Find the average of a collection of points (in 2D space) I'm a bit rusty on my math, so please forgive me if my terminology is wrong or I'm overlooking  extending a simple formula to solve the problem.
I have a collection of points in 2D space (x, y coordinates). I want to find the "average" point within that collection. (Centroid, center of mass, barycenter might be better terms.)
Is the average point just that whose x coordinate is the average of the x's and y coordinate is y the average of the y's?

Yes, you can compute the average for each coordinate separately because $$\frac{1}{n} \sum (x_i,y_i) = \frac{1}{n} (\sum x_i, \sum y_i) = (\frac{1}{n}\sum x_i, \frac{1}{n}\sum y_i)$$
