132 
071 the Prohable Errors of Frequency Constants 
We want the probable error of such a vahie. It equals r- , =a;,, whence 
Thus 
<r,^ = + cr^/J/ - 2hX [8hM)' (52), 
= J_ IQQ 1^ ^ _ ''A /, _ n,\)i 
(52 his). 
Applying this to our case we have 
a,.^ = 2-759,657, 
or the probable error of the position of the mean from the 4th dichotomic line is 
18614 mentaces. Symmetry of the result, as we might also anticipate from 
a priori reasons, shows us that this is also the probable en-or of the distance of the 
mean from the 5th dichotomic line. 
We may conclude this investigation by considering the error in the position of 
the 2nd dichotomic line, or that which divides the Slow and Slow Dull categories. 
We have «2 = = ] 35'7512 mentaces, 
h - K . 
and using (49) and (51) obtain 
a-^^ = 4-4241, 
or the probable error of a'„ is 2-9840 mentaces. 
Thus in terms of our Intelligent Range as 100 mentaces we find in mentaces 
x„ = 135-7512 + 2-9840, 
X, =~ 12-6504 ± 1-8614, 
a^:, =- 112-6504 + 1-8614, 
(74,5= 94-653 + 1-659. 
Any other dichotomic ordinate can have its probable error determined in like 
manner. 
It is clear that the positions of the dichotomic lines can be found with probable 
errors of 2 to 3 mentaces. The whole i-ange of intelligence being about 600 mentaces 
we see that with 2389 individuals, we can determine the positions of the category 
divisions within ranges of about 5 to 8 mentaces in a total range of variation of 
600 mentaces. 
