v.] NORMAL VARIABILITY. 61 



used not one Grade but two Grades for the purpose, 

 namely 25 and 75 ; but in the Normal Curve, the 

 plus and minus Deviations are equal in amount at all 

 pairs of symmetrical distances on either side of grade 

 50 ; therefore the Deviation at either of the Grades 25 

 or 75 is equal to Q, and suffices to define the entire 

 Curve, / 



The reason why a certain value Q' was stated a few 

 pages back to be equal to 1'015 Q, is that the Normal 

 Deviations at 20 and at 30, (whose average we called 

 Q') are found in Table 8, to be T25 and 078; and 

 similarly those at 70 and 60. The average of 1'25 

 and 0'78 is 1*015, whereas the Deviation at 25 or at 

 75 is 1-000. 



Two Measures at known Grades determine a Normal 

 Scheme of Measures. If we know the value of M as 

 well as that of Q we know the entire Scheme. M ex- 

 presses the mean value of all the objects contained in 

 the group, and Q defines their variability. But if we 

 know the Measures at any two specified Grades, we can 

 deduce M and Q from them, and so determine the entire 

 Scheme. The method of doing this is explained in the 

 foot-note. 1 



1 The following is a fuller description of the propositions in this and 

 in the preceding paragraph : 



(1) In any Normal Scheme, and therefore approximately in an observed 

 one, if the value of the Deviation is given at any one specified Grade the 

 whole Curve is determined. Let D be the given Deviation, and d the 

 tabular Deviation at the same Grade, as found in Table 8 ; then multiply 



every entry in Table 8 by-^-. As the tabular value of Q is 1, it will become 



changed into _. 

 a 



