A Simple Class of Measures of Skewness

In this paper, a simple class of measures for detecting skewness in samples is introduced. The new class of measures is based on a new definition of skewness that takes midrange into consideration. The proposed coefficients of skewness can be computed easily with only three of the summary statistics, i.e., the minimum value, the maximum value and the median (or the mode, or the mean). Another advantage of the new statistics is that they are bounded by -1 and +1, hence, the coefficients of skewness can be interpreted easily. The powers of the proposed statistics to detect skewness are investigated by a limited Monte Carlo simulation in order to have an idea. The preliminary results indicate that the performances of the new statistics look generally good in a limited simulation. However, a more comprehensive investigation is needed