274 PROFESSOR E. PEARSON AND MR. L. N. G. FILON 



We may add to these results the values of 2^ and 2 ft> where & and ft, are given 

 by (xliv.) ; we find 



4 p ^ 6 p 



' ' ' ' 



The distances from the mode to the mean, d, and from the mean to the end of the 

 range, a, are given by 



d = 1/y and a = - 



7 



Hence 



is 



and further 



(Ixxiv.). 



The results (xlvii.) to (Ixxiv.) must be now considered at length. 



(17.) (.) The frequency curve of the type considered is fully described by the 

 three constants, the mean, y, and p. But, since any three constants would do 

 equally well for example, what may be termed the three physical constants : mean, 

 standard deviation (or variation), and skewness it becomes of some importance to 

 inquire which constants have the least percentage of probable error. 



Now (xlviii.) shows us that the probable error in the mean is precisely the same 

 as in the case of the normal curve and 



= > 67449o-/v / n. 

 Thus, the percentage error in the mean 



A i/n 



67449 . 



= 'r X coemcient ot variation, 

 V n 



and will certainly be small whenever the coefficient of variation is small. Its value 

 is quite independent of the order of p. 



