should realise the rest of the world is out there as well. I was a bit confused becuase where is that other 65% going then.
So I had a look at the numbers, in general it appeared as if the overall exports from the UK across the years in question had gone up. It had increased in absolute values with Europe, but it had also more importantly increased by a larger amount to countries like China.
Of course I couldnt quite get to the same figures as the unmentioned politician was referring to, but no surprise there.
Other great examples, averages. Average can refer to Mean, Median or Mode.
More than 50% of people earn less than the average if we talk about the Mean… but not if we talk about the Median.
Take a look at politicians expense claims, the Guardian has the data available. Is it fair to talk about the average expense claims? The Mean and Median are very different for this data.
The language we use sometimes in stats really doesnt help us.
James,
Averages are often misleading. Using the fuller set of mean, median, mode and the range would be more useful but they don’t lend themselves to headlines, soundbites or pithy one-liners.
Perhaps, that’s the problem?
Adrian
I think you may well be very right Adrian.
Hello James
I say that ‘averages’ are for the lazy. They speak to our need-desire for simplicity. They allow us to convert a world that is squiggly into one that is square. They allow us to sweep aside and pretend that the world is uniform. And to keep is in a truthful relationship with the world as it is, it is necessary to always report and be mindful of variation. There is always variation. And the smallest amount of variation can make a big impact – that is the central insight of chaos theory, as I understand it.
All the best