Calculate whether datapoints are part of a larger distribution I have some normally distributed variables (~800) and some variables that are in some way special (~30). I need to find out whether the special ones can be considered normal members of the distribution. 

I drew a histogram of the full distribution with the special members as scatter. In addition to that, the normal distribution of all variables and that of the special members. The plot shows these graphics for the strongest difference between the calculated distributions. Green is the normal distribution of all members, orange that of the special ones.


How do I calculate the likelihood of whether the special members are part of the larger ensemble, i.e. they don't stand out?
One way addressing your question is to ask if your two datasets(regular points and irregular points) come from the same distribution?
The kolmogorov-smirnof test is a common tool for putting a number on the 'likelihood' of two datasets being from the same distribution.
python scipy has an implementation of this test.

Be aware that this test is more sensitive to differences around the means of each distribution, than to differences around the edges. From the looks of the graph in the question, its not an issue in your case, so the test should work.

This is a very concise explanation of the test