Westergaard, Harald

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Westergaard, Harald



Harald Ludvig Westergaard (1853–1936), Danish statistician, economist, and social reformer, exerted a strong influence on Danish statistics and social research for many years. He had been interested in pure mathematics from his youth, but after receiving an m.sc. degree in mathematics, he went on to study political economy and statistics.

His first major work was an essay on a subject set by the University of Copenhagen: “Summary and Evaluation of the Recent Studies of the Death Rate in Different Classes of Society.” The paper was much praised and was soon published in German as Die Lehre von der Mortalität und Morbilität (1882). This comprehensive work proved the turning point in Westergaard’s career and was one of the factors that secured him an appointment at the University of Copenhagen. The book attracted favorable notice both in Denmark and abroad and was for many years the standard manual for death-rate statistics. It deals with both theoretical and practical aspects of these statistics and contains a wealth of international statistical facts.

Westergaard’s characteristic and partly original approach appears for the first time in this work. This approach stresses the application of the law of errors—in connection with calculations of demographic frequencies (for example, death rates)—to the study of the appropriateness of the data and, at the same time, discusses the limitations caused by inadequacies in the data. These inadequacies can be exemplified by such insufficiencies in the census data as double counting, delayed recording of births and of deaths among newborns, and missing data on age of illiterates. Throughout his life Westergaard emphasized that for further development of scientific statistics the improvement of mathematical methods was less important than the attempt to procure better data (see, for example, 1916). The mathematical methods used by Westergaard in his 1882 book—for instance, his use of standard errors and of approximations by the normal distribution—were not new, but he was original in the way he adapted well-known principles of probability theory to his discussion of practical statistics.

In 1883 he joined the University of Copenhagen as a lecturer in political science and the theory of statistics, the first to teach the latter subject at the university. He was made professor of political science in 1886, a position he retained until his retirement in 1924.

Westergaard wrote well, and his textbooks in statistics, sociology, and political science were widely used in Denmark and abroad. Die Grund–züge der Theorie der Statistik (1890) developed the fundamental idea of using formal probability theory to analyze practical statistics. He was attracted by the Gaussian normal distribution, and his research was concentrated on demographic fields where this distribution is relevant and reasonable as a basic assumption. Although he was aware of the limitations of this approach, in his textbook on theory he urged the applied statistician to consider whether the absence of normality in a particular case might not simply reflect such inadequacies of the data as those discussed above. The Theorie was severely criticized for being incomplete in its proofs, for implicitly assuming proofs, and for avoiding problems. Westergaard himself recognized the limitations of his principle of making the normal distribution the keystone of all statistical work, but he did little to demonstrate the mathematical reasons for the limitations of this distribution.

In an article published in 1918, “On the Future of Statistics,” Westergaard, largely through an intuitive approach to mathematical statistics, demonstrated great clearsightedness about many problems that were not solved until much later. For example, he urged further work on testing statistical hypotheses from samples. However, the article is also permeated by his partiality toward normal distributions and his contempt for skewed distributions. He believed that the appearance of a nonnormal distribution is evidence of a failure to determine causality and that a closer study of single principal causes is profitable.

After his retirement from the university Westergaard published Contributions to the History of Statistics (1932). A work of lasting value, it remains unique in its wealth of detail and its historical meticulousness. It shows how much statistical knowledge has increased, from its small beginnings in the seventeenth century to its considerable scope at the end of the nineteenth. Westergaard placed great emphasis on the need for causal analysis. In writing about the future of statistics he said: “The great problem in all science is to find the causality, to enable us to trace the causes of a given phenomenon and to foretell coming events, where the causes in action are known” (1918, p. 499); and he sought this kind of analysis in history no less than in statistics.

Westergaard belongs to the generation of Pontus Fahlbeck, and there are striking similarities between them. Two influences were of primary importance for both: first, the work of Quetelet and, second, the rich flow of demographic data that began in the middle of the nineteenth century. At an early stage of their maturity Westergaard and Fahlbeck witnessed the rapid progress made by Galton, Pearson, and others of the English statistical school, who stressed the development of the theoretical aspects of statistics, but neither of them was able to assimilate these modern trends. Instead, their attitude toward these developments was skeptical and negative—although Westergaard was the better informed and the less negative of the two. Faced with an uncongenial intellectual situation, Westergaard took up the historical studies that led to his masterful history of statistics.

In addition to research and teaching, Westergaard was prominent in insurance, banking, and humanitarian activities. A quotation from one of his articles summarizes his philosophy: “Political economy is not solely based on facts and formal logical conclusions; it is closely connected with human interests, and consequently every theory is stamped by its author’s philosophy” (1881, p. 1).

Kai Rander Buch

[Directly related are the entriesMortality; Statistics.]


1881 Spørgsmaalet om alderdomsforsørgelse. National–økonomisk tidsskrift 18:1–30. → The extract in the text was translated by Kai Rander Buch.

(1882) 1901 Die Lehre von der Mortalität und Morbilität. 2d ed. Jena (Germany): Fischer.

1890 Die Grundzüge der Theorie der Statistik. Jena (Germany): Fischer.

1916 Scope and Method of Statistics. American Statistical Association, Publications 15:225–276.

1918 On the Future of Statistics. Journal of the Royal Statistical Society 81:499–520.

1932 Contributions to the History of Statistics. London:King.


Fortegnelse over et udvalg af Professor Harald Westergaards skrifter. 1937 National0konomisk tidsskrift 75:246–261.

Harald Westergaard. 1937 Journal of the Royal Statistical Society 100:149–150.

Harald Westergaard. 1943 Volume 25, pages 403–412 in Dansk biografisk leksikon. Copenhagen: Schultz.

Nybølle, Hans C. 1937 Harald Westergaard: 19. April 1853–13. December 1936. Copenhagen, Universitet, Festskrift udg. af Københavns Universitet i anledning af universitets aarfest.[1937]: 136–144.

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