Put it another way:
 
We have N points in some multivariate space, we introduce a point, i.e., the (N+1)th point, into this space...
How do we quantify the difference between this (N+1)th point from the other N points? Let's also say that the N points are not distributed in any particular way (i.e., not necessarily as a Gaussian point cloud or any other analytically known distribution for that matter)...
 
thanks,
p

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