Qual Quant (2009) 43:481–493 DOI 10.1007/s11135-007-9128-9 RESEARCH NOTE On measuring skewness and kurtosis Dragan - Dori´ c · Emilija Nikoli´ c- - Dori´ c · Vesna Jevremovi´ c · Jovan Mališi´ c Received: 1 August 2006 / Accepted: 1 March 2007 / Published online: 20 September 2007 © Springer Science + Business Media B.V. 2007 Abstract The paper considers some properties of measures of asymmetry and peaked- ness 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. Keywords Skewness · Kurtosis · Estimates of moments 1 Introduction The normal (Gaussian) distribution is one of the most frequently used distribution in sta- tistics. The importance and spread of the normal distribution are due to the central limit theorem which states that the sum of n independent identically distributed random variables with finite mean m and variance σ 2 is asymptotically normal, as n →∞. However, we often deal with small samples with sampling distributions other than normal, and hence the central limit theorem cannot be applied. There are some authors, like Gery (1947), who claim that normal distribution is just a myth. On occasion when we cannot assume that data are normally distributed, we have to mea- sure the magnitude of deviation of the sampling distribution from the normal distribution. This can be achieved by measuring skewness and kurtosis. The coefficient of skewness shows asymmetry of one dimensional distributions, and can be calculated on a basis of the first three D. - Dori´ c(B ) Faculty of Organizational Sciences, University of Belgrade, Jove Ilica 154, 11000 Belgrade, Serbia e-mail: djoricd@fon.bg.ac.yu E. Nikoli´ c-- Dori´ c Faculty of Agriculture, University of Novi Sad, Novi Sad, Serbia e-mail: emily@polj.ns.ac.yu V. Jevremovi´ c · J. Mališi´ c Faculty of Mathematics, University of Belgrade, Belgrade, Serbia 123