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Kindly comments on Stupid Questions December 2014 - Less Wrong
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Math competitions often have the opposite problem. The Putnam competition, for example, often has a median score of 0 or 1 out of 120.
I'm not sure this is a good thing. Participating in a math competition and getting 0 points is pretty discouraging, in a field where self-esteem is already an issue.
Interestingly enough, the scores on individual questions are extremely bimodal. They're theoretically out of 10 but the numbers between 3 and 7 are never used.