Let's say I have a binomial data set - m number of data points with a vaule of 0 and m number of data points with a value of 1. I have one data point (z) with the value of 0.5 (see below).

y x

y x

y x

y z x

----------------------------------------

0 0.5 1

We want to recognize data point z as a "maximally abnormal" (i.e. the maximum outlier possible with the given distribution) data point b/c it is furthest outside of both clusters.

How do we do this? In general, how do we take a data point and, without assuming a normal distribution, compute how "different" it is from the given distribution?

Thanks in advance.