GRADUATION AND ANALYSIS OF A SICKNESS 



TABLE. 



By W. PALIN ELDERTON, Actuary. 



"The wliole problom of cvolution is a problem in vital statistics — a problem of longevity, of 

 fertility, of hcalth iiiul of disease." Biometnhi, Vol. l. p. 320. 



G7-adiiation by Freqiiency Otirves. 



The Report by thc late William Suttoii tu the Chief Registrar üf Frieiidly 

 Societies in 189G contains between one and two thousand pages of statistics 

 dealiiig with the rates of sickness and mortality experienced by Friendly Societies 

 in Enjjianil and Wales between the years 18.5G and ISSO. Ün pages 1134 — 1151 

 a table of the rates of .sickness for 1876 — 1880 (e.xcluding the fiist three years of 

 menibership) is given which, Professor Peai-son siiggested to nie, iiiight afford an 

 intoresting study in graduation. Some gradiiated figures are given on pages 

 1167 — 1171 of the report but though they are referred to on p. xiv. of the 

 Introduction the metliod by which they were obtained is not described. The 

 ungraduated rates of sickness are obtained by dividing the nunibcr of weeks' sick- 

 ness for the year of age by the nunibcr of pcrsous of the sanie age exposed to the 

 risk of being sick. 



When an attenipt is niade to graduate a rate of sickness or mortality by a 

 fornnila we may consider that we are trying to Ht a curve to the actnal nunibcr of 

 weeks' sickness or deaths on the assumption that the number exposed to risk 

 is unity at each age. Of course, this is an iniaginary State of affairs and there 

 seems little reason for adopting it in prefercnce to taking sonic algebraic or 

 ti-igonometric curve to represent the exposed to risk and theu working on the 

 aniount of sickness or uuinber of deaths obtained from tlic hypothetical series by 

 inultiplyiiig its successive numbers by the ungraduated rates of sickness or 

 mortality for thc appropriate ages ; or, we might adopt the opposite process and 

 assume a curve for the sickness or deaths and graduate the exposed to risk. To 



