Monday, 23 May 2011

Meaningless numbers

Almost every day the media present us with numbers that make very little sense. The Times today has at least two examples.

1) There's a report on the very dry weather that we have apparently been having particularly in my part of England. I read that our rainfall for the first half of May in East Anglia was only 16% of our average rainfall for this period of 15 days, based on records from the year 1977 to the year 2000.

OK, so that 16% is clearly less than average, which is consistent with the state of the lawn in my garden. But is a rainfall as low as this actually significant in some ways? Is it rare? Unless they give me some information about the variation in rainfall, I can't tell whether I should be really worried or quite relaxed about this 16% number.

For all I know, it could be that there have been quite a few years in which the rainfall has been, say, less than 20% of the average and several years in which is its, say more than 200% of the average; in which case, I'll feel quite relaxed about this year's 16%. On the other hand, it could be that the rainfall has never in the past varied more than, say, 10% above or below the average; in which case I am seriously worried by the 16%.

Averages are on their own usually pretty useless bits of information. We also need a measure of spread, like the standard deviation, so we can judge how unlikely is a particular figure. Even a simple indication of the range of rainfall measurements would have helped me to make sense of the 16%.

2) I read also a report on the protests going on in Spain today. This told me that 'Transparency International, a group that monitors state corruption, ranks Spain 30th in the world.' No further explanation of this scale is given. So, I don't even know, for example, whether being 30th means that you are judged to be more corrupt or less corrupt than the country that comes 29th! Does coming 1st on this scale make you the least corrupt country in the world or the most corrupt? On its own, the 30 here is an absolutely meaningless piece of information.

So, there you are – a fairly typical day's sloppiness with numbers in a prestigious national newspaper.

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