XXXV XLVI] Introduction Ixvii 



Similarly from Table XXXVIII : 



& = 3-7 : V^S 3a = 12'02 - ff| [66] = H'65. 

 ft = 3-8 : VF2 A = 13-60 - f [72] = 1319. 

 Hence for , = 37342: VFS ft = 11-65 + f$&[l'54], 



V#2 ft = 12-18. 

 Thus we find, multiplying by % : 



& = -6783 -0989, 

 & = 37342 -2493. 



It is clear that the /9, and j9 s are significantly different from the Gaussian 

 ft = and & = 3. 



We next turn to the skewness, using Table XLI : 



& = 37 : VF2* = 1-98 + |} [21] = 2-10, 

 & = 3-8: VF2* = 1-88 + ff [16] =1-97. 

 Hence for & = 37342 : VJV2,* = 2'10 - ^ [13] 



= 2-06. 



Thus the skewness = '4951 '0422, or the distribution is significantly skew. 

 Passing to Table XL for the probable error of d, we have 



& = 37 : Vtf 2 d /<7 = 214 + {ft [20] = 2'25, 

 /9 2 = 3-8: VF2 d /<r = 2-03 + ^[17] = 2-13. 

 Hence for #,= 37342: V^2 d /o-=2-25-^y[12] 



= 2-21. 



Thus Probable Error of d = *i x a x 2-21 = -6111, 



and d = 6-6875 -6111. 



The probable error of AC, is to be found from the relation : 



(VNSJ = 4 (VJVS^ + 9 (VF2 ft )' - 12 (V^ a ) (V#2 fc ) x RM. (Ixxvii) 

 Thus we require R M . Table XXXIX, p. 72, will provide this: 

 & = 37 : Rf ltt = -892 + ffift [5] = '895, 

 A = 3-8 : fl ftft = -893 + |fj| [5] = '896. 



Hence for y8 2 = 37342 we may take -R/3,/3., = "895. Accordingly 

 (VJV"2,,) 3 = 593-4096 + 209-9601 - 631-8278 



= 171-5419. 



Or, V2VX, = 13-0974. 



Hence p.e. of AT, = x , x VF2., = '2681 , 



or, , = - -566,483 -2681. 



It 



