Page:Popular Science Monthly Volume 48.djvu/526

484 For example, the chest measurements of 5,738 soldiers gave the following results:

If the number of events had been five hundred thousand or five million instead of five thousand, the agreement between the computed and observed frequency of each degree of departure from the mean would have been very much closer. When the number of cases is unlimited, the agreement is perfect.

Galton gives the following illustration of the significance of a type:

Suppose a large island inhabited by a single race, who intermarry freely, and who have lived for many generations under constant conditions, then the average height of the adult male of that population will undoubtedly be the same year after year. Also—still arguing from the experience of modern statistics, which are found to give constant results in far less carefully guarded examples—we should undoubtedly find year after year the same proportion maintained between the number of men of different heights. I mean if the average stature was found to be sixty-six inches, and if it was also found in any one year that one hundred per million exceeded seventy-eight inches, the same proportion of one hundred per million would be closely maintained in all other years.

An equal constancy of proportion would be maintained between any other limits of height we please to specify, as between seventy-one and seventy-two inches, between seventy-two and seventy-three, and so on. Now, at this point the law of deviation from an average steps in. It shows that the number per million, whose heights range between seventy-one and seventy-two inches, or between any other limits we please to name, could be predicted from the previous datum of the average, and of any other one fact, such as that of one hundred per million exceeding seventy-eight inches.

Suppose a million of the men to stand in turns with their backs against a vertical board of sufficient height, and their heights to be dotted off upon it. The line of average height is that which divides the dots into two equal parts, and stands, in the case we have assumed, at the height of sixty-six inches. The dots will be found to be ranged so symmetrically on either side of the line of average that the lower half of the board will be almost