22 



THE MEASUREMENT OF VARIATION. 



venient to compare the experimental and theoretical 

 values directly by a numerical method. This is done 

 by extending the method of grades referred to above. 

 In addition to determining the magnitude of the char- 

 acteristics at grades 25, 50, and 75, one determines it 

 also at grades 5, 10, 20, 30, and so on, or determines 

 the values having respectively 5, 10, 20, 30 per cent., 

 etc., of all the measurements below them in magnitude, 

 and 95, 90, 80, 70 per cent., etc., above them in magni- 

 tude. Let the median, or value at grade 50, be now 

 subtracted from the values at all the other grades, and 

 the numbers so obtained be divided by the probable 



error, or 1 = ! . We then obtain a series of values at 



the various grades, in terms of the probable error taken 

 as unity; so that, whatever had been the magnitude of 

 the median, and of the probable error, the values are 

 now directly comparable with the theoretical values cal- 

 culated from the probability integral. These theoretical 

 values are given in the first line of the subjoined table : 



Beneath them are given the means of the values ob- 

 tained by Mr. Galton for 18 different series of measure- 

 ments on men and women, the total number of observa- 

 tions made being 9443. In the individual series the 



