I am just going to generally address the response. I just don't feel that an exercise of this sort for lack of better words constitutes much of being informative even as approximation. Can you imagine if you were to want to find the average of 20 rear ends photographed them and stiched them together it would still simply look like just yet another unique rear end! On many levels you have said that it even serves to overturn people's stereotypes that they have already formed in their minds using true to scale randomness since it is reality which informs real stereotypes and photos on magazines and such do so much to contort the issue of a person's innate subjectivity by masquerading it as some form of objectivity. The critical point you bring up is that even in pursuing stereotypes people do far better in judging for themselves but actually score inefficiently when they are presented with the average faces. Unless you can take a person's dna and create a map which shows just exactly which part of the dna will construct which part of the anatomy and then proceed to tally up the most common ones there is absolutely no way that this kind of theorization about the average of faces can actually work in producing a clear analysis of who from where looks like what which I believe you brought up repeatedly in saying that the algorithms used to process the faces are in question. The most obvious sorts of errors in the data sampling are implied by the way the photo was taken at what angle and with what lighting involved in the set up of the photo the cosmetics involved in relation to the individuals their hair blocking their forehead etc etc. I just think this sort of thing is better left to the antics of showing what kind of babies you and someone else could possibly make.
Actually, Central Limit Theorem states that if you do an random event [in your example, rear ends] numerous times it approximate the normal distribution, and that you will find that a mean exists, in this case, the 'average' looking one. So if you in fact does do an event many times, it will provide you with the more 'average' looking item, in Long Ma's case, faces.
When you mix many faces, even if they are not purely random [or fair] they do approximate even if some what biased.