What is a correct way to write using sigma notation for a problem involving an array of 2-dimensional points. Say I have 2 arrays, $P_{e}$ and $P_{a}$, both containing $N$ elements. $P_{e}$ represents the expected values of each of the $N$ points, and $P_{a}$ represents the actual value of these $N$ points on a Euclidean plane.
I would like to know how to write the summation notation for the average distance between each of the pairs of points. I don't know if it's right to express it as simply the distance between $P_{e}$ and $P_{a}$, like $\frac{\sum_{n=0}^{N}|P_{e}(n) - P_{a}(n)|}{N}$, or if I have to write it out in terms of the $x$ and $y$ values of each pair, Pythagoras-style.
Could someone give me some pointers or help writing it in a mathematically sound way? This has to go on a thesis, so I'd like to make sure I'm doing it right.