I have already written on how misleading the concept of average is for highly skewed distributions, for instance the distribution of salaries at Goldman Sachs. A recent post by XM Carreira reminded me of another source of distortion: the fact that executives with (often widely) different years of experience are lumped together to produce that magical number, the average salary. The post links to an article in New Civil Engineer Magazine entitled "Elderly graduates make nonsense of salary survey." In particular, there were some complaints related to the fact that a salary survey "quoted the average graduate salary rising 19% over the past two years to in excess of 34,000 British pounds," but in truth "graduate civil engineering salaries fall behind those of other graduates" and some survey respondents were in their 50s and 60s, with the eldest respondent being 77. The article points out: "With age comes increasing responsibility and an increased salary, which obviously skews the figure." It had always been obvious that neither the janitors nor the secretaries in Goldman Sachs had received anywhere close to the average bonus publicized in the press, but it is worth remembering that the business analysts and fresh-out-of-B-schools associates probably did not either.
The issue of age in statistics is also touched upon in Basic Economics, where Thomas Sowell points out that: "When some people are born, live and die in poverty, while others are born, live and die in luxury, that's a very different situation from one in which young people have not yet reached the income level of older people, such as their parents. [...] Because of the movement of people from one income bracket to another over the years, the degree of income inequality over a lifetime is not the same as the degree of income inequality in a given year." (p.190) Sowell also quotes another, rarely-discussed source of distortion in census numbers: the number of individuals that make one household. "Family income or household income statistics can be especially misleading as compared to individual income statistics. An individual always means the same thing - one person - but the sizes of families and households differ substantially from one time period to another, from one racial or ethnic group to another, and from one income bracket to another. For example, a detailed analysis of U.S. census data showed that there were 39 million people in the bottom 20 percent of households but 64 million people in the top 20 percent of households." (p.191) (There are a lot more single mothers in the bottom bracket than in the top one, and a lot more two-parent families with two or more children in the top bracket than in the bottom one.) As a last example, "The sizes of families and households have differed not only from one income bracket to another at a given time, but also have differed over time. [...] Real income per American household rose only 6 percent over the entire period from 1969 to 1996, but real per capita income rose 51 percent over the same period. The discrepancy is due to the fact that the average size of families and households was declining during those years [fewer children], so that smaller households were now earning about the same as larger households had earned a generation earlier." (p.192)
Sometimes it feels like numbers should come with a little label affixed to them: trust at your own risk - at least until a greater part of the population becomes math-savvy enough to challenge the assumptions that went into producing said numbers. It wouldn't take much; understanding alternative measures and asking for those as a comparison would already go a long way. You're giving me the mean for the whole company, but what's the median for people most like me? We can talk about attracting more students to science and engineering at length, but everybody - everybody - should be trained to understand what the numbers they read in the paper really mean.