Abstract
The quincunx was invented by Sir Francis Galton in 1873 to demonstrate binomial distributions. During the last 125 years it has been used to illustrate the laws of the binomial and the normal distribution. In the first part of this paper we describe the historical background of Galtons invention and take a look at the discoveries he got from it. The second part of this paper discusses the mathematical background of the quincunx. We discuss the various limit theorems which explain the phenomena observable by this apparatus.1
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Darwin, Charles (1859): The Origin of Species by Means of Natural Selection or the Preservation of Favoured Races in the Struggle for Life. New York Library, New York.
David, F. N. (1987): Galton, Francis. In: Kruskal, William H. and Judith M. Tanur (eds.): International Encyclopedia of Statistics (vol. 1). The Free Press — Macmillan, New York.
Galton, Francis (1869): Hereditary Genius: An Inquiry into its Laws and Consequences. Macmillan, London.
Galton, Francis (1874): On a proposed statistical scale. Nature, 9, 342–343.
Galton, Francis (1875): Statistics by intercomparison, with remarks on the law of frequency of errors. Philosophical Magazine, fth series, 49, 33–46.
Galton, Francis (1877): Typical laws of heredity. Proceedings of the Royal Institution of Great Britain, 8, 282–301.
Galton, Francis (1889): Natural Inheritance. Macmillan, London.
Galton, Francis (1908): Memories of my life. Macmillan, London.
Gnedenko, B. V. (1968): The Theory of Probability, 4. edn. Chelsea Publishing Company, New York.
Kendall, Maurice and Alan Stuart (1969): The Advanced Theory of Statistics, vol. 1: Distribution Theory, 3. edn. Charles Griffin, London.
Kunert, Joachim, Astrid Montag and Sigrid Pöhlmann (2000): Das Galtonbrett und die Glockenkurve. In: Link, Jurgen und Ute Gerhard (eds.): Flexibler Normalismus und Orientierung mittels “Kurvenlandschaften”: Fälle und Modelle (working title). Synchron Wissenschaftsverlag der Autoren, Heidelberg, (in preparation)
Mises, Richard von (1931): Vorlesungen aus dem Gebiet der angewandten Mathematik, I. Band: Wahrscheinlichkeitsrechnung und ihre Anwendung in der Statistik und Theoretischen Physik. Deuticke, Leipzig.
Mises, Richard von (1964): Mathematical Theory of Probability and Statistics (Ed. by H. Geiringer). Academic Press, New York.
Pearson, Karl (1895): Contributions to the Mathematical Theory of Evolution II. Philosophical Transaction of the Royal Society, A186. Royal Society, London, 343–414 and 7 plates.
Pearson, Karl (1914-1930): The Life, Letters and Labours of Francis Galton (3 vols, in 4 parts). Cambridge University Press, Cambridge.
Posten, Harry O. (1986): Quincunx. In: Kotz, S. and N. Johnson (eds.): Encyclopedia of Statistical Science (vol. 7). Wiley, New York.
Serfling, Robert (1980): Approximation Theorems of Mathematical Statistics. Wiley, New York.
Stigler, Stephen (1986): The History of Statistics. The Belknap Press of Harvard University Press, Cambridge.
Stigler, Stephen (1989): Francis Galtons Account of the Invention of Correlation. Statistical Science, 4/2. Institute of Mathematical Statistics, Hayward, California, 73–86.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Kunert, J., Montag, A. & Pöhlmann, S. The quincunx: history and mathematics. Statistical Papers 42, 143–169 (2001). https://doi.org/10.1007/s003620100048
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/s003620100048