Adolphe Quetelet Research Paper

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1. Life And Career

Born in Ghent (Belgium) to a French father and Flemish mother, the young Quetelet started his career as a teacher, and besides his interest in mathematics, he also had artistic talents.

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Quetelet was the first student to obtain a doctorate in 1819 at the newly founded State University of Ghent. In his dissertation he presented a new geometric function called the focal curve. In 1819 he was appointed mathematics professor at the Atheneum in Brussels and in 1820 he was elected to the Academie royale des sciences et des belles-lettres. The academy became the central place from which Quetelet directed all his other activities. In 1823 his scientific orientation took a decisive turn: he proposed the foundation of a new observatory to the Dutch government, and in the same year he was sent to Paris for further preparation of this plan. At the Paris observatory, contacts were established with Laplace, Poisson, and Fourier, and Quetelet’s interests in probability theory and astronomy stem from this short period in France. The construction of the Brussels observatory was completed only in 1832, but in the meantime Quetelet had also become involved in the planning of the 1830 population census.

Unfortunately this census was never completed as a result of the Belgium’s secession from The Netherlands in 1830. But, elected as secretary for life at the Academy in 1834, Quetelet remained in control not only of the activities in meteorology, astronomy, and physical geography located at the observatory, but also of the activities in demography and statistics at the Bureau de Statistique and, from 1841 on, at the Commission centrale de Statistique. The procedures to be used in the new census were tried out first in Brussels in 1842, and the nationwide census took place in October 1846. Both the method of census taking and the subsequent analyses with detailed breakdowns by age and marital status set new standards for similar undertakings in most other European countries. In the meantime Quetelet had gained an international reputation, first by the publication of his Physique Sociale in 1835, in which he brought together his earlier statistical work on demographic subjects, anthropometry, and criminology, and then by his relentless efforts to establish statistics as a new internationally oriented and empirically grounded scientific discipline. The latter was accomplished mainly through organizing a steady succession of international statistics conferences and by inspiring the foundation of statistical societies in other countries.

In 1855, however, Quetelet suffered a major stroke, and from then on his own scientific contribution was seriously reduced. But, until his death in 1874, he continued to inspire statistical applications in a wide variety of fields, and above all, to promote international comparability of statistical information. In Desrosieres’ words (1993, p. 95), ‘Quetelet was the orchestra conductor of 19th Century statistics.’

2. Quetelet’s Contribution To Statistics And Demography

Quetelet’s statistical work was profoundly influenced by early probability theory—particularly the binomial distribution of events with equal odds—and by the use that Laplace had made of the Gaussian bell curve in astronomy. From Laplace he had gained the insight that the binomial distribution could also represent measurement error in astronomical observations, and Quetelet was convinced that this would also hold for measurements in the physical, social, and ‘moral’ domains. In the 1820s, measurements and frequency distributions pertaining to these domains and based on large numbers were still very rare. Quetelet had to use the frequency distribution of the chest circumferences of over 5,000 Scottish recruits to verify his hypothesis that these would conform to the binomial distribution (Hacking 1990, pp. 108–11). In a series of heights of French recruits, however, he detected a deviation from the expected distribution and therefore suspected the presence of systematic errors associated with attempts to avoid conscription. This illustrates how Quetelet used theoretical distributions to assess measurement reliability.

His use of the bell curve led him also into far deeper water: he proposed the notion of l’homme moyen or the average man, of which all members of a given population would be imperfect copies. For Quetelet, and for many after him, the emergence of a bell curve is a strong indication that there must be a link between the individuals producing this particular frequency distribution. Individuals would be drawn as balls from the same urn, and populations would correspond to different urns. The average men, each reconstructed from a different population, would therefore facilitate comparisons between populations, which themselves would be sufficiently homogeneous. Quetelet’s ‘aver-age man’ has often been misunderstood and misused. First, Quetelet was never preoccupied exclusively by averages. Whenever possible he presented complete distributions, and one of his contributions to demography is precisely his systematic presentation of age-specific distributions of vital events or of other occurrences (e.g., crime). This is the beginning of the statistical study of the life cycle. Second, Quetelet would be quite shocked to see his average man being associated with national prejudice, e.g., the stingy Scot, the thrifty Frenchman, … , for the simple reason that these would all be unmeasured attributes. In fact, he perceived his average man as an antidote against statements based on prejudice, anecdote, and impression. It is for this reason that Quetelet can be considered as one of the founding fathers of modern empirical sociology: adequate statistical measurement presupposes operationalization with satisfactory reliability and validity.

