Saul Stahl explains how the Gaussian distribution, friend and bane of every new statistics student, came to be, well, normal. It's far from obvious that the best estimator of some unknown (but presumably fixed, measurable) quantity is the one that minimizes the squared errors of all the imperfect observations, but that's what we do when we compute a mean. And indeed, in the 17th and 18th centuries some scientists (like Robert Boyle of the Royal Society) argued that averaging all observations was a bad way to summarize data:
... experiments ought to be estimated by their value, not their number; ... a single experiment... may as well deserve an entire treatise.... As one of those large and orient pearls... may outvalue a very great number of those little... pearls, that are to be bought by the ounce...
Read as much or as little of the math in Stahl's paper as you care to.
(Link via
The Endeavour.)
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