I'm trying to find the average from a set of circular data and am using the following which is doing what I'm expecting.

               sum_i_from_1_to_N sin(a[i])
a = arctangent ---------------------------
               sum_i_from_1_to_N cos(a[i])

However I would love to be able to remove results which are furthest from the average but not sure what my approach should be.

Essentially I want to hone in on the cluster of most alike results in order to give the value which represents the average of the data in the highest density around the circle.

I'd love to just hear of any strategies I could investigate to help move this problem forward.

I'm trying to find the average from a set of circular data and am using the following which is doing what I'm expecting.

$$a = \arctan\left(\frac{\sum\limits_{i=1}^N \sin(a_i)}{\sum\limits_{i=1}^N\cos(a_i)}\right).$$

However I would love to be able to remove results which are furthest from the average but not sure what my approach should be.

Essentially I want to hone in on the cluster of most alike results in order to give the value which represents the average of the data in the highest density around the circle.

I'd love to just hear of any strategies I could investigate to help move this problem forward.