Abstract

This paper studies the mean of the probability distribution of the sample-standard-deviation for all populations, numerically by examples in the main, but followed by analytical summary observations. We find that in applications for sample sizes greater than 20 one is likely to achieve ((E(s))/sigma) greater 0.9 and that the deciding factor of ((E(s))/sigma) is the concentration of mass in the population: a higher concentration of data in the population leads to a smaller ((E(s))/sigma) than otherwise.

Citation details of the article

Journal: International Journal of Applied Mathematics
Journal ISSN (Print): ISSN 1311-1728
Journal ISSN (Electronic): ISSN 1314-8060
Volume: 31
Issue: 3
Year: 2018

DOI: 10.12732/ijam.v31i3.5

Download Section

Download the full text of article from here.

You will need Adobe Acrobat reader. For more information and free download of the reader, please follow this link.

References

1. [1] S.A. Book, Why n-1 in the formula for the sample standard deviation? The Two-Year College Math. J., 10 (1979), 330-333.
2. [2] H. Chen, Comparisons of lognormal population means, Proc. Amer. Math. Soc., 121 (1994), 915-924.
3. [3] E. Cho, M.J. Cho, Variance of sample variance, Amer. Stat. Assoc. Joint Statistical Meetings Section on Research Methods (2008), 1291-1293.
4. [4] F.M. Hossain, A. Shams, M. Arif, A.H. Joarder, Shorter variation of standard deviation for small sample, Int. J. Mathematical Education in Science and Technology, 45 (2014), 311-316.
5. [5] N.H. Wasserman, S. Casey, J. Champion, M. Huey, Statistics as unbiased estimators: exploring the teaching of standard deviation, Research in Mathematics Education, 19 (2017), 236-256.