Probability of finding the median with finite space

Question

This is a spin off of this StackOverflow question.

Assume that you have a fixed number k of storage locations, and space for two counters. You will receive

Answer 1

A wild guess: discard the element that is farthest from the mean of the currently stored values.

Comparing to the current median doesn't work if the distribution of values is multi-modal and we get values from a non-dominant mode first.