In this paper a more accurate index of asymmetry is studied. Specifically, the use of the left and right variance is proposed and an index of asymmetry based on them is introduced. Several examples demonstrate its usefulness. The question of evaluating more accurately the dispersion of data about the average emerges in all non-symmetric probability distributions. When the population distribution is non-symmetric, the average and variance (or standard deviation) of a set of data do not provide a precise idea of the distribution of the data, especially shape and symmetry. It is argued that the average, the proposed left variance (or left standard deviation) and right variance (or right standard deviation) describe the set of data more accurately.