A Letter to the Editor 12

In which The Author’s friend gets through the firewall

For a few weeks in 2006, my pal Vicki F. spent some time staying in my house, while she was between flats in Pontypridd. Strictly for the record, we never shared a bed. She slept in the spare room (which for benefit purposes is less than 70 sq ft, and therefore counts as a box room under the Housing Act 1985 s.326).
Anyway, during her brief sojourn in the box room/library, Vix took full advantage of the reading material available to her. Some of it inspired her to write to the Cynon Valley Leader, and her letter was published in the edition dated 2 February 2006.
I nearly fell off my chair laughing when I read your report on ‘average earnings’ standing at £433 a week (Leader, January 5).
This is merely another example of the abuse of the word ‘average’ which is becoming increasing prevalent in all branches of politics and the media.
It all depends which average you use!
A simple example will illustrate this. A sample of 15 measurements produces these results: 6; 5; 7; 6; 5; 6; 6; 6; 8; 4; 5; 7; 6; 7; 3.
The Arithmetic Mean – most people’s understanding of the word average – is the total divided by the sample size, 87/15, which equals 5.8.
The Median is the middle value of the sample, ranked in order, which would be 6.
The Mode is the most frequently occurring measurement in the sample, which would also be 6.
Obviously, with a large range between lowest and highest values, these three different ‘averages’ will tend to vary considerably.
Darrell Huff’s 1954 book How to Lie With Statistics contained a potential manifesto for writers working in this field.
Professor Steve Jones also devised an important example in his book The Language of the Genes.
A medieval village with 100 tenant farmers earning £100 a year, and a lord of the manor making £1,000,000 a year would have a mean income of £1,010,000/101 = £10,000.
This is clearly nonsense – and the same is true for the Cynon Valley.
For every millionaire rock star, there will be a thousand people living on benefits or earning the minimum wage, giving a rather more accurate picture of the ‘average’ income.
Given the generally poor levels of numeracy at all levels of society, it is no wonder that these ridiculous figures go unquestioned.
Is it too much to hope that our elected representatives will call into doubt this so-called ‘average’ and publish the true income figures instead of this convenient fiction?

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