I am dealing with a Monte-Carlo simulation which provides me with a value $x$ as a result. I can run the simulation $n$ times, which gives me $n$ values. I don't know in advance what the probability distribution function of the output values is. What I want to be able to do is to place an uncertainty on the sum or the mean of these values, but I need the uncertainty to be sensible even for small values of $n$.

For example, if I have $n=2$, and the two resulting values of $x$ are very similar (say 9.9 and 10.1), then intuitively, I know that the mean is still not necessarily accurate, because there are only two samples (whereas a standard error in the mean would give me a small uncertainty, because it uses the standard deviation).

Is there a formal way to deal with this kind of situation? In a way, I'm looking for something analogous to Poisson statistics, which allows one to place an uncertainty even on a single value, but in a more generalized way.

reallyhard. – András Salamon Aug 1 '10 at 2:37