THE METHOD OF AGE GRADATION 45 



It is worth noting that the distribution just cited bears a cer- 

 tain resemblance to the simplest type of distribution known as 

 Gauss' frequency curve, for this latter is not only a symmetrical 

 curve, but it is also divided by the value known as the 'probable 

 error' into three sections, and in such a manner that the middle 

 section comprises the half, and the two end-sections each one- 

 quarter of all the cases. Even a generation ago Galton advanced 

 the hypothesis that the abilities of a large group of non-selected 

 individuals would be distributed symmetrically in the form of the 

 Gaussian curve. It is true that Galton thought the Gaussian law 

 of distribution could be extended to apply to a very detailed 

 gradation (16 grades) of ability, whereas statistics at present 

 available only make it probable for a few main groups. 



Bobertag has supplemented our knowledge of this 

 matter by discovering that a similar distribution 

 holds good on other occasions when a fairly large 

 number of individuals is divided into good, medium 

 and poor groups. In statistics of marks pertaining 

 to 2772 pupils, it turned out that marks of " better 

 than satisfactory " were assigned to 25.7 per cent., 

 of "satisfactory" to 50.8 per cent., and of " unsatis- 

 factory " to 23.5 per cent, of all cases (40, IT, 

 Table IV). 



Yet it is well not to ascribe too great significance 

 to these ratios of distribution. In the first place, 

 the empirical data now at our disposal are not 

 enough to warrant as yet the assumption of a gen- 

 eral conformity to law; and even for the data now 

 at our disposal the formula holds only as a rough 

 approximation and merely as a general tendency for 

 a rather large number of cases within which the 

 numerous irregularities compensate each other 

 (compare on this point the next section). Neverthe- 

 less, the findings already secured are of sufficient in- 

 terest to be followed up farther. 6 



"Further discussion of this principle of symmetrical distribution 

 and its relation to the Gaussian curve may be found in one of my 

 previous articles (I, 248 ff.) and in Bobertag (40, II). 



