<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> 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>
when skew is equal to zero a distribution is said to be
when skew is equal to zero a distribution is said to be
symmetric
symmetric