Given min, mean, max and var of scores of several subjects

                 min mean max var
Subject 01 X_01:   2    3   5   1
Subject 02 X_02:   2    4   7   2
...
Subject 30 X_30:   1    3   5   1

where it is assumed that each $X_i$ is normally distributed, but the $X_i$ are not necessarily identically distributed.

How can 95% confidence intervals for the aggregated statistics be computed? For example, the minimum has mean $(2+2+..+1)/30$. But what is its confidence interval? Same questions for the mean of all runs, the maximum of all runs, and the variation of all runs.

Quite likely this is a standard question in statistics. Therefore a couple of key words and pointers to the literature would probably do.