The Lake Wobegon Effect

Are you an above average driver? Are you more friendly, modest, good-looking, sensible, hardworking and less stingy or perhaps a better singer than the average of the population? When it comes to the level of self-belief when it comes to certain personality traits, many of us rate ourselves as above-average relative to others in a particular group. Ambitious parents think that their children are in the top ten per cent of the school population. We might succumb to the temptation of believing that we are better than the average stock market investor when share prices are rising strongly with us having made few if any investment decisions!

The so-called The Lake Wobegon Effect is examined in a report on the current edition of More or Less - the excellent Radio 4 programme hosted by Tim Harford. Most people are above the mean for a given measurement because of a skewed distribution - the average number of convictions for traffic offences is positive so it is perfectly possible for a majority of safe and responsible drivers to be above-average in terms of their ability to stay within the law, the average is driven higher by a relatively small number of people with a large number of convictions and penalty points to their name.

But if we define the average as the median (the middle score within a group i.e. the value that splits a given group into two equal halves), only 50 per cent of people can be above the average.

More here including a series of reports on the simple mathematics of the credit crunch and a neat piece on average wages, the distribution of income and the work of Vilfredo Pareto.

For the UK - Median income for people in full-time employment is £25,123 Mean income for people in full-time employment is £31,323

The median income for people working in the public (state) sector of the economy is higher than the private sector But the mean income for people working in the private sector is higher than people working in the public sector

Credibility gap? Over recent weeks I have been filling in teacher references for students applying to US universities. The standard application form asks a teacher to rank a specific student thus

Below average Average Above average Top 10 per cent of students Top 5 per cent of students One of the top few students I have encountered in my teaching career

Invariably I completely ignore the first four options and simply choose one of the last two .... But if I choose the last option five times out of six (to do otherwise might harm a given student’s chances) am I at risk of undermining my own credibility?