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 1/25 and 0'78 ; 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 he 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-r-. As the tabular value of Q is 1, it will become 

 changed into _ . 



