Statistics: Predict 90th percentile with small sample set I have a quite small data set (on the order of 8-20) from an essentially unknown system and would like to predict a value that will be higher than the next number generated by the same system 90% of the time. Both underestimation and overestimation are problematic.
What is the mathematically "correct" way to do this?
If I could also generate a level-of-confidence estimate, it would wow my manager.
Also, let me say I'm not a math major, so thanks for any help, however remedial it may be :)

A percentile p can be estimated from a sample of size N by interpolating between sample values.
Consider the "desired rank" given by p(N + 1 ). You can express this number as an integer k plus a decimal part d:
$$p(N+1) = k + d$$
Then you estimate the percentile as
$$Y_{k} + d(Y_{k+1}-Y_k)$$
where Yi is the ith largest sample value. (The cases where k = 0 and k = N are exceptions: here you just take Y0 and YN as your estimate.) You can see more details in the NIST Statistics Handbook.
As user17762 pointed out, you can estimate the uncertainty in your estimate of the percentile by bootstrapping. Essentially, you generate a large number of new samples (of equal to size to your original sample) by drawing values from the original sample, with replacement. Each of these new samples gives you a different estimate for the percentile. By looking at the spread in these estimates, you can say something about the uncertainty in your estimate of the percentile. 
