282 Trans. Acad. Sci. of St. Louis. 
have the same average(10). The best measure of the degree 
of dispersion or deviation of the individual members of a series 
from their common mean or average is that afforded by the 
Probable Deviation. The probable deviation is that devia- 
tion from the middle value, which, in a large series of obser- 
vations, is as often exceeded as attained (Lexis). In other 
words, half of the whole number of observations fall short 
of the probable deviation, while the other half exceed it. A 
deviation which exceeds is as probable as one that does not 
reach this value. The probable deviation can be calculated 
with the formula — 
= 
2 
d == + 0.6745,/ — (2) 
In this formula: 
d = the probable deviation. 
20? =the sum of the squares of the individual deviations 
from the mean or average. 
n = the number of observations in the series. 
In the place of this formula, in which the calculation of 
20" requires much labor when the number of observations is 
great, a simpler formula may be safely used in getting the 
deviation in a large series. 
d = + 0.8453 “2 (3) 
The:formula says that all the individual deviations from the 
mean or average‘of a series must be added together without 
regard to whether they are plus or minus and divided by the 
total number of observations. The working of the formula 
will be illustrated by finding the probable deviation from the 
average height of girls aged 8. 
