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We're going to be doing a fundraising competition, and I'm not sure as to the fairness. We will determine the winning group by just comparing the average amount raised by each group. Is this mathematically fair, or is their a better way? For some reason I can't help but think that it'd be unfair for a group of 10 people to compete against a group of 100 people. I think the group with 10 people will most likely win, but I don't know why. Any advice will be appreciated.

Thanks