I am reading about using the Monte Carlo method for uncertainty analysis of physical experiments. In the GUM's supplement 1, page 29 (section 7.6, https://www.bipm.org/utils/common/documents/jcgm/JCGM_101_2008_E.pdf), it is said that the average and the standard deviation of the computed quantity are an estimate y of Y and the standard uncertainty u(y) of y.
But I do not really understand why this would be the case. I could undertsand if the PDF obtained (the histogram of y) would be a Gaussian for example, but in general we deal with asymmetric PDF's. Why don't we report the median and the 68.3% CL instead of the average and the standard deviation?