The most fundamental critique of the average man came from A. Lexis who discovered that the variances of observed distributions are generally too large to uphold the thesis of balls drawn from the same urn. The hypothesis of a homogeneous population ceased to be tenable, and this would have major consequences for the advancement of statistics and for theories in the biological and social sciences (cf. Desrosieres 1993, 111ff). In present day multivariate analyses we now routinely calculate ‘little average men’ in terms of subgroup means, odds ratios for different subpopulations at risk, and for different combinations of categories of co-variates. Furthermore, these numerous ‘little average men’ are compared and the results are tested for the presence or absence of significant differences.

The use of the bell curve was taken one step further by Quetelet’s younger colleague and professor of mathematics at his alma mater in Ghent. Pierre Francois Verhulst (1804–49) imagined that the growth rate r of a population would evolve according to a normal distribution. The size of a population, or of any other stock, would then follow a logistic curve, i.e. the elongated S-curve, with 50 percent of the total growth corresponding to the maximum of r, and then leveling off toward a saturation plateau. The logistic curve proved to have many applications: later demographic transitions produced population evolutions that very closely resemble the logistic curve, and diffusion processes modeled along the principle of contagion (of rumors, knowledge, disease, technology, etc.) or of competition commonly led to growth curves in accordance with Verhulst’s logistic.

It is rather ironic that Verhulst’s view of this particular form of population change did not feed back into Quetelet’s own demographic work. Quetelet continued to think within the framework of a stationary population. Like several observers before him (e.g., Vauban, Sussmilch), Quetelet had been impressed by the observation that both numbers and distributions of vital events (deaths, births, marriages, ages at marriage, and age differences between spouses) showed a remarkable stability over time. His early work with Smits on the demography of the low countries had convinced him even more. Only major disturbances, such as a revolution, were capable of producing a temporary distortion (cf. his causes constantes et causes accidentelles in the Physique sociale). Quetelet kept thinking in terms of a homeostatic model, in the same way as Malthus had before him.

In his construction of the Belgian life table of 1841–50, centered around the census of 1846 and in his ‘population tables’ (population by age, sex, and marital status simultaneously) of 1850, Quetelet explicitly discusses the properties of a stationary population and shows that the actual age composition ought to be the same as the lx or nLx functions of the life table (lx = number of survivors at each exact age x; nLx = number of person-years lived in the age interval x to x + n). Furthermore, Quetelet goes on to show that the hypothesis of constant mortality could be relaxed (1835 p. 310, 1850 p. 16): ‘the necessary condition for deducing a population table (i.e., an age structure) from a life table is that the deaths by age annually preserve the same ratios [in French: rapports] between them’ (present author’s translation and clarifications).

Quetelet was clearly on the way to show that there exists a neutral mortality decline which does not affect the shape of the age distribution (for the proof see A. J. Coale 1972 pp. 33–6). What Quetelet never developed—probably because there was not yet a need for it in pre-transition Belgium—was the model of a stable population with a growth rate different from zero. Yet, his demographic work shows that he can be considered as an early founding father of the branch of contemporary demography called ‘indirect estimation.’ In this branch extensive use is made of population models (stationary, stable, quasistable), of model life tables, and of the mathematical properties of particular model distributions for detecting and correcting errors in recorded data, and especially for estimating basic demographic parameters of mortality, fertility, and nuptiality on the basis of fragmentary information. Modern historical demography and the demography of developing countries progressed rapidly thanks to these techniques and ways of thinking.

3. Quetelet’s Contribution To Sociology

In contrast to Auguste Comte, Quetelet never developed a general plan for a new social science, and by 1900 many of his ideas had already become outdated (cf. J. Lottin 1912, pp. 391–515). He is, however, highly typical of the beginnings of sociology: there is this new entity, called ‘society,’ that can be studied and analyzed from the outside with objective methods. This entity follows its own ‘laws’ (i.e., patterning, regularities) and these can be detected via statistical methods. At first, Quetelet’s sociology had a deterministic ring, and his distinction between causes constantes and causes accidentelles led straight into the debate pitting collective determinism against individual freedom of action. Quetelet is clearly more impressed by the causes constantes, but in various places in his work he also proposed a solution to the conundrum. In an early letter to Villerme of 1832, for instance, Quetelet writes the following: ‘As a member of society [in French: corps social], the individual experiences at each moment the social requirements [la necessite des causes] and pays them regular tribute; but as an individual he masters these influences [causes] to some extent, modifies their effect and can seek to reach a superior state’ (quoted in Desrosieres 1993, pp. 103–4; present author’s translation). In other words, through socialization the actor becomes an integral part of society, but individual and institutional agency (for Quetelet: the advancement of the sciences) play decisive roles in social change.

