92 BIOMETRY 



be expressed shortly as a. a- represents a distance from 

 the mode equal to #-^0-6745. Thus if <j is known, q 

 can be readily determined, and vice versa. The reason 

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

 determinable with greater accuracy from an actual 

 series of variates.* 



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 a pair of values lying one 

 above and one below the true value required e.g., the 

 average stature of the whole of a race such that it is 

 an even chance that the value actually found will lie- 

 between them. Or the same thing may be expressed 

 in another way. If we plot in the form of a curve a long 

 series of actual determinations of a particular value, 

 the probable error of a single determination will be 

 nearly equal to the quartile of the curve so obtained. 

 We may illustrate this state of things from our example 

 of tossing coins, or still better by the essentially similar 

 case of drawing balls out of a bag which contains a very 

 large number of balls black and white in equal 

 numbers. Here the value to be determined experi- 



* a- 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, ex- 

 tracting 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 ' Structural Methods ' may 

 be consulted. 



