48 



STATISTICAL METHODS. 



Now the left-hand side in these equations is known ; it is \a 

 of Table IV. From this table the right-hand value of the 



FIG. 11. 



equations is found; it is the entry corresponding to the argu- 

 ment Ja. Thus /ij and 7t 3 I = J are found, and hence L^/a 



and L z /a and the entire range of the middle class, 



in terms of a, is known. Call the range in absolute units I. 

 Then Z=Z/ 3 + I/ 1 and I/ 'a is known and for a second series I/ a* 

 can be similarly determined. Hence a/a', the ratio of the 

 variabilities of the two series, is determined. 



Again, since LJa and - 1 are known, ^/(Z/g + Z/j) is 



known, and this gives us the ratio in which the mean divides 

 the true range of the central class. (Pearson and Lee, 1900.) 

 The foregoing method may sometimes be advantageously 

 employed where the data are quantitative. In this case 

 the numerical value of I is known. (Macdonell, 1902.) 



Consequently \ 4- h 2 = 



is known and hence 



-=J r 2 

 "-i ~\~n 3 



, the standard deviation, is found. Since L, = h^ = 



the distance of the mean from the left-hand boundary of n 2 , 

 the position of the mean is known. 

 The probable error of a is 



E. =t fV7^o A + 8 Wn-Q , n 3 (n-n 3 ) 



where 



- 



V 2* 



an d 



