I know the difference between the mean and the median.
- The mean of a set of numbers is the sum of all the numbers divided by the cardinality.
- The median of a set of numbers is the middle number, when the set is organized in ascending or descending order (and, when the set has an even cardinality, the mean of the middle two numbers).
It seems to me that they're often used interchangeably, both to give a sense of what's going on in same data.
Do they mean (pun intended) different things? When should one be used over the other?