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Original Articles

Mean, Median, and Skew: Correcting a Textbook Rule

References

Theoretical literature

  • Ageel, M.I. (2000), “The Mean-Median-Mode Inequality for Discrete Unimodal Probability Measure,” Far East Journal of Mathematical Sciences, 2, 187–192.
  • Cytel Software Corporation (2004), “StatXact Example 3: FDA Animal Toxicology Data Yields Sky-Scraper Distribution for Stratified Trend Test,” Accessed 18 February 2004. Available at www.cytel.com/StatXact/example_03.asp
  • Dharmadhikari, S.W., and Joag-dev, K. (1983), “Mean, Median, Mode III,” Statistica Neerlandica, 33, 165–168.
  • Dharmadhikari, S.W., and Joag-dev, K. (1988), Unimodality, Convexity, and Applications, Boston: Academic Press.
  • Dudewicz, E.J., and Mishra, S.N. (1988), Modern Mathematical Statistics, New York: Wiley.
  • Dyson, J.E., and Williams, D.A. (1997), The Physics of the Interstellar Medium, Bristol, UK: Institute of Physics.
  • Groeneveld, R.A. (1986), “Skewness for the Weibull Family,” Statistica Neerlandica, 40, 135–140.
  • Groeneveld, R.A. (1991), “An Influence Function Approach to Describing the Skewness of a Distribution,” The American Statistician, 45, 97–102
  • Groeneveld, R.A., and Meeden, G. (1977), “The Mode, Median, and Mean Inequality,” The American Statistician 31 (3), 120–121.
  • MacGillivray, H.L. (1981), “The Mean, Median, Mode Inequality and Skewness for a Class of Densities,” Australian Journal of Statistics, 23 (2), 247–250.
  • Silverman, B.W. (1986), Density Estimation for Statistics and Data Analysis, London: Chapman and Hall.
  • Zwet, W.R. van (1979), “Mean, Median, Mode II,” Statistica Neerlandica, 33, 1–5.

Textbooks for introductory data analysis

13 textbooks that teach the relationship between skew, median, and mean

  • Agresti, A., and Finlay, B. (1997), Statistical Methods for the Social Sciences, 3rd ed., Upper Saddle River, NJ: Prentice Hall.
  • Bartz, A.E. (1999), Basic Statistical Concepts, 4th ed., Upper Saddle River, NJ: Prentice Hall.
  • Frankfort-Nachmias, C., and Leon-Guerrerro. (2002), Social Statistics for a Diverse Society, 3rd ed., Thousand Oaks, CA: Pine Forge.
  • Freund, J.E. (2004), Modern Elementary Statistics, Upper Saddle River, NJ: Pearson Prentice Hall.
  • Gravetter, F.J., and Wallnau, L.B. (2000), Statistics for the Behavioral Sciences, 5th ed., Belmont, CA: Wadsworth.
  • Kendrick, J.R. (2005), Social Statistics: An Introduction Using SPSS for Windows, Boston: Pearson.
  • Knoke, D., Bohrnstedt, G.W., and Mee, A.P. (2002), Statistics for Social Data Analysis, 4th ed., Itasca, IL: Peacock.
  • Levin, J., and Fox, J.A. (2003), Elementary Statistics in Social Research, 9th ed., Boston: Allyn and Bacon.
  • Levin, J., and Fox, J.A. (2004), Elementary Statistics in Social Research: The Essentials, Boston: Allyn and Bacon.
  • Maxwell, N. (2004), Data Matters: Conceptual Statistics for a Random World, Emeryville, CA: Key College Publishing.
  • Moore, D.S. (2000), The Basic Practice of Statistics, 2nd ed., New York: Freeman.
  • Moore, D.S., and McCabe, G.P. (2003), Introduction to the Practice of Statistics, 4th ed., New York: Freeman.
  • Ritchey, F. (2000), The Statistical Imagination: Elementary Statistics for the Social Sciences, Boston: McGraw-Hill.
  • Thorne, B.M., and Giessen, J.M. (2000), Statistics for the Behavioral Sciences, 3rd ed., Mountain View, CA: Mayfield.

4 textbooks that do not teach the relationship

  • Aron, A., and Aron, E.N. (2002), Statistics for the Behavioral and Social Sciences: A Brief Course, 2nd ed., Upper Saddle River, NJ: Prentice Hall.
  • Berry, D.A. (1996), Statistics: a Bayesian Perspective, Belmont, CA: Wadsworth.
  • Sweet, S.A., and Grace-Martin, K. (19xx), Data Analysis with SPSS: A First Course in Applied Statistics, 2nd ed., Boston: Allyn and Bacon.
  • Watkins, A.E., Scheaffer, R.L., Cobb, G.W. (2004), Statistics in Action: Understanding a World of Data, Emeryville, CA: Key College Publishing.

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