In all the programs I have interviewed at (Clinical and Counseling PhDs) the average tends to be 3 for a strict mentorship model and 4 for more general program wide admissions.
Personally, I would be distrustful of a program who invites 12 per spot, or much more than 3-4 per spot. That says to me that the school is still far from finalizing their interest in any one person. It also tells me that despite all the work applicants put in that the program feels uncomfortable using the letters, statements, C.V.'s, scores, etc to compare to a reasonable point. If a program has 200 applicants, inviting half is too much- especially in this economy. I'm not even sure if I would go to one of those interviews- at most I would probably do a phone interview. That also speaks to me about the degree of encouraged competitiveness within the program- something I'm just not interested in between my cohort. I think the emphasis placed by some programs on being 'elite' for the sake of bragging is silly anyway.