Edit: Ignore this Most of this doesn't make sense and is beyond edits but its too late to delete. If I make too many edits I could be kicked out of this sub like I was in math stack exchange.
I don't have a statistical background but I believe my ideas can be explained using statistics. For now, I will explain using pure mathematics.
Motivation
I want a way to determine how evenly distributed a set of values are.
For example, I believe $\left\{0/6,1/6,2/6,3/6,4/6,5/6,1\right\}$, should be one of many sets with the most even distribution since the differences between consecutive elements are the same throughout.
Method for determining Even Distribution
Suppose we have a set of values
$\left\{a_1,a_2,...,a_n\right\}$
Take the difference between consecutive values:
$\left\{a_2-a_1,a_3-a_2,...,a_{n}-a_{n-1}\right\}$
Out of the set of differences, we take of the largest difference, the largest plus second-largest difference, the largest plus the second-largest plus third largest difference, and continue until we get the largest difference plus all the way to the n-th largest difference (aka the smallest difference).
Finally, we take the mean of these values.
The closer the result is to $1/2$ the more evenly distributed the original set of values are.
Even if $n\to\infty$, there should be instances, for certain sets of values, where my results can be determined.
Question
Is there a statistical definition for this? If or if not, how do express this in terms of mathematics/statisitcs?
