78 THE RATE OF GROWTH [ch. 



the slow beginning, the rapid increase of velocity, the point of 

 inflection, and the subsequent slow negative acceleration *. 



Variability and Correlation of Growth. 



The magnitudes and velocities which we are here deahng with 

 are, of course, mean values derived from a certain number, some- 

 times a large number, of individual cases. But no statistical 

 account of mean values is complete unless we also take account 

 of the amount of variability among the individual cases from which 

 the mean value is drawn. To do this throughout would lead us 

 into detailed investigations which he far beyond the scope of this 

 elementary book ; but we ^ may very briefly illustrate the nature 

 of the process, in connection with the phenomena of growth 

 which we have just been studying. 



It was in connection with these phenomena, in the case of 

 man, that Quetelet first conceived the statistical study of variation, 

 on hnes which were afterwards expounded and developed by 

 Galton, and which have grown, in the hands of Karl Pearson and 

 others, into the modern science of Biometrics. 



When Quetelet tells us, for instance, that the mean stature 

 of the ten-year old boy is 1-273 metres, this implies, according to 

 the law of error, or law of probabihties, that all the individual 

 measurements of ten-year-old boys group themselves iti an orderly 

 ivay, that is to say according to a certain definite law, about this 

 mean value of 1-273. When these individual measurements are 

 grouped and plotted as a curve, so as to show the number of 

 individual cases at each individual length, we obtain a characteristic 

 curve of error or curve of frequency; and the "spread" of this 

 curve is a measure of the amount of variabihty in this particular 

 case. A certain mathematical measure of this "spread," as 

 described in works upon statistics, is called the Index of Variabihty, 

 or Standard Deviation, and is usually denominated by the letter cr. 

 It is practically equivalent to a determination of the point upon 

 the frequency curve where it changes its curvature on either side 

 of the mean, and where, from being concave towards the middle 

 line, it spreads out to be convex thereto. When we divide this 



* Cf. Chodat, R., et Monnier. A., Sur la courbe de croissance des vegetaux. 

 Bull. Herb. Boissier (2), v, pp. 615, 616, 1905. 



