I have a points dataset. I want to identify the cluster area first, and then, find the center of this cluster area.

I was thinking to use "**K-Means**", but I'm working on a single cluster, so I believe this method is not fitting with my case.

Now, I'm thinking to use either "**Mean Center**" or "**Median Center**" tool after identifying the cluster area by using the "**Optimized Hot Spot Analysis**". However, I'm confused between the mean and median. I'm dealing with only locations without any required weights, which means that I just want to find the center location of the points.

Which one of the two methods is the most proper and accurate for my case? And why?

** I read a lot about them, but I couldn't find the answer for my case.*

** In the attachment, you can see the dataset and the cluster area marked by the red circle.*

Thank you in advance

the mean center is going to be the arithmetic average of the coordinates which will be influenced to a greater degree than the median because of that outlier to the right/east The median can be calculated in several ways, but typically it is the middle value of the ranked X and Y coordinates, hence, outliers have less impact on the value. If you are looking to get your measure of centrality in the ellipse you have identified, there is no guarantee that you will get it with either measure. In such cases where you have outliers, one can use a trim mean which looks at 95% of the data points with 2.5% trimmed off the extremes from the sorted list of X and Y, this is not implemented in ArcMap.

Other alternatives, although less employeed, would be to produce a Delaunay triangulation (TIN) and determine the area of the triangles. A sorted list of their areas would identify areas from which you could select the points as candidates for the mean or median, after trimming the triangle list so that 90% or so of the area is represented.. You can do the same with successive removals of convex hulls. determine the convex hull, remove the points on the hull and recalculate until you are left with a certain percentage of area (perhaps 90% or even 50%)

Centrality has no 'accurate' measure, only 'best'... so in short, go with the median, or if you want to trim, do a trim median.

Other options are possible but more esoteric.