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Mean, Median and Mode in Binomial Distributions

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  • R. Kaas
  • J.M. Buhrman

Abstract

Summary While studying the median of the binomial distribution we discovered that the mean median‐mode inequality, recently discussed in. Statistics Neerlandica by Runnen‐burg 141 and Van Zwet [7] for continuous distributions, does not hold for the binomial distribution. If the mean is an integer, then mean = median = mode. In theorem 1 a sufficient condition is given for mode = median = rounded mean. If median and mode differ, the mean lies in between.

Suggested Citation

  • R. Kaas & J.M. Buhrman, 1980. "Mean, Median and Mode in Binomial Distributions," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 34(1), pages 13-18, March.
    • Handle: RePEc:bla:stanee:v:34:y:1980:i:1:p:13-18
    DOI: 10.1111/j.1467-9574.1980.tb00681.x
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    Cited by:

    1. Philipp an de Meulen & Christian Bredemeier, 2012. "A Political Winner’s Curse: Why Preventive Policies Pass Parliament so Narrowly," Ruhr Economic Papers 0336, Rheinisch-Westfälisches Institut für Wirtschaftsforschung, Ruhr-Universität Bochum, Universität Dortmund, Universität Duisburg-Essen.
    2. repec:zbw:rwirep:0336 is not listed on IDEAS
    3. Narayanaswamy Balakrishnan & Efe A. Ok & Pietro Ortoleva, 2021. "Inferential Choice Theory," Working Papers 2021-60, Princeton University. Economics Department..
    4. Doerr, Benjamin, 2018. "An elementary analysis of the probability that a binomial random variable exceeds its expectation," Statistics & Probability Letters, Elsevier, vol. 139(C), pages 67-74.
    5. Baland, Jean-Marie & Somanathan, Rohini & Wahhaj, Zaki, 2013. "Repayment incentives and the distribution of gains from group lending," Journal of Development Economics, Elsevier, vol. 105(C), pages 131-139.
    6. Hamza, Kais, 1995. "The smallest uniform upper bound on the distance between the mean and the median of the binomial and Poisson distributions," Statistics & Probability Letters, Elsevier, vol. 23(1), pages 21-25, April.
    7. Sundararajan, Mukund & Yan, Qiqi, 2020. "Robust mechanisms for risk-averse sellers," Games and Economic Behavior, Elsevier, vol. 124(C), pages 644-658.
    8. Mariusz Bieniek & Luiza Pańczyk, 2023. "On the choice of the optimal single order statistic in quantile estimation," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 75(2), pages 303-333, April.
    9. an de Meulen, Philipp & Bredemeier, Christian, 2012. "A Political Winner's Curse: Why Preventive Policies Pass Parliament so Narrowly," Ruhr Economic Papers 336, RWI - Leibniz-Institut für Wirtschaftsforschung, Ruhr-University Bochum, TU Dortmund University, University of Duisburg-Essen.
    10. Bethmann, Dirk, 2018. "An improvement to Jensen’s inequality and its application to mating market clearing when paternity is uncertain," Mathematical Social Sciences, Elsevier, vol. 91(C), pages 71-74.
    11. Janson, Svante, 2021. "On the probability that a binomial variable is at most its expectation," Statistics & Probability Letters, Elsevier, vol. 171(C).

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