This question is not an easy one to solve, and many intelligent people approach it from many different angles. Debates rage over its interpretation and its answer. The main thing to keep in mind is that you are not trying to determine the average ratio of the long bone to the short bone. That is obviously unknowable without measuring the bones yourself. The Bone Man is essentially asking "what is the most likely average ratio of this pile of 10,000 bones." In other words, what average ratio should you tell him such that you have the best chance of not losing your leg?
After some work, however, I believe that I have solved the problem, assuming that "average" indicates "mean" and assuming that the Bone Man will tell you to what accuracy he can measure the bones.
Unfortunately, the analysis entails many equations and graphs that would be a hassle to put on my web page here, so I wrote up a Microsoft Word document that happens to be over 20 pages long. The gist of it is that the answer depends on the accuracy at which the Bone Man can measure the lengths of the bones. Here is a brief report of the answer, but if you want an explanation, click on one of the two links below.
|Bone Man's Precision||Your Best Guess to save your leg|
|Anything More Precise||18.002|
|Even Infinite Precision||18.002|