A New coefficient of Skewness for grouped data

Abstract

The primary objective of this paper is to introduce a new measure for detecting skewness for grouped data, which is simpler than the current measures in its application. The new proposed coefficient of skewness based on the cumulative frequency data and hence uses more information from the tails of the distribution and thus will be more appropriate to detect asymmetry in the data. Another advantage of the new statistic is that it is bounded by -1 and +1; hence, the coefficients of skewness can be interpreted easily. Simulation study is employed to assess the performance of the proposed coefficient of skewness with three of the classical measure of skewness appeared in the literature using the mean square error (MSE) and mean absolute error (MAE). The simulation study strongly supports the use of the proposed measure for comparing the degrees of skewness of different frequency distributions.