## Skewness |

In **skewness** is a measure of the asymmetry of the

For a *tail* is on the left side of the distribution, and positive skew indicates that the tail is on the right. 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 can also be true for an asymmetric distribution where one tail is long and thin, and the other is short but fat.

- introduction
- relationship of mean and median
- definition
- applications
- other measures of skewness
- see also
- references
- external links

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:

*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.^{[1]}*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.^{[1]}

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