280 PROFESSOR K. PEARSON AND MR. L. N. G. PILON 



Probable Error. Percentage Probable Error. 



p '125659 3-4211 



y -019130 1-7854 



Correlation of errors in i> and y = '9581 

 a -061202 1-7853 



.y,, 'J-8029 -5174 



y l 23-5465 1-3951 



mean = -014600 = '073 year, 



mode = -024126 = '121 year. 



These are the constants which determine the position and algebraical equation to the 

 frequency curve, and we see at once that they are all determined with a close degree 

 of accuracy. The largest percentage probable error is in p, but this is under 

 3 - 5 per cent., and, owing to the high correlation between p and y a much larger 

 error would produce no sensible change in the shape of the curve. 



Two important facts may also be drawn from these results, which indeed follow 

 from the general formulae, namely : 



(i.) The position of the mean is sensibly more exactly determined than the position 

 of the mode. Here about 1'7 times as accurately. 



k/ 



(ii.) The modal frequency, on the other hand, is sensibly more accurate than the 

 mean frequency. Here about 2 - 8 times as accurate. 



Hence the advantage of using the mean as origin of measurement for the curve is 

 accompanied by the counterbalancing, and here relatively greater, disadvantage of 

 the increased inaccuracy of determination of the mean frequency. 



Passing to the "physical" constants of the curve, we have 



Probable Error. Percentage Probable Error. 

 a- -012693 "6291 



Sk. -022815 1-3445 



d -016663 17854 



These fully determine the non-symmetrical nature and spread of the curve, and 

 since the errors in the skewuess and in the distance between the mean and mode are 

 less than 1-4 and 1*8 per cent, of the respective values of these quantities, we 

 conclude that skewness and divergence between mode and mean are characteristic 

 features of enteric lever distribution, and not mere anomalies due to a random 

 selection of cases. They are significant constants peculiar to each type of fever 

 distribution and no description of such a distribution is sufficient unless their values 

 are stated. 



Before giving a table of the correlations between what we have termed the 

 " physical " constants, it may be well to write down some of the correlations between 

 the errors in the physical and algebraical constants, which arise in the course of their 

 calculation. We find 



