444 



KEPORT — 1897. 



months 

 parents 



latter, under the direction of Professor Earl Barnes. In both of these 

 series the same plan, excepting details, was followed. 



The measurements embrace the following data : Stature without shoes, 

 finger-reach, height sitting, weight. A series of special measurements of 

 the head were taken, which, however, include only a few hundred indi- 

 viduals. The following statistical data were collected : Age, in years and 

 place of birth ; nationality of grandparents ; place of birth of 

 occupation of parents ; number and ages of brothers and sisters ; 

 order of birth of the child measured ; and the mental ability as judged 

 by the teacher. , " 



In treating this material I have endeavoured to exclude a certain 

 series of errors. The number of children of various ages which have been 

 measured is not equal. The series begins with comparatively few children. 

 The number increases from year to year, until, beginning with the ninth 

 year, it decreases again. It follows from this fact that among the six- 

 year-old children, for instance, there are more of the age six years and 

 eleven months than of six years and no months ; and that, on the other 

 hand, among the fifteen- year-old children there are more of the age 

 fifteen years and no months than of fifteen years and eleven months. In 

 treating the various series of observations all children between six and 

 seven, seven and eight, &c., have been grouped together, and usually the 

 series is assumed to represent sizes for the average ages ; that is, for 

 six and a half, seven and a half, &c. On account of the varying fre- 

 quency for the several months, this is not quite correct. Among the 

 younger children the average will be a little more than six and a half, 

 seven and a half, &c., while among those near the upper limit I judge it 

 will be a little less than fourteen and a half, fifteen and a half, &c. By 

 tabulating the various frequencies of various months for the children of 

 Toronto the following results were obtained : — 



The error resulting from this series may be very easily corrected by 

 adding to the average a correction proportional to the deviation of period. 



While the average may be corrected in this manner without much 

 difficulty, the variability of the series for the whole year is affected in a 

 much more complex manner. (I call the variability the square root of 

 the mean of the squares of the individual deviations.) We will suppose 

 that the variability did not change much in the course of one year, which, 

 at certain periods of life is, however, not the case. Since the values of 

 the average increase from month to month, it is clear that the range of 

 variation for the early periods must begin at a lower point than for the 

 l.ater periods, so that the variation for the total year covers a wider series 

 than the variations at a given moment do. It is possible to make the 

 necessary reduction by a consideration of the number of individuals 

 measured for all the different periods, and of the varying amount of varia- 

 tion. The amount of reduction due to this cause is shown in the fol- 

 lowing table, which refers to the measurements of American children, the 

 series including measurements taken in Boston, Milwaukee, Toronto, 

 Worcester (Mass.), St. Louis (Mo.), and Oakland (Cal.). 



