506 



Determination of the Modulus of Errors. 



best to take in the neighbourhood of the apparent centre 

 of gravny, that which is obtained from the unreduced dis- 

 continuous data. Between and the highest compartment 



P_j P" 



p 2 



inclusive we must calculate superior limits for the contribution 

 of each compartment upon the principle above employed for 

 the highest compartment ; and for the rest, proceed as before. 

 Suppose, for instance, we are given the number of deaths 

 in each quinquennium after the age of 65 of a certain number 

 of persons who have attained that age, the population being 

 supposed stationary — in short, part of a very imperfect 

 column d x of a life-table. We want to know the constant 

 which governs investigations like the following * : — The mean 

 age-at-death of a certain number of total abstainers being less 

 than the general mean, is the difference accidental or signi- 

 ficant ? 













31 





40 



35-5 





25 





13 



70-75 



75-79 



80-84 



85-89 



90-94 



95-99 



The accompanying figure represents an imperfectly gra- 

 duated column d x . Each of the divisions of the base-line 

 corresponds to a quinquennium, except the one on the extreme 

 left, which is limited to four years in order that the result may 

 be compared with what I have elsewhere given, obtained by a 

 more accurate calculation. The apparent centre of gravity 

 occurs in the third compartment, corresponding to the period 

 75-79. I take for O the left corner of that compartment, and 

 for the unit of length one of the equal divisions of the abscissa. 

 Here ^ = 35*5 ; h 2 =% 31, is a little larger. Hence the maxi- 

 mum distribution is afforded by supposing the highest com- 



* See my paper on "Methods of Determining Rates," Journal of 

 Statistical Society, Jan. 1866, 



