Editorial 
125 
their group by using the probability integral and actually determining from them 
the mean and standard deviation of the total fre(juency, the very quantities we are 
seeking to lind by a more accurate process. 
It may be said why not arrange the material in order of magnitude i The 
answer is that this is not an easy task if the observations run to hundreds or 
thousands. And further, while a mean may give accurately a result to j^th of an 
inch, it may be far from desirable or possible to measure to more than I", e.g. in 
the case of stature. Hence the decile individuals will be only known to \" and the 
median found from a pair of deciles will only at best be known to the \". The 
whole theory indeed supposes the characters of the decile individuals measured to 
very near the same accuracy as we need the mean. There are none of the 
advantages which arise from grouping after measuring in fairly coarse units, and 
then averaging up to get the mean. The application of the decile method should 
therefore be confined to cases where the numbers are not too large for ranking, 
where the distribution is approximately normal and where the character has been 
determined with considerable exactness at least for individuals in the region of the 
deciles. These limitations take much of our material out of the field of grade 
treatment. 
(6) We can now adopt the same process as we have applied to the determination 
of the median to find if possible a more accurate value for the standard deviation 
by aid of ranking. 
We take as before a-gs' = \(^s + ^s'<^s'> 
where A,., and A,,' are to be chosen so that 
is a minimum. 
Accordingly we have for the minimum value of a^^^, the equation 
— [So-,, So-, ] o-v^ - [So-sSo-^.'] 
A.S = '—^ — ,N , ^s' 
r 
...(89). 
We already know (see p. 119) the values of a^^, a^^, as found from any 
symmetrical pair of grades, i.e. 
It is easy to show that 
Hs'k' N\ N 
1 - 
2n. 
V 1 
[8aM,] = <r.,<r., ' / (40) 
N 
where is alwaj's less than Tig-. 
It will be seen that the first requisite is to table ?V^<,^,. We have 
