[theory students] 1-d clustering

[Eric Bach <bach@xxxxxxxxxxx>]

This is a problem I wonder about every time I have to assign
course grades.  I have a bunch of numbers X1 <= ... < Xn.
To be definite let me say that these are the order statistics
from i.i.d. U[0,1] random samples.  I want to put them into
a small number of bins (e.g. at UW: F, D, C, BC, B, AB, A).
One time honored method is to use large (or relatively large)
"gaps" between the Xi to define the bins.  One presumes that
this will minimize student complaints.   But what does it 
really do?  For example, if you use the six largest gaps to
make UW grading bins, are the expected sizes of the bins
equal?  (I doubt it.)  Etc.

Eric

PS. CC to Jerry in case the ML people have thought about this.