Skewness And Kurtosis. Skewness is a measure of symmetry or more precisely the lack of symmetry. A distribution or data set is symmetric if it looks the same to the left and right of the center point.
If skewness is not close to zero then your data set is not normally distributed. Now let s look at the definitions of these numerical measures. Skewness tells you the amount and direction of skew departure from horizontal symmetry and kurtosis tells you how tall and sharp the central peak is relative to a standard bell curve.
Kurtosis is descriptive or summary statistics and describes peakedness and frequency of extreme values in a distribution.
Another less common measures are the skewness third moment and the kurtosis fourth moment. So we can conclude from the above discussions that the horizontal push or pull distortion of a normal distribution curve gets captured by the skewness measure and the vertical push or pull distortion gets captured by the kurtosis measure. It is the degree of distortion from the symmetrical bell curve or the normal distribution. It differentiates extreme values in one versus the other tail.
