How to find the median element when each element has three scores?

Question

I know how to find the median with a list of one element but what to do with a list like this one:

\begin{array}{|l|cr} & math & info & gestion\\ \hline Nelim & 0 & 4 & 0\\ Jean & 1 & 3 & 1 \\ Li & 2 & 3 & 2 \\ Lisa & 3 & 1 & 1\\ Marius & 4 & 0 & 0 \end{array}

Because it is not in order and I think we can't.

Answer 1

The concept of the median (or minimum, maximum, quartiles, etc) is based on having a total order between elements. There is no one preferred order between triples of real numbers, so there is no single "canonical" notion of median for this list of five people.

That said, you can decide to order them somehow based on the scores, and then the concept of median applies. Some ideas for ordering:

1. Order by total score (4,5,7,5,4). Then both Jean and Lisa qualify as a median.
2. Order by median score (0,1,2,1,0). Same result as in 1.
3. Order lexicographically: e.g., compare math scores first; if they are equal, compare "info", etc. Then Li is the median.