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SUBMIT YOUR IDEALooking at the Alteryx weekly challenge solution, using summarize to create a centroid point is a lot nicer and easier to do than manually finding the minimum total distance from every other point in the region (which is what I did). I forgot that you can do spatial functions in summarize (I rarely need to do spatial analysis unfortunately so this is good practice).
My solution is brutally ugly and I'd imagine that using centroids in Transform functions can lead to errors. Somehow I thought I needed to use a Macro so the bulk of this is in an extended series of Transforms, Joins and Appends (in the totally unnecessary Macro)... But hey it works! Now off to review finer solutions and Spatial tools which make this one simple...