Skewness is a characteristic associated with probability distributions which measures a distributionâ€™s degree of asymmetry. Under the normal distribution, an equal proportion of the data should be represented on both sides of the distribution curve, thus the curve should be symmetrical. However, sometimes a curve may not be perfectly symmetrical and a larger proportion of data may fall on either of the two sides. This skewness results when the assumptions of a normal distribution are violated and can be both visually and numerically evaluated.

Numerically, the skewness of a distribution can be evaluated because symmetry represents the third moment about the mean. The formula which can be used to measure skewness is as follows^{1}:

Ï’1 = Î¼_{3}/Î¼_{2}^{3/2}

Variables:

Î¼ = the mean of the ith moment

Ï’ = skewness

Visually, the skewness can also be evaluated. For example, using a histogram it is very easy to identify whether a distribution is skewed to the left or to the right. When a distribution is skewed to the left, the result is a distribution which is negatively skewed. Negative skewness results because the mean is less than the mode when the left tail is longer than the right^{2}. On the other hand, a positively skewed distribution is when the right tail is longer than the left and the mean is greater than the mode^{2}.

In statistics, understanding the concept of skewness is important in analyzing the distribution of data. Furthermore, this concept is integral to evaluating whether or not a data set is normally distributed.

Reference:

1. http://mathworld.wolfram.com/Skewness.html

2. http://whatis.techtarget.com/definition/skewness

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