Editorial 
121 
To find when this is a maximum, we must differentiate with regard to ?ii and 
put da,„ldnj = 0 or 
}_ _dHi _ ^dH^dh, _l h, 
" 'dTxl ~ If, dih dn,~NH]' 
Thus 
Putting 
.(26). 
h, = -60 -277,687 -274,253 
•61 -271,487 -270,931 
•62 -265,471 -267,629 
-63 -259,629 -264,347 
• 
we see that lies between -61 and '62 and thence reach by interpolation -612,0014 
as the required value of h,. This leads to 
= -270,268, 
or the right value of is a little more than the quartile, or a:, — x, instead of being 
•67449(7, = •61200tr. This leads us to 
o-„,= 111120-/V]? (27), 
or the median found from the nJN = -270268 grades is more than twice as accurate 
as when found directly. 
As these grades do not differ very much from n,/N' = -25 or the quartiles we note 
that the cr^ of the median found from the two quartiles is 
<r,„= ril26cr/ViV" (28). 
The difference in accuracy between (27) and (28) is too small to be of any 
importance for most statistical purposes, and accordingly the quartiles may be used 
to determine the median, and this with double the accuracy of direct investigation 
of the mid-individual. We can put into a table the results for finding the median 
from each pair of the following series : 
TABLE IV. Accuraci/ of Deterniination of Median from Paii's of 
Symmetrical Grades. 
TiilN 
] o 
-25 
max. 
■270268 
1-3858 o-/V^ 
1-2741 aj^N 
1-1295 al-J'N 
1-1126 ajs'^ 
1-1112 ajsl'N 
l-113a(7/N^yV 
1-1576 aj^^ 
1-2533 0-/VF 
Syuibol for 
median 
m-i 
'"5 
Mo 
8—5 
