1922.] P. C. Mahalanobis : Analysis of Stature. 17 



The Probable Error of Mean ' 



•6744898 



v / w 



a = Xi°". 



Probable Error of Standard Deviation 



•6744898 

 = ~7=r- ." r = Xs'°-. 



Probable Error of Coefficient of Variation 

 •6744898 



V2« ^ \IOO/ J 



We find, Probable Error of Mean = 0*32906 cm. 

 Probable Error of S.D. =0-32267 cm. 

 Probable Error of V =0-14166. 



The Probable Error of S.D. requires correction for skewness. 

 The P.E. of S.D. 



_ '6744898 . o- 



y- \/{H-t(ft-3)} 



V2W 



cr 



which reduces to the usual expression involving __ for normal 



V2W 



curve, since £ 2 ~3 = approximately in this case. Making this 

 correction we get P.E. of S.D. = 0-3643 cm. This correction has 

 been made in all subsequent work, but the difference made is not 

 considerable in any case. 



The probable errors of /ij and /3 2 > skewness and d were found 

 from Table XXXVII, XXXVIII, XI and XII pp. 68-77 of Tables 

 for Biometricians. 8 



Probable Errors of /?,. Table XXXVII p. 68. 



/?i = -0332 



ft = 3*5 v'N 2^ = o + ^(r37) = 0-9069 



(c) " On the # Probable Errors of Frequency Constants," Biometrika Vol. 2 



(1903)* pp. 272. 



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



ment," Phil. Trans. Roy. Soc, Vol. 198A (1902), pp. 274 — 279. 



(e) "Probable Errors of Frequency Constants," Part II, Biometrika, Vol. 9 



(1913), pp. 



1 Tables were published by W. Gibson and Raymond Pearl (Biometrika 

 Vol. pp. 385 — 393) to facilitate the calculation of probable errors. These have been 

 now reprinted as Tables V and VI in " Tables for Satistfcians and Biometricians " 

 (Cambridge University Press, 1914). 



2 Karl Pearson, Editorial Note on a paper by Raymond Pearl : " On Certain 

 Points concerning the Probable Error of the Standard Deviation," Biometrika 

 Vol. 6 (1909), p. 1 17. 



8 These tables were originally published by A. Rhind in Biometrika Vol. 7 

 (1910), pp. 126-147 and pp. 386-397. Rhind gives an excellent summary of the 

 whole subject. 



