Central limit theorem in a skewed leptokurtic distribution

Nor Aishah Ahad

Abstract

According to the central limit theorem, the distribution of the sample mean is approximately normal if the sample size, n, is sufficiently large, regardless of original data distribution. However there seems to be a difference in opinion on how large n should be. Some books said that n = 25 is sufficient enough while some considered n = 30 to be sufficient. This paper investigates the size of n that would allow us to apply the central limit theorem when samples taken are from a population. Keywords normal, central limit theorem

References

Anderson, T. W. and Slove. S. L. (1974). Introductory Statistical Analysis. Houghton Mifflin Company.

Bluman, A. G. (2007). Elementary Statistics a Step by Step Approach. Sixth Edition. New York: McGraw

Hill.

Chen, L. (1995). Testing the mean of skewed distributions. Journal of the American Statistical

Association, 90, 767-772.

Freund, J. E. and Simon, G. A. (1995) Statistics A First Course. Sixth Edition. New Jersey: Prentice Hall.

Johnson, R. and Kuby, D. (2007). Elementary Statistics. Tenth Edition. Belmont, CA: Thomson

Lovric, M. M. (2007). Note on the correct interpretation of the Central Limit Theorem. Retrieved 24th

May, 2011, from http://www.bmj.com/content/310/6975/298/reply.

Mann, P. S. (2005). Introductory Statistics. Fifth Edition. Noida, India: Wiley.

Milton, J. S. and Arnold, J. C. (2003). Introduction to Probability and Statistics (4th ed.). New York:

McGraw Hill.

Newbold, P., Carlson, W. L. and Thorne, B. (2007). Statistics for Business and Economics (6th ed.). New

Jersey: Pearson Education.

SAS Institute Inc. (1999). SAS /IML User’s Guide version 8. Cary, NC: SAS Institute Inc.

Smith, P. J. (1998). Into Statistics (2nd ed.). Springer.

Smith, Z. R. and Wells, C. S. (2006). CLT and sample size. Paper presented at the annual meeting of the

Northeastern Educational Research Association, Kerhonkson, New York.