Calculating mean centers for global data

Discussion created by colina on Dec 11, 2013
Dear ArcGIS users

I'm trying to calculate weighted mean centres for global cinema venues around the world.  When I project the data (using an equidistant projection) I get different mean centres when the origin of the projection differs (as I expected because distance is preserved near the origin and distorts further away).  Is there any projection (or can I calculate spheroid distances someway using geographic coordinates) that I can use to calculate the mean centre correctly for global point locations?  Thank you.