XC1V 



Tables for Statisticians and Biometricians 



[XIV 



(a) Let us find fa, fa, fa and fa from Table XIV. It is not needful to find the 

 $'s with extreme accuracy and therefore the hyperbolic interpolation equation will 

 suffice. 



= -33412, = -66588, ^ = -48825, i/r = -51175, 

 <f = -340,764, </>x = -325,1 16, 6ty = -170,986, 6^ = -163,134. 



& 



%)= 11*84156, Z(a= 12-41053, 2 10 = 12*45475, z n = 13'04962, 

 hence fa = z ex = 12*328,464. 



The exact value calculated from equation (i) is 12*333,049, but the difference is 

 of little importance, when the ft's are to be substituted in probable error formulae. 



For/3 4 



2oo = 46*67828, 2 01 = 50-67464, 2 10 = 45-11667, z n = 48*92245, 

 hence fa = z ex = 48'076,648. 



For/3 5 



2oo=188*48207, 2 01 = 213*91770, * M = 184-62341, z n = 208-87083, 

 hence fa= 199*417,923. 



^00 = 859-71417, 2oi=1029*10666, 2 10 = 76376288, z n = 908-47666, 

 hence fa = 906-334,872. 



We can compare the values to two decimal places of results obtained by hyper- 

 bolic interpolation from Table XIV with the exact values from equations (i). 



From Table From Equations 

 fa 12-33 12-33 



fa 48-08 48-03 



fa 199-42 199-08 



fa 906-33 900-47 



Second differences of the /3's are at this point of the Table considerable, and 

 the accordance between the values from Table and Equations would have been 

 closer, had they been used. At the same time the agreement is adequate for most 

 statistical purposes. 



