Find the average of a collection of points (in 2D space)

Question

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?

Answer 1

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

Answer 2

There are different types of averages. Only the average of numbers is unambigious. The average you are looking for depends on what you want to use it for. If you take the avg. x and y coordinates separately, that will give you the center of mass.