Page:Transactions NZ Institute Volume 29.djvu/80

54 It is not intended in the present investigation to carry these results past age 75, as the available data are insufficient to warrant satisfactory results. It must also be borne in mind that the colony dates from 1840, and the above tables terminate at 1891, consequently all results past age 51 cannot relate to native-born New-Zealanders.

Column $$l_x$$: This column shows how many out of 10,000 born alive reach each year of age up to 75. Thus, $$l_{25}$$ (males) = 8,112, and $$l_{25}$$ (females) = 8,316, or, out of 10,000 males born alive, 8,112 reach the age of 25, and out of 10,000 females born alive 8,316 reach the age of 25.

The two columns $$l_x$$ for males and females are not strictly comparable, for they do not represent the actual numbers born, but only numbers proportional to them. As is well known, the number of male births exceeds the number of female births. The columns show for each sex how, out of 10,000 born, the numbers gradually diminish.

Column $$d_x$$: This colunm shows the deaths each year out of 10,000 born alive. Thus, $$d_{25}$$ (males) = 43, and $$d_{25}$$ (females) = 45, or 43 males die between the ages 25 and 26, and 45 females die between the ages 25 and 26.

Column $$p_x$$: This column gives the probability of living a year at each age. Thus, $$p_{25}$$ (males) = .9947, and $$p_{25}$$ (females) = .9946, or 9,947 males out of 10,000 alive at age 25 survive the year; and 9,946 out of 10,000 females alive at age 25 reach age 26.

Column $$q_x$$: This column gives the probability of dying in a year at each age. Thus, $$q_{25}$$ (males) = .0053, and $$q_{25}$$ (females) = .0054, or 53 males out of 10,000 alive at age 25 die in the year; and 54 out of the same number of females alive at 25 die in the year.

Plates III. and IV. show the results of the life tables graphically. From the column $$l_x$$ it will be observed that the males are reduced to half the number born between the ages 63 and 64, while it is not till between the ages 66 and 67 that the females are similarly reduced.

The whole of the calculation was done in duplicate, and every care has been exercised to insure accuracy. Some of the results have been checked graphically, results true to four significant figures being easily obtained by this process.

In conclusion, I have to express my thanks to my friend, Mr. Morris Fox, A.I.A., Actuary to the Government Life Insurance Department, for his ever-ready and valuable assistance in the preparation of this paper.