I$22.] 



P. C. Mahai^anobis : Analysis of Stature. 



27 



paper was to investigate the full corrections for curtailed blocks of 

 frequency. 



The general shape of our curve showed that there was no 

 significant curtailing, still I thought it advisable to investigate 

 this point more carefully. 



We choose 50 mm, unit of grouping as our standard and find 

 1 raw " moments about one end of range, i.e. 1430 mm. 



Stature in 



Frequency 



mm. 



= y. 



1430-1480 



3 



1530 



5 



1580 



14 



1630 



45 



1680 



60 



1730 



48 



1780 



20 



1830 



3 • 



1880 



2 



Total . . 



200 



Raw Moments are: — 

 "/ = 45250 

 V= 22 '38 

 i/ 3 ' = 118*0262 

 < = 657-4275 



Note. — These lead to the same moments 

 about Mean as obtained from raw moments 

 about. 1655. Hence there is an absolute check 

 on the Arithmetic. 



Instead of working with n{ . n^ . . . (the proportional 

 frequencies), we can work with y l3 y. 2) . . . the actual frequen- 

 cies, and then divide the whole by 200. Thus we get the follow- 

 ing (slightly modified) formulae from p. 233 of the paper cited 

 above. 



«i = - d>o • M l6 3yi - l6 3y 2 + i37y s ~ 6 3y4 + 123/5} 



« 2 = +2^0 -tV( 45yi-i09y 2 + io5y 8 -5iy,+ ioy 5 } 

 «b=-<R>o-i ( Wi- 54?s+ 64V3-34V4.+ 7y 5 } 



<*4= +21)0 { 3y,- iiy 8 + i5y 3 - 9n+ 2 y 5 } 



H = - 2^0 ( y 1 ~ 4y^ + 6y s - 4y 4 + y 5 } 

 and for 6's 



&i = + 2^0 A 1 i37y^ - *6zy P - 1 + ^yjy P - 2 - 63y, - B + I2 y? - *} 



^=-2^0 t 2 ( 45y/>-ioQy^_ 1 + io5y ; ,- 2 -5iy / ,. 3 + ioy ;j _ 4 ) 

 &3 = +2^0 i-( *7y P - 54y^-i+ 64y / ,. 2 -34y^_ 3 + 7y^- 4 l 



^=-2^0 { 3y P - ny P -i+ i5y P -g- 9% -3 + 2y p _. i } 

 & B =+2uo { y P - 4yp-i+ 6y p _ 2 - 4y P -s+ yp-^l 



In our case 



y- = 3, y 2 = 5, y* = *4> y* =45, y E = 6 ° 



yp = 2, y^-i=3, y P -2 = 2o, y p _ 3 = 48, y r ^ = 6o 



