>Just out of curiosity, should you round up, down, it doesn't matter, or depends on the analysis context?

Up, usually - the most common case I see is where you want to have the median be in rounded dollars, without cents. If it's big money, you may round several digits even.

However, I think this might be a case to help use statistics to lie slightly for you - choose the rounding method that makes your median look best for you. Then, as you say, it depends on context :)