OF EEROES OF JUDGMENT AND ON THE PERSONAL EQUATION. 
249 
(6.) On the Means and Standaixl Deviations of Growped and Ungrouped 
Observations. 
It is well known that if the distribution of errors follows the normal law, the 
“ best ” method of finding the mean is to add up all the errors and divide by their 
number, the “best” method of finding the square of the standard deviation is to 
Moveable 
cross-piece. \ 
:t U'iyr'\ 
Mirror | '-pp /,i 
Knife ed^. 
Detia.iL of Levers aC A . 
Fig. 1.—Apparatus for Personal Equation. 
form the sum of the squares of the deviations from the mean and divide by their 
number, and the “ best ” method of finding a coefficient of correlation is to take the 
product of corresponding deviations from the respective means and divide by the 
product of the two standard deviations and the number of observations. These 
“ best ” methods become far too laborious in practice when the deviations run into 
hundreds or even thousands. The deviations are then grouped together, each group 
VOL. GXCVIir. — A. 2 K 
