Excerpt from Graduation of Mortality and Other Tables

Statistics of various kinds for successive calendar years belong to the class of serial statistics. In mortality statistics in particular an analysis of death claims by cause of death would be an example of non-serial statistics, whereas an analysis of the same claims by attained age or by duration of insurance would be an example of serial statistics. Tables of the kind just described showing the relative frequency with which different values of the characteristic used as the basis of analysis appear in a given group of individuals are called frequency distributions.

If the events occur only at isolated values of the variable they may be represented graphically by using the variable as abscissa and erecting ordinates proportionate to the frequencies at those points. Such a diagram would be used, for example, to show how many heads appear in a fixed number of tosses of a coin in a series of such experiments. It is customary to render the outline of the diagram more readily visible by joining the ends of the ordinates by straight lines. If, however, we are tabulating the frequency of a continuously varying quantity, we obtain the number of occurrences corresponding to an interval and not to isolated points. This may be represented graphically by erecting a series of rectangles, each with its respective interval as a base and enclosing an area proportionate to the frequency for that interval. It is usual to assume that if the number of cases oh served were indefinitely increased the frequencies of the successive values would form a continuous series; and the continuous curve drawn through the ends of the ordinates, or such that the ordinate for any value of the characteristic is proportionate to the prob ability oi that value, is known as a frequency curve. Tables of the exposed to risk and of the deaths in a mortality experience, are examples of frequency distributions.

In the examples given above, the range of the possible values of the characteristic is limited in both directions, but in certain cases the range of values may for practical purposes be taken as unlimited. This is especially the case in connection with the statistics of any business enterprise or of a state or country for the successive calendar years, with the additional special feature that at any particular time the complete range of the table cannot by nature of things be known.

About the Publisher

Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com

This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.