Probably the most common statistic that people deal with is the average, which can often be a good approximation of the typical or general case. However, there are many cases where the average fails, and the most extreme example I’ve seen in recent data is lawyers’ salary distributions.
The NALP has been publishing salary distributions for a few years, and the blog Social Evolution Forum provides a good overview of the distribution. Since 2000 or so, the distribution is extraordinarily bi-modal, making the average, as well as the median, a poor statistic to represent the typical case.
In these situations, the average is meaningless, and it is better to report the two ( or three ) modes.
The Blog Empirical Legal Studies has more of the charts and a discussion about the system that created them.