While the median of a set often is close to the mean of the set, it doesn't have to be at all (as you know). For example, if you have a set with 18 0s, a 1, and a 19999, the mean is 10000, but the median is 0. Youcoulddescribe the median as the member of the set which is a greatest upper bound for the smaller half of the set and also a least lower bound for the larger half of the set.