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.
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Kaas et al. (1980) studied this question.
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