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The employment of interpolation in statistics*

Published online by Cambridge University Press:  18 August 2016

Harald Westergaard
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Extract

[After some interesting preliminary remarks on the subject of statistics generally, and the utility of interpolation in their preparation, Professor Westergaard points out that in vital statistics the enumeration of the population at each year of age is seldom wanted, and, in fact, owing to the well known exaggeration in census returns of the numbers living at decennial ages, an adjustment is generally needed. He then proceeds:] The decennial reports by the English Registrar-General of births, deaths and marriages, contain full materials for the study of the mortality of professional men. The report published in 1875 gives a very detailed classification of ages, but it is not so with the next decennial report, which divides the ages into five periods only—15–20, 20–25, 25–45, 45–65, 65 and upwards.

Type
Research Article
Information
Journal of the Institute of Actuaries , Volume 32 , Issue 4 , January 1896 , pp. 276 - 286
Copyright
Copyright © Institute and Faculty of Actuaries 1896

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References

page 277 note * [The function designated by Professor Westergaard as“Mortality Coefficient” appears to correspond with our “Central Death Rate.”—ED. J.I.A.]

page 277 note † [J.I.A., xiv, 28.]

page 278 note * There appears to be some miscalculation in the numbers here given. By Newton's formula (to third differences) the numbers are respectively y35 =8,434, y 55=4,170, y 75=444.—D. A. B.

page 279 note * [It would be interesting to compare Professor Westergaard's suggested method with that adopted by Mr. G. F. Hardy, and mentioned in Ms paper on “The Rates of Mortality among the Natives of India” (J.I.A., xxx, 229).—ED. J.I.A.]

page 279 note † [It is not apparent that any advantage is gained by the use of this function (ax ). The direct interpolation of zx (or zx —1) would be the more obvious course. In Table III a column giving the figures by this method is added, from which it appears that the results are somewhat more satisfactory.—ED, J.I.A.]