Quality and Quantity

, Volume 43, Issue 3, pp 481–493 | Cite as

On measuring skewness and kurtosis

  • Dragan Đorić
  • Emilija Nikolić-Đorić
  • Vesna Jevremović
  • Jovan Mališić
Research Note


The paper considers some properties of measures of asymmetry and peakedness of one dimensional distributions. It points to some misconceptions of the first and the second Pearson coefficients, the measures of asymetry and shape, that frequently occur in introductory textbooks. Also it presents different ways for obtaining the estimated values for the coefficients of skewness and kurtosis and statistical tests which include them.


Skewness Kurtosis Estimates of moments 


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  1. Blest D.C. (2003). A new measure of kurtosis adjusted for skewness. Aust. N. Z. J. Stat. 45: 175–179 CrossRefGoogle Scholar
  2. Byers, R.H.: On the maximum of the standardized fourth moment. Working paper (2000)Google Scholar
  3. Cramer H. (1957). Mathematical Methods of Statistics. Princeton University Press, Seventh Printing, Princeton Google Scholar
  4. D’Agostino R.B., Belanger A. and D’Agostino R.B. (1990). A suggestion for using powerful and informative tests of normality. Am. Stat. 44: 316–321 CrossRefGoogle Scholar
  5. Darlington R.B. (1970). Is kurtosis really ‘peakedness’. Am. Stat. 24: 19–22 CrossRefGoogle Scholar
  6. De Carlo L.T. (1997). On the meaning and use of kurtosis. Psychol. Methods 2: 292–307 CrossRefGoogle Scholar
  7. Dyson F.J. (1943). A note on kurtosis. J. R. Stat. Soc. 106: 360–361 CrossRefGoogle Scholar
  8. Fisher R.A. (1930). The moments of the distribution for normal samples of measures of departures from normality. Proc. R. Soc. London, Series A 130: 16–28 CrossRefGoogle Scholar
  9. Geary R.C. (1947). Testing for normality. Biometrika 34: 209–242 Google Scholar
  10. Gosset W.S. (1927). “Student” Errors of Routine Analysis. Biometrika 19: 151–164 Google Scholar
  11. Hopkins K.D. and Weeks D.L. (1990). Tests for normality and measures of skewness and kurtosis: their place in research reporting. Educ. Psychol. Measure. 50: 717–729 CrossRefGoogle Scholar
  12. Jarque C.M. and Bera A.K. (1987). A test for normality of observations and regression residuals. Int. Stat. Rev. 55: 163–172 CrossRefGoogle Scholar
  13. Kaplansky I. (1945). A common error concerning kurtosis. J. Am. Stat. Assoc. 40: 259 CrossRefGoogle Scholar
  14. Kendall M.G. and Stuart A. (1958). The Advanced Theory of Statistics, vol. 1. Charles Griffin, London Google Scholar
  15. Pearson K. (1895). Contribution to the mathematical theory of evolution, II: Skew variation in homogenous material. Philos. Trans. R. Soc. London 186: 343–414 CrossRefGoogle Scholar
  16. Pearson E.S. and Hartley H.O. (1958). Biometrika Tables for Statisticians, vol. 1. Cambridge University Press, Cambridge Google Scholar
  17. Stoyanov J.M. (1987). Counterexamples in Probability. John Wiley & Sons, New York Google Scholar

Copyright information

© Springer Science + Business Media B.V. 2007

Authors and Affiliations

  • Dragan Đorić
    • 1
  • Emilija Nikolić-Đorić
    • 2
  • Vesna Jevremović
    • 3
  • Jovan Mališić
    • 3
  1. 1.Faculty of Organizational SciencesUniversity of BelgradeBelgradeSerbia
  2. 2.Faculty of AgricultureUniversity of Novi SadNovi SadSerbia
  3. 3.Faculty of MathematicsUniversity of BelgradeBelgradeSerbia

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