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What would be appropriate metaphors to call the entropy of a question? I was thinking along the lines of "information value," but this would clearly be inappropriate, because it is the answers that contain information, not the question, and an unanswered question has no information value.

Each question has its entropy, which is the weighted average of the amounts of information contained in all possible answers. The weight of each possible answer is its a priory probability, and the amount of information is minus the logarithm of its probability: $$ S(q) =\sum_{a\in\operatorname{possible-answers}(q)}-P(a)\log(P(a)) $$

An interactive questionnaire where new questions depend on previous answers similarly has its entropy, and having a more descriptive term would be nice.

Having an appropiriate descriptive term would help to explain entropy to students and to use it in such contexts as estimating the minimal possible average cost of a comparison sort algorithm or analysing efficiency of a binary search tree. I would like to be able to say something like: "the local informativeness of this node in this binary search tree is such and such, and the (global) informativeness of the whole tree is the sum of the (local) informativeness of its root and the weighted average of the (global) informativeness of its left and right subtrees."

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