Properties of the Standard Deviation that are Rarely Mentioned in Classrooms


  • Mohammad Fraiwan Al-Saleh Department of Mathematics, University of Sharjah, UAE
  • Adil Eltayeb Yousif Department of Mathematics and Physics, Qatar University, Qatar



Unlike the mean, the standard deviation ¾ is a vague concept. In this paper, several properties of ¾ are highlighted. These properties include the minimum and the maximum of ¾, its relationship to the mean absolute deviation and the range of the data, its role in Chebyshev’s inequality and the coefficient of variation. The hidden information in the formula itself is extracted. The confusion about the denominator of the sample variance being n ¡ 1 is also addressed. Some properties of the sample mean and variance
of normal data are carefully explained. Pointing out these and other properties in classrooms may have significant effects on the understanding and the retention of the concept.


Al-Saleh, M. F. (2005). On the confusion about the (n ¡ 1)-divisor of the standard deviation. Journal of Probability and Statistical Science, 5, 139-144.

Bland, M. (1995). An Introduction to Medical Statistics. New York: Oxford University Press.

Bluman, A. G. (2007). Elementary Statistics: Step by Step Approach (6th ed.). New York: McGraw Hill.

Heath, D. (1995). An Introduction to Experimental Design and Statistics for Biology. London: CRC Press.

Moore, D., and McCabe, G. (1993). Introduction to the Practice of Statistics. New York: W. H. Freeman and Company.

Samuels, M., andWitmer, J. (1999). Statistics for the Life Sciences. New Jersey: Prentice Hall.

Siegal, A., and Morgan, C. (1996). Statistics and Data Analysis: An Introduction. New York: John Wiley & Sons.



How to Cite

Al-Saleh, M. F., & Yousif, A. E. (2016). Properties of the Standard Deviation that are Rarely Mentioned in Classrooms. Austrian Journal of Statistics, 38(3), 193–202.