A PROPOSED COEFFICIENT OF SYMMETRY

Most frequency distributions obtained - in practice - from a limited set of readings are asymmetrical to a degree. Several measures of skewness(departure from symmetry) are available in the literature. Probably the most accurate and suitable for general use is the standardized third moment about the mean. In the literature,it is agreed that the third moment will be zero for a symmetric distribution, negative for skewness to the left and positive for skewness to the right. However,the third moment, can equal zero without the distribution being symmetrical. In other words, symmetry can not be expressed in terms of one or two moments - it requires an infinity of them. The proposed coefficient of symmetry presents the solution for this problem. For a distribution, if the proposed coefficient (ks) equals one then the associated distribution is perfectly symmetric. The values of ks less than unity indicate less symmetry.