434 Prof. F. Y. Edgeworth on the 



meters (the centre and the modulus) for the primary and for 

 the dislocated curves ; namely, from the Arithmetic mean, 

 and from the distance between certain percentiles which are 

 given by observation. In the primary group, above the point 

 69*5 occur 305 observations, '305 of the total thousand ; and 

 below the point 66*5 occur 264 observations, "264 of the total. 

 Whence between the Mean and the point 69*5 there should 

 occur '5 — *305 = '195 of the total; and between the Mean 

 and the point 66*5, *236 of the total. Now it is found from 

 the tables that *195 of the total number corresponds to '361 

 of the Modulus, -236 of the total to *447 of the Modulus. 

 Accordingly we have *808 ( = *361 + *447) modulus, equated 

 to the interval between 66*5 and 69*5 inches = 3 inches. 

 Whence the modulus = 3-f-*80S = 3*71 inches. 



Let us now apply this result to predict the number of 

 observations at particular heights (not too near the ex- 

 tremity, where the fulfilment of the Probability- curve is not 

 to be looked for). To predict the number above 70'5 (which 

 gives the number between 69*5 and 70*5, the number above 

 69*5 being already taken for granted) we are to employ the 

 Arithmetic mean, which is 68*20. 70*5 — 68*2 = 2*3 inches 

 = *62 modulus. Now, according to the Tables, the proportion 

 outside the point which is at a distance of *62 modulus from 

 the Mean=i(l-*6194) of the total =\ x *380x 1000 = 190. 

 The real number is 184. 



To find the number above 71*5 we have 71*5 — 68*2 = 3*3 

 inches =*89 modulus; corresponding to |(1 — *7918) of the 

 total = |*2082 x 1000 = 104. The real number is also 104. 



Proceeding similarly with the lower limb, to predict the 

 number below 65*5, we have 68*2 — 65*5 = 2*7 = nearly *728 

 modulus; corrresponds to i(l — *6971) total =^'302x1000 

 = 151. Whereas the real number is 147. 



By parity we find below 64*5, 79 by calculation, against 

 72 observed. 



The question is now whether we shall fare equally well when 

 we apply the same method to the group which is formed by 

 squaring each observation in the manner explained. By 

 parity of calculation the modulus of the new curve x *808 



= (69*5 2 -66*5 2 ) inches =408. 



Whence the new modulus =505 inches. Also the Arithmetic 

 mean of the new group is 4657*38. Accordingly, to predict 

 the number of observations above (70*5) 2 we have 



4970*25 -4657*38 = 312*87 = *62 modulus. 



Whence the calculated number is 190, exactly the same result 



