ccviii Tables for Statisticians and Biometricians [XLIII 



Illustration (i). Given the following 21 ordinates spaced at 0*05, find the area 

 of the corresponding curve. 



Z Q = -394,4793 -352,0653 '277,9849 



zi = -391,0427 -342,9439 -266,0852 



2 2 = -386,6681 -333,2246 -254,0591 



z 3 = -381,3878 -322,9724 z v _ 9 * -241,9707 



375,2403 -312,2539 * p _ a = '229,8821 



368,2701 -301,1374 z^ = -217,8522 



360,5270 -289,6916 z 9 =-205,9363 



Here 



2^-20- (z 9 - z 9 _i) = -008,4793, z 2 - ^ - (z 9 _i - z p _ z } = '007,6553, 



z 3 -2 2 - (z p _2 - z v _s) = -006,8083, 

 and .4 C , = -31 5,273,355. 



From the Table for p = 20 trapezettes 



Ci = -163,7782, C z = -123,0418, G 3 = -043,1061 . 

 Hence 



A G -315,273,355 



+ d {(a* - z ) - (z v - z 9 _d\ h + -000,069,436 



- #2 {(z 2 - zi) - (z v _i - z v _ 2 )} It - -000,047,096 

 + C 3 {(z 3 - 2 2 ) - (z v _i - 2 V . 3 )\ h + -000,014,674 



A = -315,310,369 



or, to seven figures = -315,3104, which is the correct value of the area required to 

 those figures. 



Illustration (ii). Let us take alternate ordinates of the above example. Our 

 scheme is now 



z = -394,4793 -342,9439 z v _ 3 = -277,9849 



zi = -386,6681 -322,9724 ^_ 2 = -254,0591 



22 = '375,2403 -301,1374 z^i - -229,8821 



z 3 = -360,5270 z 9 = -205,9363 



and h = 0*1, 



Gi = -179,1068, Cg = -172,2411, G 3 = -085,4119, 

 whence we have 



A c -315,162,300 



+ GI {(zi - ZQ) - (z v - z^)\ h + -000,288,982 



- GI {(z 2 - 2$ - (z^i - Zf-t)} h - -000,219,594 

 + G 3 {(z 3 - zi) - (z 9 . t - 2 V _ 3 )} h + -000,078,686 



A = -315,310,374 



or A = '315,310,374, only a difference in the ninth figure from the previous result. 

 Thus 10 trapezettes would have given as good a result as the 20 originally taken. 



