LIFE, MEAN DURATION OF. By this term is meant the average length of life enjoyed by a given number of persons of the same age. . Suppose we look at the Northampton table of mortality, we find that, of 3,63'persons aged 40, 3,559 reach 41, 3,482 reach 42, and so on, the whole failing at ninety-six. The average age, then, attained by the 3,635 persons tieing ascertained on these data would be the mean duration of life after the age of forty has been reached. Suppose, then, that a be the given number alive at a given age by a given mortality table, and b the number alive at the end of the first year, c the number alive at the end of the second, and so on; then there die at the end of the first year, a —b ; and assuming that those who have died have, on an average, lived half a year, the aggregate length of life enjoyed by those who have died the first year will be years; then b being still alive, the a persons have enjoyed, at the end of the first year, b = b) years. In the second year, the a persons enjoy (b c); in the third, the c persons enjoy (c d) and so on. Summing these,
and dividing by the original number of lives, so as to ascertain the average, gives b hence the role: Add the numbers alive at each age above that given, divide a by the number alive at the given age, and add half a year. The mean duration of life at a given age is often called. the "expectation of life;" but this is clearly a wrong term to use. Of 1000 lives at twenty, suppose 500 to reach forty-five; then a man aged twenty has an equal chance of reaching forty-five, and twenty-five years would be his expecta tion of life. But it clearly does not follow that taking the 500 who have not reached twenty-five, along with the 500 who have survived it, we should find, on extinction of the whole, that the mean duration was twenty-five years. It might be either greater or less. The term "expectation of life," as generally applied by assurance companies to denote mean duration, is, therefore, a wrong one. In convection with this subject, see MORTALITY; also MAN.