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POPULAR SCIENCE MONTHLY. 



For example, the chest measurements of 5,738 soldiers gave the 

 following results : 



If the number of events had 

 heen five hundred thousand or 

 five million instead of five thou- 

 sand, 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 agree- 

 ment is perfect. 



Galton gives the following il- 

 lustration of the significance of a 

 type: 



Suppose a large island inhab- 

 ited by a single race, who inter- 

 marry 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 

 difi'erent 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 pro- 

 portion of one hundred per million would be closely maintained 

 in all other years. 



An equal constancy of proportion would be maintained be- 

 tween 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 sufiicient 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 



