>That is the median of a distribution, not the median value of a set of values. This is why it is defined in terms of probabilities.

Exactly - that's what I was referring to earlier as different/unusual distributions having different median measures. But a given set of data points has a very standard median, as we've discussed.

For some reason, a great many people want to make the median value more difficult than it really is :) It's really extremely simple.