Some drawbacks in using the mean probability

Because there is often insufficient data to accurately estimate the probability P of an event, the uncertainty in P is usually expressed by an uncertainty distribution U based on the available data and expert judgment. The mean of U is often used for regulatory decision-making. However, an important drawback in using the mean is that it may destroy essential information about P contained in U. Replacing U by its mean can foreclose some options available to a decision-maker and lead to a non-conservative or an overly conservative action. Although it is sometimes useful to replace an uncertainty distribution by a single number, the mean may not be the best summary statistic. If a summary statistic is evaluated by the degree to which it reflects the uncertainty , is stable, is conservative, and provides a constant level of assurance, then a high percentile (e.g. the 85th) can be preferable to the mean