234 Trans. Acad. Sci. of St. Louis. 
series containing many measurements may be calculated by 
the approximation formula 
xO 
d = + 0.8453 — (1) 
where d = Probable Deviation, 
6 = Deviation of individual from median value, 
sd = Sum of individual deviations, 
n = Total number of observations. 
The Probable Deviation contains the Error of Observation, 
as well as the Physiological Difference of the Individual from 
the Type. The Error of Observation, in a large series of 
‘Ineasurements, is always relatively small. Its insignificance 
can be made clear in several ways. If the height of one boy 
at any age is measured 1000 times, the Probable Deviation 
will be much smaller than when the heights of 1000 boys at 
that age are measured once. Compare, for example, the 
Probable Deviation from the average height of one boy aged 
17 measured 78 times with that of 78 boys aged 17 measured 
once, the measurements being made under conditions as nearly 
alike as possible in both instances. 
One Boy aged 17 78 Boys aged 17 
Measured 78 times, Measured once. 
Average Height 176.28 em. 165.13 cm. 
Probable Deviation -— 0.24 em. + 5.15 * 
In the single boy, the Difference of the Individual from the 
Type is not present andthe Probable Deviation is very small : 
in the 78 boys, the opposite is true. Yet the difficulty of cor- 
rect measurement and hence the Error of Observation in each 
measurement in the two series cannot differ greatly. It fol- 
lows that by far the greater portion of Probable Deviation is 
made up of the Physiological Difference of Individual from 
Again, the Error of Observation is inversely as the square 
root of the number of observations and should, were it an 
important constituent of the Probable Deviation, cause the 
latter to increase as the number of observations decreased. 
