I am trying to represent a situation with an equation that is fairly conceptually simple, but I am not sure what is the proper way to represent it as a formal mathematical equation.
I have a set of n [1x692] arrays. I will take the sum of each array compared to each other array (except itself). They will be compared using this formula (the coeffficient of variance root mean squared error- CVRMSE)
${CVRMSE(y,{y}')} = \sum_{i = 0}^{n}\frac{(\frac{(y_{i}-y_{i}')^{2}}{n-1})^{1/2}}{\frac{y_{i}}{n}}$
This I will divide by n Choose 2 combinations.
So essentially I am creating a term that approximates the average amount of difference between the n vectors.
If each vector has length $m$ (in your case I guess $m=692$), and the vectors are $y_i=(y_{i1},y_{i2}, \dotsc, y_{im})$ for $1\le i\le n$, then the formula you want may be \begin{align*} \frac{1}{\binom{n}{2}}\sum_{i=1}^n\sum_{j=i+1}^n CVRMSE(y_i, y_j) &= \frac{1}{\binom{n}{2}}\sum_{1\le i<j\le n} CVRMSE(y_i, y_j) \\ &= \frac{1}{\binom{n}{2}}\sum_{1\le i<j\le n} \sum_{k = 1}^{m}\frac{\left(\frac{(y_{ik}-y_{jk})^{2}}{n-1}\right)^{1/2}}{\frac{y_{ik}}{n}}. \end{align*}