Part of the point is any of those metrics are the correct one if they model the discrepancy you want.
You pick the one that treats discrepancy the way that's appropriate.
E.g., using the mode is like saying "if you're not the right answer, you're all equally bad".
Using the median is like saying "if you're not the right answer, you're as wrong as however far off you are".
Using the mean is like saying "if you're not the right answer, you're more and more wrong the further away you are, and the amount you're penalized itself gets more and more, so you're really incentivized to be closer"
Which of these is appropriate depends on the real thing you care about in whatever your numbers actually signify.
Caculate every value, check which has the lowest discrepancy and be done.