# Getting 5 percent tail of an empirical distribution

In an analysis where I have 213 individuals and 524 genetic markers, the table below is the distribution of errors per individual. 1 means out of 524, 1 marker had an error in that individual and so on.

I want to statistically determine when there are too many errors, that is I would like to get the values that would be in the 5% tail of the distribution of errors for large errors and treat them as real errors. How can I achieve this?

The table of data:

0   0   1   1   1   1   1   1   1   1   1   1   1   1   1   1   1   1
1   1   1   1   1   1   1   1   1   1   1   1   1   2   2   2   2   2
2   2   2   2   2   2   2   2   2   2   2   2   2   2   2   2   2   2
2   2   2   2   2   2   2   2   2   2   2   2   2   2   2   2   2   2
2   2   2   2   2   2   2   3   3   3   3   3   3   3   3   3   3   3
3   3   3   3   3   3   3   3   3   3   3   3   3   3   3   3   3   3
3   3   3   3   3   4   4   4   4   4   4   4   4   4   4   4   4   4
4   4   4   4   4   4   4   4   4   4   4   4   4   4   5   5   5   5
5   5   5   5   5   5   5   5   5   5   5   5   5   5   5   5   5   5
5   6   6   6   6   6   6   6   6   6   6   6   6   6   6   7   7   7
7   7   7   7   7   7   8   8   8   8   8   8   9   9  10  21  41  42
42  46  47  49  64  70  77  81  84  92 101 102 105 122 123


Thanks!

It sounds like you're asking for the .95 quantile, which is the quantity $q$ associated with a random variable such that, roughly, draws have a .05 probability of exceeding $q$. I don't know enough genetics to know if the .95 quantile will really help you, but at least it's easy to estimate. There are several slightly different kinds of sample quantile. The basic idea is to sort the values (as you already have) and take the $i$th, where $i$ is approximately the number of data values multiplied by .95.