Mean, median and mode of salaries

Pic: Young British civil engineers do not believe the ICE's average salary. Full opinion here, in New Civil Engineer Magazine.

Although the intelligence quotient of the population fits a Gaussian bell well, the salary distribution is skewed and largest salaries are much too large to match a normal pattern. Plots of the population density of income distribution for various countries are well reproduced by a gamma function. In a Gaussian process, mean, median and mode coincide, but the same cannot be applied to a gamma distribution.

The arithmetic average of the salaries does not give us the information we want. Suppose you are looking for a job. You have an interview with a company that has ten employees, and the interviewer tells you that the average daily salary is 200€. Wow, that seems good money! But for this particular company you could work for a quarter of that. Imagine that seven employees make 50€ each, two managers each make 400€, and the owner makes 850€. Yes, the average salary is 200€ but note that the median and the mode are 50€ and that is probably what you would get.

It is clear that the mean alone is a bad salary estimator and some staticians (i.e. Gini) tried to measure the dispersion of incomes. However, the mean provides optimistic expectations and no goverment or institution dares to change it.
Pic: Gross annual salary distribution in Spain (2002). Click on the image to enlarge.