Ixxii 



Tables for Statisticians and Biometriciatis [XLVIII 



We must interpolate between these two series for n = 79, that is we must take 

 0'42 times the first series and OoS times the secoud series. The results are 

 given below, and set against the direct calculation from formula (Ixxx), using 

 Table XLIX. 





Bj Interpolation. 



Direct Calculation. 





H = 7!), y- = 4, /« = 40 



H = 79, 7; = 4, m = 40 



u 



14-9130 



12^6143 



1 



^ 21-1943 



21 



9379 



3 



19-3642 



22 



5152 



S 



14-7828 



17 



6667 



i 



10-3562 



11 



6727 



5 



6-9472 



6 



8143 



6 



4-.W78 



3 



6137 



7 



2-9529 



1 



7713 



8 



1 -8940 





8118 



9 



1-2004 





3507 



10 



-7489 





1436 



11 



•4582 





0560 



12 



•2740 





0208 



IS 



•1598 





0074 



U 



•0908 





0025 



15 



•0503 



■0008 



16 



•0271 



) 



17 



•0142 



>-0003 



IS aud over 



1 



•0140 



. ) 





The interpolation does not give a result very close to the actual series. For 

 example, not more than three syphilitics might be anticipated in 70 °/^ of samples 

 of 40 by the interpolated series ; actually not more than 3 are to be expected 

 in 75 °/^ of samples. At the same time the result is much better than the 

 normal curve theory provides. In the latter case we have 



Mean = 40 x J^ = 2 025, 



Hence 



Standard-Deviation = ViO x ^ x ^ = 1-387. 

 (3-5 - 2-025)/l-387 = 1-064 



and by Table II this value of *■ corresponds to ^ (1 + a) = -86, i.e. in 86 7o per cent, 

 of samples of 40, we should have not more than 3 cases. It will be seen therefore 

 that (i) the values at the latter end of the Table are not close enough to obtain 

 very accurate results by interpolation, but (ii) that the Gaussian gives a still 

 poorer approximation. 



IllustratioJi (ii). Of 10 patients subjected by a first surgeon to a given 

 operation only one dies. A second surgeon in performing the same operation 

 on 7 patients, presumably equally affected, loses 4 cases. Would it be reason- 

 able to assume the second surgeon had inferior operative skill ? 



