[Vol. XXIII, 1922.] P. C. Mahalanobis : Analysis of Stature. 15 





te. 



















Group 



CO 





01 



















X 



3 



#;y 



*2-y 



x l'y 



x*'y 



xb-y 



x §-y 



(mm.) 



O 



1 



5 





01 



u 



ft 



II 















1430— 1480.. 



1455 



-4 



3 



— 12 



48 



— 192 



7 68 



-30 72 



I 22 88 



1480— 1530.. 



I505 



~3 



5 



-15 



45 



-135 



4 05 



— 12 15 



36 45 



1530— 1580.. 



1555 



— 2 



H 



-28 



56 



— 112 



2 24 



— 24 48 



8 96 



1580 — 1630 . . 



1 60S 



— 1 



45 



-45 



45 



-45 



45 



-45 



45 



1630— 1680 . . 



1655 







60 



— 100 





-484 





-47 80 





1680 — 1730 . . 



1705 



+ 1 



48 



48 



48 



48 



48 



48 



48 



1730— 1780 .. 



1755 



+ 2 



20 



40 



80 



160 



3 20 



6 40 



12 80 



1780 — 1830 . . 



1805 



+ 3 



3 



9 



27 



81 



2 43 



7 29 



21 87 



1830— 1880.. 



1855 



+4 



2 



8 



32 



128 



5 12 



20 48 



81 92 





• • 



1 



j 

 200 



+ 105 



381 



+ 417 



25 65 



+ 34 65 





TOTAI, . . 



+ 5 



-6 7 



-13 15 



'2 85 81 



Dividing by the total, 200, we get for the " raw' ' moments, 

 S denoting a summation for all groups. 



, c (xy) 



•025 



2 N 



1-905 



, (* 3 y) 



Vq = J) _ T = — 



0*335 



/ c (**y) . 



4 AT 



12-825 



, n (* 6 y) 



5 A7 



6-575 



, (* 6 y) 

 i/ 6 '=s 1 -zj 1 = + 142-905 



The true Mean is given by 



1655 + (-025 x 50) = 1656*15 mm. 

 Transferring * to the true Mean with the help of ; — 



Pi = v 2 



n 



?z = v z -Z v \ v i + 2v i 



'3 



A*4 = l V-4 , 'lV 



+ 6v 1 'V-3»'i 



'4, 



3 T w "] 



/"b = V-5"i V + iov/ V ~ IOl/ i / V + 4"i' 6 - 



1 Karl Pearson : " Contributions to the Mathematical Theory of Evolution — 

 On the Dissection of Asymmetrical Frequency-curves," Phil. Trans. Roy. Soc, 

 Vol. 185 A (1894), p. 71. 



