Only numeric data (interval and ratio scales) can have a mean or median. And you're right, when data are skewed the median is always a better measure of central tendency. My question to everyone is, how can you tell when data are skewed and the median is a better measure? What clues do you look for?
In my local newspaper, the Salt Lake Tribune, they routinely publish the median home prices by zip code for the region. Why would they print the median and not the mean?
The same newspaper every Saturday publishes average (mean) gas prices for the region. Why would they publish mean gas price but median home price?