Among statisticians there is total agreement on how to define median for a finite multiset of numbers: Order the numbers, repeating them according to multiplicity. If there's a unique middle number, then that's it. If there are two middle numbers, then it's the halfway point between them. —Dan William Cordwell wrote: ----- If we have a finite set of discrete real numbers, {x_i}, then we can ask: What values of a,b,c minimize, respectively \sum_i | xi - a |^2 \sum_i | xi - b |^1 \sum_i | xi - c |^0 a = mean b = median c = mode, if we define 0^0 = 0 (or 0.0^0 = 0) I find this useful when discussing mean, median, and mode with middle-school students, as a way of looking at the values in a more abstract way. I note that there does not seem to be agreement on how to define median. -----