ON LIFE CONTINGENCIES. l63 



Total, 215 + 



Hence 75 individuals, aged 92, enjoy 215 -f- -J- of 75 

 years, and each has, one with another, the 75th part of 

 this, or 3*37 years. 



RULE. To find the mean duration of life from a 

 table of the living at every age out of a given number 

 born, add together the numbers in the table for all the 

 ages above the given age, divide by the number at the 

 given age, and add half a year to the result. 



The preceding rule is mathematically incorrect, being 

 only an approximation to the truth, even supposing the 

 tables perfectly correct. The error of computation 

 may be found, nearly, as follows. Divide the number 

 who die in the year next following the given age by 

 twelve times the number in the table at that age, and 

 diminish the result of the preceding rule by the quotient. 

 Thus, in the instance before us, 21 divided by 12 times 

 75 is -02, so that 3'35 is nearer the truth. This error, 

 however, is immaterial for practical purposes. 



A more important question is that of the degree of 

 confidence which may be placed in tables of mean 

 duration, the errors of observation, being supposed to be 

 as likely to be positive as negative. In order to 

 estimate this, we must compute the mean square of the 

 duration of life ; that is, multiplying the time which 

 each individual lives by itself, we must add the results 

 together and divide by the whole number of individuals. 

 To make a rough approximation to this in the case 

 before us, remember that 



M& 

 <9 