For many of his contemporaries the deterministic ring of the Physique Sociale of 1835 continued to be a source of steady criticism, particularly when Quetelet went on with his assertion that the causes accidentelles merely compensate each other. Later on, however, Emile Durkheim viewed the social influence on individuals and the feedback stemming from individual and collective action in very much the same way as Quetelet. Durkheim’s equally holistic view of society, as in his Formes elementaires de la vie religieuse, was directly influenced by Quetelet’s work.

In actual practice, however, Quetelet remains essentially a master of ‘comparative statics’ rather than of ‘social dynamics.’ He paid little attention to the effects of early industrialization (definitely a cause constante) or to the impact of the economic, social, and health crises of the 1840s. This is very surprising for a chief statistician and demographer. The social reform movements, the rise in real wages, and the decline in adult mortality in Belgium since the 1860s also remain without comment. His successors in sociology were much more alert to analyzing the dynamics of the major societal transformations they were witnessing.

4. Contributions To Psychology

Quetelet’s 1835 work on the development of human faculties has also had a major impact on the field of developmental psychology (Baltes 1983, Lindenberger and Baltes 1999). His work is the first effort to consider, based on empirical evidence, the nature of intellectual development from childhood into old age. Treating human-ontogenetic development as a lifelong process is a fairly recent advent in psychology.

Researchers in this field have been drawn to Quetelet’s early efforts in this regard. They have also emphasized that Quetelet in his discussion of methodological issues was able to prefigure some of the issues that are of high significance for modern researchers. Among these are the role of period effects and selective survival.


  1. Academie Royale de Belgique 1997 Actualite et universalite de la pensee scientifique d’Adolphe Quetelet. Classe des sciences, actes du colloque 24–25.10.96, Brussels, Belgium
  2. Baltes P B 1983 Life-span developmental psychology: Observations on history and theory revisited. In: Lerner R M (ed.) Developmental Psychology: Historical and Philosophical Perspectives. Erlbaum, Hillsdale, NJ, pp. 79–111
  3. Coale A J 1972 The Growth and Structure of Human Populations—A Mathematical Investigation. Princeton University Press, Princeton, NJ
  4. Desrosieres A 1993 La politique des grands nombres—Histoire de la raison statistique. Editions la Decouverte, Paris
  5. Hacking I 1990 The Taming of Chance. Cambridge University Press, Cambridge, UK
  6. Lindenberger U, Baltes P B 1999 Die Entwicklungspsychologie der Lebensspanne (Lifespan-Psychologie): Johann Nicolaus Tetens (1736–1807) zu Ehren. Zeitschrift fur Psychologie 207: 299–323
  7. Lottin J 1912 Quetelet, statisticien et sociologue. Institut Superieur de Philosophie, Louvain, France
  8. Mailly E 1875 Essai sur la vie et les ouvrages de L-A-J. Quetelet. Annuaire de l’Academie Royale de Belgique 41: 5–191
  9. Porter T M 1986 The Rise of Statistical Thinking. Princeton University Press, Princeton, NJ
  10. Quetelet A 1832 Sur la possibilite de mesurer l’influence des causes qui modifient les elements sociaux—Lettre a M. De Villerme. Correspondance Mathematique et Publique 7: 321–46
  11. Quetelet A 1833 Recherches sur le penchant au crimes aux differents ages. M. Hayez, Brussels, Belgium
  12. Quetelet A 1835 Sur l’homme et le developpement de ses facultes, ou essai de physique sociale. Editions Bachelier, Paris [2nd edn. 1869 eds C. Muquart, Brussels]
  13. Quetelet A 1847 De l’influence du libre arbitre de l’homme sur les faits sociaux, et particulierement sur le nombre des marriages. Bulletin de la Commission Centrale de Statistique Brussels 2: 135–55
  14. Quetelet A 1846 Lettres a S.A.R. le Duc Regnant de Saxe Cobourg et Gotha, sur la theorie des probabilites, appliquee aux sciences morales et politiques. M. Hayez, Academie Royale, Brussels, Belgium
  15. Quetelet A 1848 Du systeme social et des lois qui le regissent. Guillaumin et Cie, Paris
  16. Quetelet A 1849 Nouvelles tables de mortalite pour la Belgique. Bulletin de la Commission Centrale de Statistique, Brussels 4: 1–22
  17. Quetelet A 1850 Nouvelles tables de population pour la Belgique. Bulletin de la Commission Centrale de Statistique, Brussels 4: 1–24
  18. Stigler S M 1986 The History of Statistics—The Measurement of Uncertainty Before 1900. Belknap Press of Harvard University Press, Cambridge, MA
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