v.] NORMAL VARIABILITY. 59 



should have to express ourselves from another point of 

 view, and at much greater length, and say " the Prob. 

 Deviation of any, as yet unknown measure in the Scheme, 

 from the Mean of all the measures from which the 

 Scheme was constructed." 



The primary idea of Q has no reference to the existence 

 of a Mean value from which Deviations take place. It 

 is half the difference between the measures found at the 

 25th and 75th Centesimal Grades. In this definition 

 there is not the slightest allusion, direct or indirect, to 

 the measure at the 50th Grade, which is the value of M. 

 It is perfectly true that the measure at Grade 25 is 

 M Q, and that at Grade 75 is M + Q, but all this is 

 superimposed upon the primary conception. Q stands 

 essentially on its own basis, and has nothing to do with 

 M. It will often happen that we shall have to deal 

 with Prob : Deviations, but that is no reason why we 

 should not use Q whenever it suits our purposes better, 

 especially as statistical statements tend to be so cum- 

 brous that every abbreviation is welcome. 



The stage to which we have now arrived is this. It 

 has been shown that the distribution of very different 

 human qualities and faculties is approximately Normal, 

 and it is inferred that with reasonable precautions we 

 may treat them as if they were wholly so, in order to 

 obtain approximate results. We shall thus deal with an 

 entire Scheme of Deviations in terms of its Q, and with 

 an entire Scheme of Measures in terms of its M and Q, 

 just as we deal with an entire Circle in terms of its 



