# UNIQUENESS OF A MEDIAN OF A BINOMIAL DISTRIBUTION WITH RATIONAL PROBABILITY

@article{Nowakowski2020UNIQUENESSOA, title={UNIQUENESS OF A MEDIAN OF A BINOMIAL DISTRIBUTION WITH RATIONAL PROBABILITY}, author={Szymon Nowakowski}, journal={arXiv: Probability}, year={2020} }

In this paper we show that the median of the binomial distribution $B(n, p)$ is unique for all rational $p$ with the only exception of $p=\frac{1}{2}$ and $n$ odd

## One Citation

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## References

SHOWING 1-10 OF 17 REFERENCES

### The smallest uniform upper bound on the distance between the mean and the median of the binomial and Poisson distributions

- Mathematics
- 1995

### Mean, Median and Mode in Binomial Distributions

- Mathematics
- 1980

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]…

### Mean, median, mode IV

- Mathematics
- 2008

This note continues the discussion about the well‐known mean‐median‐mode inequality (Runnenburg, 1978, van Zwet, 1979, and Dharmadhikari and Joag‐dev, 1983). A discrete analogue of this inequality is…

### Bounds for median and 50 percetage point of binomial and negative binomial distribution

- Mathematics
- 1994

Inequalities for comparing the binomial distribution function/operating characteristic function with value 0.5 have been established long ago. It is a trivial task to infer from these inequalities…

### Mean, Median, and Skew: Correcting a Textbook Rule

- Education
- 2005

Many textbooks teach a rule of thumb stating that the mean is right of the median under right skew, and left of the median under left skew. This rule fails with surprising frequency. It can fail in...

### THE MEAN-MEDIAN-MODE INEQUALITY: COUNTEREXAMPLES

- MathematicsEconometric Theory
- 2005

Let x be a random variable whose first three moments exist. If the density of x is unimodal and positively skewed, then counterexamples are provided which show that the inequality mode ≤ median ≤…

### Mean, median, mode II

- Business
- 1979

Summary In a delightful note Runnenburg [2] has recently discussed the celebrated mean-median-mode inequality. The present note continues this discussion.

### Mean, median, mode

- Business
- 1978

Summary This note is an attempt to avoid doing the same search for the third time. It happened twice in my life that I wished to prove that the median is located between mean and mode for certain…

### Mean, Median, Mode III*

- Mathematics
- 1983

Abstract Recently, Van Zwet (1979) has discussed several conditions under which the celebrated mean‐median‐mode inequality holds. This note points out that Van Zwet's basic condition and its variants…

### Correcting a Textbook Rule

- J. Stat. Educ
- 2005