I've got a simulation that tries to calculate the highest energy eigenstate of a Hamiltonian and obtains a value $\langle A\rangle$ as its best effort. I do this once each time for a number of different problem instances, say $i$ many. For each of these instances, I have the true value $A_{\max}$ for each instance and so I can calculate $ r = \langle A \rangle / A_{\max} $ for each case. I can then calculate the mean of $r$ to see how well the simulation does. My question is, how would I report the spread of the $r_{\text{mean}}$?

It doesn't represent repeated measurements of the same value, so the standard error $ \sigma/ \sqrt{i}$ doesn't seem appropriate. But then, neither does just taking the standard deviation of $r_{\text{mean}}$. What is the best practise in this case ?



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