PROBABLE ERROR 99 



be expressed shortly as <r. o- represents a distance from 

 the mode equal to ^-f 0-6745. Thus if a- is known, q 

 can be readily determined, and vice versa. The reason 

 for the more frequent use of <r is that it happens to be 

 determinate 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 100. 

 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 



* or 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 



72 



