Average Nonsense

http://www.thisisjersey.com/2008/08/27/average-pay-up/

Average pay up by Richard Heath

AVERAGE annual earnings in Jersey have increased by 4.3 per cent to £31,200 in the past year, according to official figures. But the increase is 0.4 per cent lower than in the previous 12 months, and the gap between pay rises and the increasing cost of living in Jersey has narrowed. The figures, released yesterday by the States Statistics Unit, shows that average weekly earnings have increased from £580 per week in June last year to £600 per week this year. But the increase in earnings was just 0.2 per cent higher than the RPI, which measures the rate of inflation, compared to 1.2 per cent higher in the previous year.

The regular report of misinformation is in the JEP again. All across the world, the measurement of national earnings have moved from the arithmetic mean, commonly known as the "average" to the median. The arithmetic mean is obtained by adding all the items up, and dividing by the number of items. The median is a statistical measure obtained by looking at the middle item in a distribution.

For wages, the distribution is not a balanced one - the normal distribution or "bell curve" - but a highly skewed one, with a few higher wages grossly outbalancing the majority, which is why the median is a much better measure.

As an example, consider (as wages in thousands), the following cluster:

25,25,25,25,25,25,25,25

Now this results in Average = 25, Median = 25. (For the average - the mean - we sum, and divide by 8 in this case, for the median, we take the middle of the distribution when laid out in ascending order.)

Now let's change two of the numbers to 20.

25,25,25,25,25,25,20,20

Note that we now have Average = 23.75, Median = 25. The average has slipped down slightly.

Finally, let's just replace one of those 20s with a salary of a managing directors of a medium sized finance company (and I'm sure there are plenty with higher wages) at 120. We now have:

25,25,25,25,25,25,20,120

Average = 36.25, Median = 25

Note how rapidly the average wage has shifted. We now have 87.5% of our sample well below the "average wage", but the median is still drawing substantially the most accurate picture.

If you want to see it graphed out with differences in the UK, go to:

http://www.ssa.gov/OACT/COLA/central.html

(I've put a smaller version of that at the top of this blog, click on it for a bigger picture)

The UK, regarding the minimum wage, notes that:

When measuring minimum wage rates against the general level of earnings in the UK economy, we have regarded median, rather than average (mean), earnings as the more appropriate comparator. This is because of the disproportionate influence on the UK's earnings distribution of a relatively few high earners ­ which drives up the mean earnings figure.

http://www.lowpay.gov.uk/lowpay/lowpay2007/appendices4.shtml

All across Europe, Australia, America etc, the earnings statistics on wages use median rather than average. They did use average, but it was so misleading that they decided that a the median would provide a much better and more consistent measure, for the reasons outlined here.

The reason given in Jersey is that it is too difficult to get employers to supply information, yet such information is readily available from the Income Tax department, especially since the introduction of ITIS, and names and personal data could simply be stripped from the figures before number crunching. For now, take the figures given as representing the movement in wages that are appreciably higher than average, in order words, with as showing a general trend, but not one that is necessarily representative of the workforce as a whole. As a mathematician, I sigh every time these kind of statistics are trotted out, especially as they are never reported with any caveat about how misleading they are, and are no doubt swallowed whole by the general public.