This depends on the bounds you to set to define the problem in the first place. If you take the last 15 degree of arc off the west edge and add it to the east edge. The calculation changes???? Same applies to north south direction. The answer depends on your arbitary start view of the 2D coordinate set.
Start pont is arbitary and is just a "convention" for practical reasons that poles are 90 lat, and 0 E/W passes through a particular point so east west limits on projection are 180E, 180W. This does not need to be. Change this convention and answer would be different.
Very Europe centric answer. Near the centre of the arbitary bounds. You could make it Indian, NEMA, Latin American, South East Asian, Polynesian or even Bermuda centric by changing the start view. Please play the "lost in space" theme at this point.
The 2D coincidence in the med is only the arbitary start. The real 3D centroid based on area at the surface exclusive of convention would be kinda hot.