Take the 2-minute tour ×  Has any work been done on generalizing
statistical computations to arbitrary structures? I was
wondering what would be necessary for them to be meaningful. For
example, the mean of a set is the "sum" of the set (probably a
commutative monoid, since finite multisets are "free commutative
monoids"?) but then how would one deal with the division by the
size of the set?  I apologize if this isn't a very well-formed
idea, but I've been playing with generalizations of common "real
number" things to see what kinds of structures they'd need.  I
tagged this with group theory even though I'm not sure groups
would be involved (except maybe the division aspect of the sum,
but that's division by a natural?) because I wasn't able to find
a general "algebra" tag.  share|improve this question  1 Answer
1  up vote 3 down vote accepted  There is a whole research area
called Algebraic Statistics, although its boundaries are pretty
blurry in my opinion. But you could do worse than to start with
Seth Sul