<P> In probability theory and statistics, skewness is a measure of the asymmetry of the probability distribution of a real - valued random variable about its mean . The skewness value can be positive or negative, or undefined . </P> <P> The qualitative interpretation of the skew is complicated and unintuitive . Skew does not refer to the direction the curve appears to be leaning; in fact, the opposite is true . For a unimodal distribution, negative skew indicates that the tail on the left side of the probability density function is longer or fatter than the right side--it does not distinguish these two kinds of shape . Conversely, positive skew indicates that the tail on the right side is longer or fatter than the left side . In cases where one tail is long but the other tail is fat, skewness does not obey a simple rule . For example, a zero value means that the tails on both sides of the mean balance out overall; this is the case for a symmetric distribution, but is also true for an asymmetric distribution where the asymmetries even out, such as one tail being long but thin, and the other being short but fat . Further, in multimodal distributions and discrete distributions, skewness is also difficult to interpret . Importantly, the skewness does not determine the relationship of mean and median . In cases where it is necessary, data might be transformed to have a normal distribution . </P> <P> Consider the two distributions in the figure just below . Within each graph, the values on the right side of the distribution taper differently from the values on the left side . These tapering sides are called tails, and they provide a visual means to determine which of the two kinds of skewness a distribution has: </P>

When data are skewed to the left the measure of skewness is more likely to be