Indeed, the median works better in general, even on degenerate distributions. The Cauchy distributions has no defined mean, but still has a median.

We need to upgrade the FAQ to be more specific with the methods we use.

To be quick: The price come from many exchange. We exclude suspicious points. Then we do aggregation function like the average.

Averaging may not technically be the best method, but it is simple, and it has a wide support. And with the number of data points we have, we assume the Law of Large Number apply.

Still it could be interesting to use the median. I need to think more about it.