Consider a lottery ticket.

The 50% "confidence level" payoff is zero.
The expected payoff is maybe 30 cents - infinitely greater.

You encounter this situation whenever you have a skewed distribution of possibilities. In other words, whenever it is probably nothing, but it could be a jackpot.

You have to understand the difference between the median and the mean, but given the lack of reliable data, it probably doesn't make much difference.