You are looking for a new job and have a choice between two companies. After doing some research, you discover that the average salary at Company A is €2,600, while at Company B it is €3,000. Naturally, you are very tempted to apply to Company B. But when you dig deeper, you find that managers earn more at Company A than at Company B (€5,000 versus €4,000), and that non-managerial employees also earn more at Company A than at Company B (€2,000 versus €1,500). So whatever your position, you would be better off joining Company A—but overall, you would be better off working for Company B! What a paradox!
In fact, as is often the case, the situation only seems paradoxical. The paradox arises only because we instinctively consider salary levels, not the sizes of the corresponding groups. The workforce structures at Companies A and B are very different, so the average salary is lower at Company A than at Company B not because salaries are lower in every category, but because a greater proportion of its workforce are employees rather than managers (see box).
This "paradox" was first introduced in 1903 by the Scottish statistician George Udny Yule (1871–1951) and popularized in 1951 by the English statistician Edward Simpson (1922–2019). In this example, the paradox is fairly easy to resolve. In everyday life, however, it arises in many situations because we have only a rather vague idea of the sizes of the subpopulations involved.
The paradoxical median ---------------------