2G8 Graditatiou and Auahjsix of a Skkness Table 



7 and a have been found, the table is given below. The normal curves weve 

 obtained by comparing the column of first differences in the table of the integral 

 in Galloway's Probahility with the data to which it was required to fit the 

 curve. The normal curvo was tricd in cach cjxse and when it failed to give a 

 satisfactory representation a Type III. curve was substituted. The work was 

 originally done with four figures and afterwards reduced to three and I made it a 

 rule in finding my curves not to pass a diffurence larger than 30 when the figure 

 in the "f" column was more than 1000, my reason for cboosing the limit being 

 that the Square of the difference divided by the frequency is a measure of the 

 goodness of fit, and I noticed that if each of tliese measurea was about "8 the 

 fit would be ver}- good. As will be seeu from the table most of the differences 

 were considerably smaller ; the two differences entered as 3 for ages 23 and 24 lie 

 between 2'5 and 3 0. The average difference shewn by the table is '9 and this 

 seems good cvidence that though the mothod adopted was tedious it had the 

 raerit of bringing out a satisfactory result. 



I have drawn out the "f" column obtained from the graduated sickness table 

 and the values of the same function for the Manchester Unity table* are also 

 given in the diagram. In order to bring out the connection between the "/" 

 (sickness) and " d" (mortality) columns I have also shewn the " d" column 

 obtained fi-omthe "l" column given on p. 1176 of Sutton's work relating to 10,000 

 living at age 5 and the same column from the English No. IV. table altered .so 

 as to give the same number living at age 5. The analysis of the " f" curve is 

 also given. The ages at the bottom of the diagram are at the ceutre of the 

 groups to which they refer ; so that /so is above age 30 not 30"5. 



We may however view the comparison between the rates of sickness and 

 mortality from the point of view of our sickness graduation and find the curve 

 that will represent the number of deaths if the e.xposed to risk is the same series 

 as that assumed in the sickness gradtiation. Mr Sutton in bis Report gave 

 a table of the ungraduated rates of mortality (from the graduated rates the " d" 

 column referred to above was calculated) obtained from the sanic experience as 

 that from which the sickness rates were found and I applied the method of 

 graduation to theso rates and l'ound that the number of deaths could be represented 



by y=\l\V.) 



X 



■^ (i8-0265 



43-7927J 



having its origin at age 6r9319. To obtain this curve the arcas of the normal 

 curve wci'e multiplied by the corrcsponding values of q^ by Crelle's Tables and 

 not more than three figures were used in the products which were grouped 

 in fives bofore the nioments were calculated. These ahbreviations saved a great 

 deal of labour and though, combined with the irregularity of the data before 

 age 20 and after age 75, they render the gi-aduated rates somcwhat unsatisfactory 

 at the ends of the experience (probably above 87 and undor 12) they would only 



* When these values were calculated it was as.sumed that the value of /i.j„ by the Manchester Unity 

 table was the same as that given by Sutton's Sickness table. Some such assuniption was necessary 

 because Bowser's tables begiu at age 20. 



