The Emperor of China's Nose
A method of high precision measurement
The story goes that a long time ago, in a faraway, and mythical country, which we'll call China, everyone wanted to know how long the Emperor's nose was. Of course to be seen even trying to look closely at the Emperor's visage - let alone to hold up a (different!) ruler to it - would have invited instant, or I should say, far from instant, death. But so many people were curious, that a group of sages got together to look for a method of finding the answer, and this is what they came up with.
Questionnaires were printed and sent out in bundles to cooperating village chiefs, who distributed them to the peasants. Literacy was at a sufficient level that most were able to complete the single question, which was, of course: "How long do you think the Emperor's nose is?"
When the forms were collected, mathematicians added up all the values, and divided by the number of forms. Thus it was known that the length of the Emperor's nose was 6.734602 cm. The complete set of data was of course preserved, and many years later, with advances in statistical understanding more advanced mathematicians pointed out that fringe values - obviously the product of deranged minds - were distorting the honest opinions of the rest, and by eliminating them and using the very latest numerical modelling techniques, the mathematicians corrected this value to 4.980403 cm. To this day, no-one has produced a better estimate.
(Actually, all this suddenly reminds me of the "Tankan" index, which appears to proceed on the same basis.)