BIOMETRICS 153 



(or MQ^ gives us a convenient measure of variability of 

 the material in question. As curves drawn from an 

 actual series of observations are never absolutely sym- 

 metrical, the mean of MQ and MQ X is taken, so that 



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This q is called the " Probable Error " of variation, 

 because it is practically identical with what the mathema- 

 ticians call the " Probable Error of the Normal Frequency 

 Curve." This, then, gives us the " measure of variability." 

 In Fig. 68 we see that the variability of the poppy race (III.) 

 is greater than the variability of either of the individual 

 poppies. 



In practice it is difficult to determine mathematically the 

 quart ile of a given curve. But q can easily be determined 

 in another way by calculation. Taking Galton's table of 

 the strength of pull, we find in the fourth column that 

 37 per cent, of all the men have a strength of pull under 

 70 pounds, and 70 per cent, of them one under 80 pounds. 

 We can calculate from this that 50 per cent, have a 

 pull of under 74 pounds, or, in other words, the mean 

 of the whole group M equals 74 pounds. Similarly, it 

 can be calculated that 25 per cent, would have a 

 pull under 66 pounds, and 75 per cent, one of under 

 82 pounds i.e., Q=66 pounds, Q 1 = S2 pounds. We 

 get therefore : 



MQ = 74 -66 = 8 pounds MQ + MQj 8 + 8 



82- = 8 rf -J- = 8pounds. 



The Probable Error is therefore q = 8 pounds. 



If we compare this 8 pounds with the average strength 

 of pull, which is 74 pounds, we find it is 10-8 per cent. 

 of that amount, and we get the " Relative Probable 

 Error " as 10-8 per cent. This, then, is the " Index of 

 Variability " we searched for. The greater the index the 

 greater the variability of the given character, and vice versa. 



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