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Dec 2000 Journal

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SCIENCE NOTEBOOK

Averages

In September, various news media carried stories about the increase in the number of pensioners living on low incomes – “below the poverty line”. How was this line defined? Some papers (The Independent, The Times) took it as 50% of the mean income of all pensioners, others (Daily Mail, Daily Telegraph) as 60% of the mean income, while Radio 4 on Today said poverty was defined as below 60% of median income. This agrees with the adoption of 60% of median income as the fairest threshold indicator of low incomes by European statisticians.

Just what sort of averages are mean and median? Consider as an example a group of five pensioners. Suppose one lucky pensioner get £33,000 a year while the others have annual incomes of £6,000, £5,000, £4,000 and £2,000, respectively. Their mean income (ie the arithmetic average) is £10,000, obtained by dividing the total income of the group by five. This is clearly an unfair representation of the group’s incomes since it is greatly biased by the very high income of just one person. A fairer measure of the average is the median income, the figure in the middle when the group’s incomes are ranked in order, in this case £5,000. Only one person in the group receives less than 60% of the median, ie less than £3,000.

The report of the Department of Social Security on which the media were commenting (Opportunity for All. Second Annual Report 2000. Cm 4865) gave the following figures for the percentages of pensioners living on low incomes in 1998/99:

Below 50% of mean income 25% - Below 60% of mean income 42% - Below 50% of median income 12% - Below 60% of median income 23%. As in the example above, the mean incomes were larger than the median incomes. More pensioners therefore had incomes below 50% (or 60%) of the mean than of the fairer median income. The different thresholds selected by the media help us to see why the (pro-government) Daily Mirror could display the headline “100,000 more OAPs living on breadline” while the (anti-government) Daily Mail concluded from the same DSS report “an increase of 400,000 (pensioners in poverty) over three years”.

Manipulation of different ‘averages’ is quite common. Thus the management of a firm will quote the mean salary of their staff to show how well paid they are while the union will cite the median wage to illustrate the opposite. An arbitrator might well consider yet another average called the mode, the income earned by the largest number of employees. All sides will call their figures ‘the average’. Disraeli once wrote “There are three kinds of lies: lies, damned lies and statistics”. But statistics only mislead if the basis of the numbers has not been properly explained; an unqualified ‘average’, for example, is almost meaningless. And did you notice that this article did not define what was meant by ‘income’?                                                                                         
Prof Michael Spiro

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