Editing Skewness (section)

== Introduction ==
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:
# ''{{visible anchor|negative skew}}'': The left tail is longer; the mass of the distribution is concentrated on the right of the figure. The distribution is said to be ''left-skewed'', ''left-tailed'', or ''skewed to the left'', despite the fact that the curve itself appears to be skewed or leaning to the right; ''left'' instead refers to the left tail being drawn out and, often, the mean being skewed to the left of a typical center of the data. A left-skewed distribution usually appears as a ''right-leaning'' curve.<ref name="cnx.org">{{Cite web |last=Illowsky |first=Barbara |last2=Dean |first2=Susan |date=2020-03-27 |title=2.6 Skewness and the Mean, Median, and Mode – Statistics |url=https://openstax.org/books/statistics/pages/2-6-skewness-and-the-mean-median-and-mode |access-date=2022-12-21 |website=[[OpenStax]] |language=en}}</ref>
# ''{{visible anchor|positive skew}}'': The right tail is longer; the mass of the distribution is concentrated on the left of the figure. The distribution is said to be ''right-skewed'', ''right-tailed'', or ''skewed to the right'', despite the fact that the curve itself appears to be skewed or leaning to the left; ''right'' instead refers to the right tail being drawn out and, often, the mean being skewed to the right of a typical center of the data. A right-skewed distribution usually appears as a ''left-leaning'' curve.<ref name="cnx.org" />

[[Image:Negative and positive skew diagrams (English).svg|thumb|left|upright=2]] Skewness in a data series may sometimes be observed not only graphically but by simple inspection of the values. For instance, consider the numeric sequence (49, 50, 51), whose values are evenly distributed around a central value of 50. We can transform this sequence into a negatively skewed distribution by adding a value far below the mean, which is probably a negative [[outlier]], e.g. (40, 49, 50, 51). Therefore, the mean of the sequence becomes 47.5, and the median is 49.5. Based on the formula of [[nonparametric skew]], defined as <math>(\mu - \nu)/\sigma,</math> the skew is negative. Similarly, we can make the sequence positively skewed by adding a value far above the mean, which is probably a positive outlier, e.g. (49, 50, 51, 60), where the mean is 52.5, and the median is 50.5.

As mentioned earlier, a unimodal distribution with zero value of skewness does not imply that this distribution is symmetric necessarily. However, a symmetric unimodal or multimodal distribution always has zero skewness.
[[File:Asymmetric Distribution with Zero Skewness.jpg|434px|thumb|right|Example of an asymmetric distribution with zero skewness. This figure serves as a counterexample that zero skewness does not imply symmetric distribution necessarily. (Skewness was calculated by Pearson's moment coefficient of skewness.)]]