Generating the centroid of multiple points

[StuartGerber]

I am getting to the point where I am over thinking the problem.  I have a street layer and I have generated a geodatabase street network, so I can get the intersection points for the street network.  This not a single line street network, but regular streets layer where collector roads can have two line segments representing the E-W or N-S directions on separate line segments.  My issue is where two sets of collector roads meet at one intersection.  At this location I can have 8 arcs feeing into 4 intersection points to represent one one road intersection.  See attached document.

I need to find the point centroid of the intersect!!!  I was going down the route of finding the clusters of points and buffering, with the intention of creating a point centroid of the buffer polygon.  This has not been working so well because there is not a common attribute to dissolve of buffers on for each polygon.

I then went down the path density based clustering, but cannot determine the proper attributes once again.   Any help would be greatly appreciated.

[ChrisDonohue__GISP]

Just an idea (not tested) based on other posts by folks here on GeoNet with a similar challenge:

Extract out the 4 points for the intersection as its own feature class.

Create a polygon from the "Minimum Bounding Geometry" bounding box.

Find the centroid of that polygon (Feature to Point)

Resource for the Minimum Bounding Geometry part:

Buffers With Points - A Tool for Creating Rectangular Buffers | GISNuts.com

Chris Donohue, GISP

[XanderBakker · Accepted solution]

Did you try the Mean Center and Median Center (Spatial Statistics) tools? ArcGIS Help (10.2, 10.2.1, and 10.2.2)

Use the case field to identify the points for each intersection.