Given the results of a number of runs,

     X: min mean max var
Run 01:   2    3   5   1
Run 02:   2    4   7   2
...
Run 30:   1    3   5   1

where it is assumed that X is normally 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.

Probably, the assumption that all runs are distributed by the same random variable is at fault. What if

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

and the X_i are independent and identically distributed? What if they are all normal but not necessariliy identically distributed? Again, keywords and pointers to the literature would probably suffice.