ccl Tables for Statisticians and Biometricians 



(a) Halving the Subranges. 



We have, if v denote the area on the half-subrange : 

 g _ 2 . 76 = -^ (256n s _ 2 . 5 437w s _i-5 + 718/i s _. 5 668?i 8+ -5 -f 322 sf i 5 63n 8+2 - 5 ), 



s -i-75 = 2ic( +1937i s _ 1 . 5 -122 8 _. 5 + 88n s+ . 5 - 38 s+1 . 5 + 



s-i-25 = sic ( + 63 /z 8 _i. 5 + 122w 8 _. 5 - 88n g+ - 5 + 38n s+1 . 6 - 7r* 8+2 5 ), 



,_ 75 = OXG ( + 1n,-i-6 + 158w 8 _. 5 - 52r? 8+ . 5 + 18n 8+1 . 5 - 



22n s _. 5 +128n, s+ . 5 - 22-w, s+1 . 5 + 

 . 5 -f 128n g+ . 5 + 22n s+1 . 5 - 

 . 5 + 52n s+ . 6 + 98, +rB - 

 - 3w 8 _ r5 + 18n 8 _. 5 - 52ro,+. 5 + 158w, + i. 5 + 7w 8+2 . 6 ), 

 7w,_ r5 + 38n,_. B - 



+ . 5 - 718n, +1 . B 

 ' 63n,-iv + 322w g _. 5 - 668w 8+ . 5 + 718n -+1 . 6 - 437n 8+2 . 5 + 256n 8+3 - 6 ). 



(b) We have for the areas on the whole subrange round the bounding ordinates 

 of the original areas : 



15n 8 _ r 5 - 420n s _. 5 + 378w g+ . 5 - 180n 8+1 . 6 + 35w 8+2 . 5 ), 

 35n s _ r5 + 140?i 8 _. 6 - 70rc g+ . 5 + 28w 8+1 . 5 - 

 5n t _i. 5 + 60w 8 _. 5 + 90rc g+ . 5 - 20n 8+1 . 5 + 



28n 8 _- 5 - 70n 8+ . 5 + 140n s+1 . 5 + 35n 8f2 - 5 ), 

 . 5 + 378w 8+ . 6 - 420n 8+1 . 5 + 315w g+2 . 5 ). 



By means of the first and last results of (a) and the present results (b), we can 

 redistribute our areas (or frequencies) into terminal half-subranges and inter- 

 mediate whole ranges. 



