1 6 Records of the Indian Museum. [Vol. XXIII, 



we get moments about Mean (without correction) 



H>= l'90 43 75 



= - '47 7 8 43 77 

 /« 4 = 12-86 56 42 58 



/& 6 = — 8-i8 04 93 98. 



The moments were checked by calculating the cc raw" 

 moments about 143*0 cm. (end of range) as base unit The 

 11 raw " moments were 



^'=-4-52 5, v,'= -22-38, r/=-u8'02 625, 1/= -65742 75, 



./= -3846-6203125, 



but after transferring to the Mean, the same values as before were 

 obtained. 



The Standard Deviation ] (S.D.) is given by o- = \//»2 

 Thus cr= + 1-38 in working units 



= + 69*00 mm. 



The Coefficient of Variation ' 2 (V) is defined by — — - and we get 



7 = 4-1660. 

 We must now proceed to find the other frequency constants 3 



/?, = /' 3 7/v /?,= -033204 



& = M 4 W & = 3'547534 



Skewness = Sk.= -069858 



where skewness = i-llLJ. — iL_. 



2(5^-^,-9) 



Distance between Mode and Mean = d = o- x skewness. 

 It is now necessary to find the Probable Errors. 4 



' Also See Appendix I. 

 Karl Pearson: " Regression, Heredity and Pan-mixia," Phil. Trans., hoy. 

 . Vol. 1S7A 1 [896), p. 203. See footnote on p. 34. 



(i) Karl Pearson: — "Skew Variation in Homogeneous Material,'' Phil. 

 Trans., Roy. Sac. Vol. 186A (1895), pp. 343 — 414, Supplement, Vol. 

 197A ('<)<»i), pp. 443—459- 

 Karl Pearson: "On the Mathematical Theory of Errors of Judg- 

 ment," Phil. Trans., Roy. Soc. Vol. 198A (1902), pp. 274 — 270 and 

 p. 277. 

 Mm 'Sluw Frequency Curves," Biometrika, Vol. 4 (1905), pp. 169—212; 



Biometrika Vol. 5 1 1906), pp. 168 — 171 and pp. 172 — 175. 

 (iv) W. Palin Elderton : — " Frequency Curves and Correlation" (Charles 

 and Edwin Layton, London) with Addendum and Errata, 10J7. 

 •> The fundamental memoirs are Karl Pearson and L. \. G. Filon : (a) "On 

 the Probable Errors of Frequency ( onstants and on the Influence of 

 indom Selection on Variation and Correlation," Phil. Trans. Roy. 

 ^ Soc, Vol. 191 A (1898), pp. : . 1 1. 



( W. F, Sheppard: "On the application of the Theory of Error t< 



<>i Normal Distribution and Normal Correlation," Phil. 'Trans. 

 Roy. Soc, Vol. [92A (1899), pp. 101—167. 



