I'm using a monte-carlo technique to simulate a physical process, and I'm measuring a quantity from my simulation, <x> where <x> is the average of x over n steps.

What's a good way for me to estimate the statistical error in <x> due to only averaging over n monte-carlo steps? Whereas in the real world the average would be over a clean statistical distribution.

Is a good enough estimate or can we do better (or is it completely wrong)?

I have also calculated , if that helps somewhere. I also have a record of each x in the average.

Any ideas guys? I was always bad with errors :)