20 THE MEASUREMENT OF VARIATION. 



lated, therefore, that 50 per cent, of them had a 

 strength of pull under 74 Ibs., or, in Mr. Galton's nota- 

 tion, the strength of pull at Grade 50, was under 74 

 Ibs. This, then, is the average strength of pull, or M , 

 of the whole group. Fifty per cent, of the men pulled 

 less than this amount, and 50 per cent, of them more. 

 Similarly, also, one can calculate that 25 per cent, of the 

 men would have a pull of less than 66 Ibs., and 75 per 

 cent, one of greater amount, whilst 75 per cent, would 

 have one of less than 82 Ibs., and 25 per cent, one of 

 greater. That is to say, the strengths of pull at Grades 

 25 and 75 were respectively 66 and 82 Ibs. The prob- 

 able error of variation in pull, or Q J? is therefore equal 

 to 74 66 = 8 Ibs., and also to Q 3 , or 82 74 = 8 



Ibs., whilst the mean value which is always in practice 



8-4-8 

 adopted as the probable error, or Q, is ~ = 8 Ibs. 



This probable error is 10.8 per cent, on the magnitude 

 of the average strength of pull, and this value accu- 

 rately represents the variability of this group of men in 

 respect of this particular characteristic. Supposing an- 

 other group were found to have a probable error of only 

 5.4 per cent, on the magnitude of the average, then 

 one would be justified in saying that th^ir variability, 

 or range of variation, was only half as great; or if it 

 had been 21.6 per cent., then twice as great. 



This relative probable error is therefore a con- 

 venient index of variability of any characteristic. 

 A few examples may be quoted in order to give 

 an idea as to its range. From the anthropometric data 

 obtained by Mr. Galton, it is calculated that the index 

 was 2.50 per cent, for man's stature, and 2.52 per cent. 



