Wilhelm Lexis: The Normal Length of Life as an Expression of the “Nature of Things”

By Jacques Véron, Jean-Marc Rohrbasser


At the first International Congress of Demography held in Paris in 1878, the German statistician Wilhelm Lexis argued for the notion of a normal length of human life governed by a law of nature. His conception was based on Quetelet’s “average man” and the law of normal distribution of errors formulated by Laplace and Gauss.
The normal length of life, which differs from the average length of life, is, according to Lexis, a “true value” characteristic of the mortality of the human species.
Lexis classifies ages at death into three groups, of which the most important is “the normal group”. He seeks to define its boundaries by distinguishing normal deaths from “premature” ones. Normal mortality is then described by three values: normal age at death, the proportion of deaths included in the normal group, and probable error.
The discussions generated by Lexis’s paper, most notably Bertillon’s remarks on infant mortality, reveal distinct perceptions of the mortality process. A few years later, specialists such as Bodio, Perozzo, Levasseur, and Pareto took up the theory and method of Lexis, acknowledging the originality of his mathematical and statistical analysis of mortality, though not endorsing his hypothesis of a law of nature.

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