# More context for formula wanted

1. Jan 31, 2012

### birulami

For a set of values $v_1,\dots,v_n$ I recently stumbled over the formula

$$\frac{1}{N^2} \sum_{i<j} (v_i-v_j)^2$$

where the sum is meant to be a double sum over j between 1 and N and i between 1 and j. First I thougth it should have something to do with variance. But this is obviously not the case. In my case, the $v_i$ are vectors, but this may or may not be important for the question:

Does this formula ring any bells? Is it something with a name? Does it have an interesting simplification?

Any hints appreciated.

Last edited: Jan 31, 2012