Strong Asymmetry and the Mode, Median, and Mean Inequality


  • J. Gama UFMG, Av. Pres. Antônio Carlos, 6627, Belo Horizonte, Brazil
  • C. E. Suárez IMPA, Estrada Dona Castorina 110, Rio de Janeiro, Brazil


skewness, Mode-Median-Mean inequality, Measures of dispersion


This paper introduces the consoled strong asymmetry and variation coefficient as generalizations of the standard measures of Pearson skewness coefficient and variance. Using these new measures, the concept of strong asymmetry is introduced. We prove that the median-mean inequality is valid for that kind of distribution, but even in that case, there is no relation between mode and median. A property similar to first-order stochastic dominance is proved for the variation coefficient. We also discuss the implications of that concept into economics.


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How to Cite

J. Gama, & C. E. Suárez. (2022). Strong Asymmetry and the Mode, Median, and Mean Inequality. American Academic Scientific Research Journal for Engineering, Technology, and Sciences, 90(1), 204–213. Retrieved from