Mean, Median and Mendacity

For quite a while now the lawyers and the politicians have been locking horns over the income of the Bar. To a certain extent this is a red herring. We get paid by the case and the argument should be about how much the case is worth relative to the amount of time spent on it whilst factoring in the seriousness of the charge. We are piece workers – we get paid by the piece. However that is another blog for another time.

So there has been lots floating around about what the average income is for the Criminal Barrister. Sheilash Vara issued the definitive answer when he told anyone who would listen that the stats showed that the average income was £84,000 per year. That figure did not seem to be available anywhere else other than in the pronouncements of Vara so some of us contacted the Statistics Authority to get some clarity in the situation. And the clarity seems to be – Vara doth speaketh utter crap.

Before I show why it is utter crap, the science bit. There are two statistical mechanisms for working out the way you would describe the average of something. They are the mean or the median.

The mean is when you simply add up all the figures that you have and divide it by the number of parties that contribute towards the total. So 16 apples in four bags has an average of four apples in each bag. Of course in truth no single bag may contain anything close to four apples. The problem with using the mean is when you have a large disparity of values, some very low and some very high. Statisticians call these outliers. A big range of values with some very small and some very big can skew the final average.

The median is where you list all the values in ascending order. You then take the value that lies at the middle. This is universally seen as the more sensible and reliable way of discovering the central tendency in a set of values.

So now the science bit is out of the way can I get back to bashing the minister, and no, that is not a euphemism. You see Vara and the MoJ had a set of figures that ranged from £10K to 700K. From these figures the mean figure was £72k and the median figure was £54K. Now the cynical amongst you will say that I would pick the median figure as it suits my argument so more of that later. The astute amongst you will have spotted that Vara did not even use the mean figure. What he did was to take out all those that received less than £10K because they probably were not doing a lot of crime. In other words, he cooked the books. He took out one set of outliers and kept in the higher end of the range. The high end of the range are outliers that could easily be explained as representing more than one years earnings or the earnings of more than one person as they were making claims for other advocates due to the instructed advocate method of billing.

So was he wrong to use the mean rather than the median? Or is it just me, twisting it to make a cheap point. Well the Statistics Authority (who may know a thing or two about which of the figures he used would be more reliable) had this to say about it “use of the mean, rather than the median, results in a higher estimate as the calculation is influenced by a small number of larger payments”. I suspect that is a rebuke in the world of statistics.

So did the Government just fall into error with their use of the (higher and inflated) mean income figure of £84K? Did they know no better? Funnily enough in December 2013, just weeks before these statistics were being issued the Government produced a document containing their evidence to the Pay Review Body for Senior Salaries. In this document the Government relied upon the “average” income of senior civil servants. The method they used to reach the figure? The median figure. Of course they would. This is the reliable method for showing the general tendency in such figures. Using any other method is irresponsible and is done for the purposes of being misleading.

As a matter of interest you might want to know what the median figures for the Senior Civil Service are. They are split into four pay bands and are (roughly) £73K, £77K, £98K and £131K. Interestingly all well in excess of the median figure for barristers of £54K. And don’t get me started on what their pension provision means in addition to these figures. The Government recommendation for those fatcats? A pay rise. Go figure.