The school's brochure said that the average class had twenty pupils. A parent who had seen her daughter's classroom did not believe it, and asked for the details.
She got them, and the brochure was right. There were five classes in that year: four of them had ten pupils, and one had sixty. That is a hundred pupils in five classes, and a hundred divided by five is twenty.
But now count the same year from a pupil's point of view. Sixty of the hundred pupils are in the class of sixty. Forty are in classes of ten. So the class size that the typical pupil actually experiences is forty — twice what the brochure says.
Both numbers come from the same five classes and neither is wrong. They average different things. The brochure averages classes; the parent was asking about pupils, and there are far more pupils in the big class than in the small ones.
The median class size tells a third story: line the five classes up and the middle one has ten. Three sentences, three numbers, one set of facts.
She pointed out that this is not only a school problem. Any average taken over groups of different sizes will differ from the same average taken over the people inside them.
The parent's request to the school was not that the brochure be corrected. It was that it should say which average it means.