Statisticians often make quite a fuss about the various ways of measuring the average – and that’s because averages used wrongly can give a very misleading impression.
The following story, based on a survey of 2000 drivers, appeared in the Metro newspaper. And it raises quite a lot of questions.
A typical driver will jump 87 red lights, spend 99 days stationary on gridlocked roads and share 680 kisses during a lifetime behind the wheel. Motorists will get stuck in traffic 10,000 times, make 1,992 phone calls and check for emails or texts more than 1,000 times. The average driver will cover 269,296 miles. And the typical adult will have sex 4 times in the car from the age of 17.
The best place to start is with the numbers. How reliable are they? Does anyone really know the number of red lights they jump, or the number of kisses they share? Why is the number of phone calls (1,992) so precise, while the number of times stuck in traffic (10,000) is a round number which sounds like a guess? And how can it possibly be justified to quote the distance travelled by the average driver (269,296 miles) to six significant figures?
Then there are the issues to do with the different types of average. It is not clear whether the figures are means, medians or modes – or a mixture of all three. Perhaps the most common number of red lights to jump is 87, in which case it is the mode. Or perhaps 50% of motorists jump fewer than 87 red lights and 50% jump more, in which case it’s the median. And if the total number of red lights jumped divided by the total number of motorists comes to 87 it’s the mean.
But does this distinction matter? Yes! Look at the last sentence in the story. My guess would be that motorists are divided into two groups: those who do and those who do not. And I would further guess that those who do not are in the majority. So the modal number of times for a motorist to have sex in a car is, I imagine, zero. And then for those who do, both the mean and median will be much higher than 4.
Combining two quite distinct subgroups can give a completely misleading impression. It’s not just a matter of saying what sort of average you are using, but also thinking carefully about whether any sort of average is appropriate at all.
goodStats (communicating the information in numbers)
Some great and some not-so-great stats and thoughts on how bad stats can be made good
Neil Sheldon has taught at The Manchester Grammar School for 40 years. He is a Chartered Statistician and Fellow of the Royal Statistical Society. He has been an RSS Guy Lecturer since 2007. He is also course leader for the Certificate in Teaching Statistics offered by the RSS Centre for Statistical Education