TABLE 8 



Number of Boys and Girls, and Actual and Smoothed Weights 



for Each Inch of Height, for the Years 14 to 15 and 



15 to 16 



The "smoothed" values in this table will serve health 

 officers and others as a more satisfactory standard than the 

 actual averages, since the former are based on the assumption 

 that the law which operates for the bulk of the material also 

 holds good at the extremes.* An examination of this table 

 shows that with an increase of one inch in height, there is an 

 increase in weight ranging from three to five pounds for each 

 sex and for each year. 



*The "smoothed" series of average weights was obtained in the 

 following manner: We denoted heights in inches by x, and weights in 

 pounds by y. We then assumed that for each value of x, the proper value 

 for y was obtained from the equation 



y - 80 = a + b (x - 61) + c (x - 61) 2 + d (x - 61) 3 



for certain values of the coefficients. The latter were evaluated by the 

 method of "least squares." On this basis, we obtained the equations 



y - 80 = 21.68 + 4.73 (x - 61) + .09 (x - 61) 2 - .02 (x - 61) 3 

 y - 80 = 23.09 + 4.51 (x - 61) + .05 (* - 61) 2 - .01 (x - 61) 3 

 y - 80 = 24.60 + 3.28 (x - 61) + .06 (x - 61) 2 + .004(* - 61) 3 

 y - 80 = 26.08 + 3.44 (x - 61) + .12 (x - 61) 2 - .03 (x - 61) :i 



giving, respectively, the relations of weight to height for boys 14 to 15 

 years, boys 15 to 16 years, girls 14 to 15 years, and girls 15 to 16 years. 



16 



