My method and estimate:
The actual answer was 11.53.
(Full disclosure: actually first I picked 24 = something slightly under 50%*50, because I don't even know why, then later my brain said "hey why'd you do that??" and I picked 11 under a new name Guy "Oops" Srinivasan.)
NPR's Planet Money is running an experiment which could be an interesting way to test your other-people-modeling skills.
This is a guessing game. To play, pick a number between 0 and 100. The goal is to pick the number that's closest to half the average of all guesses.
http://www.npr.org/blogs/money/2011/10/03/133654225/please-help-us-pick-a-number?sc=fb&cc=fp
The other people guessing are self-selected, I would assume primarily NPR listeners.