Solution 1, found the average of the latitudes, and then the average of the longitudes. This gives x, and y coordinate for the central point.
Solution 2, create a polyline between the points. Use the spatial info tool to get the centroid of that line (gives the midpoint)
Solution 3, created two additional points (NW point and SE point composed of a mixture of the x, and y coordinates of original points). Created a rectangle by joining the points using convex hull, then spatial info to get the centroid of the object (midpoint)