# The Theory of the Construction of Tables of Mortality and of Similar Statistical Tables in Use by the Actuary; A Course of Lectures

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This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1909 edition. Excerpt: ...ordinates than by means of groups or areas. The formula to 4th differences is ux---= + nearly, and in order that the resulting 4th moment should agree exactly with that obtained from the use of the grouped figures, or areas, with Sheppard's corrections, the 4th difference is required, but for practical purposes it is not often needed. The use of the central ordinates of the groups has the incidental advantage, which is very considerable in the case of a mortality or similar experience, of giving trustworthy values of the force of mortality, or corresponding function, for the ages corresponding to the position of the ordinates. In the usual plan of summarizing a mortality table by giving the numbers at risk and deaths in consecutive age groups, the ratio of the deaths to the numbers at risk in each group is not a useful function, as it does not correctly represent the mortality for the central age, except near the middle of the table, where the numbers under observation in successive years is nearly constant. We may apply this method to the example already dealt with on p. 55, viz., the experience of ascending premium policies. The calculations as set out in the following tabular form are sufficiently clear: Table X. Mortality experience of lives assured by ascending Premiums, 1863-1893. Duration 10 years and upwards. Taking 5 years as the unit, computing by formula ux--ux represents the number in columns (3) and (4). By this formula there are--11 persons exposed to risk at age 22'5; these have been included in the group 25-30. If the values of the moments are computed from columns exactly as was done with the Binomial Curve (Table VIII, p. 53) they will be found to be practically identical with those found above. The estimated values of fix for...