PROBABLE ERROR 99 
be expressed shortly aso. o represents a distance from 
the mode equal to g+0'6745. Thus if o is known, g 
can be readily determined, and vice versa. The reason 
for the more frequent use of o is that it happens to be 
determinable with greater accuracy from an actual 
series of variates.* 
We have still to find a measure which will enable us 
to compare the variability of parts or organisms so 
different that they require to be expressed in units of 
quite different magnitudes. For this purpose what is 
known as the coefficient of variability is used. This is 
a purely abstract number obtained by dividing the 
standard deviation by the magnitude of the mean in 
any particular case, and multiplying the result by roo. 
In this way a measure of variability is arrived at inde- 
pendent of the particular kind of units of measurement 
which were employed in obtaining it, and variabilities 
previously expressed in terms of different units can 
thus be compared together. 
The circumstance that half the total number of 
variates lies outside the limits of the quartiles and half 
within leads us to the consideration of what is known 
as the probable error. The probable error of any 
statistical determination is obtained by finding a pair 
* ¢ is found by multiplying the square of the deviation of each 
class from the mean (or mode) by the frequency of the class, 
adding together the series of products so obtained, dividing 
this number by the total number of variates, extracting the 
square root of the result, and multiplying by the number of 
units in the class range (this last number is very often unity). 
For further details with regard to the properties of the normal 
curve Davenport’s ‘Statistical Methods’ may be consulted, 
7—2 
