XXXV — XLVI] Introduction Ixvii 



Similarly from Table XXXVIII : 



/3, = 3-7 : ViV^S^^ = 12-02 - 1^ [66] = 11-65. 

 ;8o = 3-8: ^^2^, = 13-60 -Iff [72] = 18-19. 

 Hence for /3, = 3-7342 : ^/N^^, = 11-6.5 + ^^2^ [1-54], 



^Nl^, = 12-18. 

 Thus we find, multiplying by ;;^i : 



/3,= -6783 + -0989, 

 /So = 3-7342 ±-2493. 



It is clear that the /3i and ^., are significantly different from the Gaussian 

 ;S, = and /3., = 3. 



We next turn to the skewness, using Table XLI : 



A = 3-7: VFS.t = 1-98 + Iff [21] = 2-10, 

 A = 3-8: VFS,t = 1-88 + Iff [16] = 1-97. 

 Hence for /S^ = 3-7342 : ViVS^t = 2-10 - -5^42. [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 



/3, = 3-7: Vi^2rf/<r = 2-14 + |fi§ [20] = 2-25, 

 /3o = 3-8: VF2d/o- = 2-03 + Iff [17] = 2-13. 

 Hence for /3.,= 3-7342: ^N^al(7=2-2o-f^[\^ 



= 2-21. 

 Thus Probable Error of tZ = ^i x o- x 2-21 = -6111, 



and cZ = 6-6875 + -6111. 



The probable error of k^ is to be found from the relation : 



{^/Nl^,r = 4 (VFSp,^)^ + 9 {^Nl^,y - 12 i^Nt^) WNt^,) X R^,^,. (Ixxvii) 

 Thus we require iJ^,p . Table XXXIX, p. 72, will provide this: 

 y3, = 3-7: i2,,,, = -892+ffH5] = -895, 

 ^, = 3-8 : Rp^p.^ = -893 + ff § [5] = -896. 

 Hence for yS, = 3-7342 we may take R^^^., = '895. Accordingly 

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

 = 171-.5419. 

 Or, VFS,, = 13-0974. 



Hence p.e. of /c, = ^i x V]?2,, = -2681 , 



or, «i = - -566,483 + -2681. 



i2 



