Average of data-points

Question

I am trying to solve clustering problem. After step 1 i.e putting each data-point to a cluster now I want to calculate the mean or average of all of the data-points in a specific cluster. let suppose I have some data-points like A(2,3), B(4,5), C(6,7), D(8,9) in a cluster. How can I calculate their average?

Answer 1

One of 2 ways, depending on what you need.

Average of points is a point

If so, then average each coordinate separately to get the center of mass $C$

Average of points is a number

You can then compute average distance from the center of mass $C$ above, or compute all pairwise distances in the cluster and average those.