TOO BIOMETRY 



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 determina- 

 tions 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 draw- 

 ing 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 experimentally is 

 the relative number of black balls to white, which we 

 know as a matter of fact to be equality; and our 

 single determination may consist in drawing out a 

 hundred balls, which are afterwards returned to the 

 bag. If we do this 1,000 times, and plot the number 

 of black balls drawn each time, we shall arrive approxi- 

 mately at a curve having its mode at 50, and possessing 

 a standard deviation which it is possible to determine 

 from the instructions given in the footnote to p. 99. 

 Multiplying a by 0*6745 gives us the quartile, which 

 represents the probable error of a single determination. 

 That is to say, it is an even chance whether any single 

 determination differs from 50 by more or less than q. 

 In this particular example the quartiles would be found 

 to lie very nearly at 46-6 and 53-4, so that the value of 

 the probable error is 3-4. 



The properties of the normal curve tell us a number 



