Median figures are not very valuable, because they mask all sorts of information. For example, the fact that the average patient lives 8 months is useless when you find out that those that live beyond 8 months tend to live a long and regular life, whereas those that live less than 8 months tend to die very quickly. This is asymmetry. Asymmetric outcomes mean that payoffs are not equal, and differ from the average by a wide margin.
Asymmetry can be countered by considering the expected values. This means multiplying the probability of an event by the value of its outcome to get the expected value of the event, and then adding up the total of the expected values. This will give you a figure which lets you know what you expect the entire scenario to result in. Usingthe patiente example above, it may show you that the expected lifespan with that illness is quite a bit longer than 8 months!
Taleb introduced the Rare Event Fallacy, which is the failure to account for extremely rare events. The problem is that such events are extremely difficult to detect. As we take more samples, we only very slowly learn about the relative infrequency of the rare event, however as soon as one happens, our knowledge improves quickly.