Note 16 — Chapter XVII · OF CHANCE AND ITS ELIMINATION.

In the preceding discussion, the mean is spoken of as if it were exactly the same thing with the average. But the mean for purposes of inductive inquiry, is not the average, or arithmetical mean, though in a familiar illustration of the theory the difference may be disregarded. If the deviations on one side of the average are much more numerous than those on the other (these last being fewer but greater), the effect due to the invariable cause, as distinct from the variable ones, will not coincide with the average, but will be either below or above the average, whichever be the side on which the greatest number of the instances are found. This follows from a truth, ascertained both inductively and deductively, that small deviations from the true central point are greatly more frequent than large ones. The mathematical law is, "that the most probable determination of one or more invariable elements from observation is that in which the sum of the squares of the individual aberrations," or deviations, "shall be the least possible." See this principle stated, and its grounds popularly explained, by Sir John Herschel, in his review of Quetelet on Probabilities, Essays, pp. 395 et seq.