When the mean is meaningless

The media often report averages of random variables without saying anything about the shape of the distribution. When the distribution is skewed, this is completely uninformative (or even highly misleading, as most people probably think of "average" as "the most typical value").

For example, the mean monthly salary in Poland is 2,600 PLN (about $830). The mean probability of survival of an airplane incident involving casualties is 38%. What does the mean actually mean here? Not much, as both distributions are positively skewed. About 2/3 of the labor force in Poland earn less than the average salary, and 40% of plane crashes have an extremely low survival rate of 0%.