XXXV — XLVI] Introduction lxvii 



Similarly from Table XXXVIII : 



ft - 3-7 : \/Nl^ = 1202 - §{$[66] = 11-65. 

 ft = 3-8 : VFSfl, = 1360 - }$ [72] = 13-19. 

 Hence for ft = 37342: V^S^ = 11-6.5 + ^^[1-54], 



\fNSp, - 12-18. 

 Thus we find, multiplying by ^ : 



ft= -6783 + -0989, 

 ft = 3-7342 ±-2493. 



It is clear that the ft and ft are significantly different from the Gaussian 

 ft = and ft = 3. 



We next turn to the skewness, using Table XLI : 



ft = 3-7: \/NZ sk = 1-98 + fff [21] = 2-10, 

 ft =3-8: VF2 8i = 1-88 + ffj [16] =1-97. 

 Hence for ft - 37342 : </N2* = 210 - flfa [13] 



= 206. 

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

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



ft = 3-7 : ViV tajo = 214 + fgf [20] = 2-25, 

 ft = 3-8: *JNZ d l* = 2-03 + $$ [17] = 213. 

 Hence for ft=3-7342: ViV2 rf /<x = 2-25- T ^[12] 



= 2-21. 

 Thus Probable Error ofrf = X ,x<rx 221 = 6111, 



and d = 6-6875 ±6111. 



The probable error of K t is to be found from the relation : 



(VF2,,) 2 = 4 (Viv% a ) 2 + 9 (V^2 ft ) 2 - 12 (V^) (Vtf 2 fc ) x ii ft A . (Ixxvii) 

 Thus we require ii PlP . Table XXXIX, p. 72, will provide this : 

 ft = 3-7 : iJ ftft = -892 + m [5] = -895, 

 ft = 3-8 : R„ lh = -893 + ffflf [5] = -896. 

 Hence for ft = 3'7342 we may take R Plh = -895. Accordingly 

 (V^S»,) 2 = 593-4096 + 2099601 - 631-8278 

 = 171-5419. 

 Or, VFS,, = 130974. 



Hence p.e. of «, = X i x ^iVX, = 2681 , 



or, k, = - -566,483 ± "2681. 



ii 



