Sometimes when people have some ordinal values, they use a misleading number representation. Then, they aggregate data with arithmetic mean. For example, we have to aggregate the grades of an exam evaluated by an ordinal scale: Excellent,...,Very Poor. Sometimes people do this mapping:
5 - Excellent, 4 - Very Good, 3 - Good, 2 - Poor, 1 - Very Poor.
Then they say "The arithmetic mean is 3". besides they compare that mean with means of other previous exam. But that is an ordinal scale, we cannot do a mean!
Ok, formally it is not correct but what are the concrete problems of using a mean for ordinal values? Might be some kind of rank reversal while comparing different average values?