☄️ Skewness

Skewness is the property of an observed distribution that indicates absence of specularity with respect to any vertical axis. When the data are evenly distributed on both sides of the central axis, the distribution is symmetrical (e.g., Normal distribution).

Skewness is important to have insight into the shape of the distribution, in order to know whether the observed data predominantly take values below or above the mean value or are approximately symmetrically distributed around the central tendency measure.

For example, in finance, skewness can be useful to a broker or trader in order to know whether the daily returns of a security are more frequently above or below the mean value and whether they tend to arrange themselves symmetrically around the fashion, mean, and median values.

In a positively skewed distribution the longest tail is to the right of the central axis. For this very reason, positive skewness is also called right skewness. Positive asymmetry: Mode<Median<Median.

In a negatively skewed distribution, the tail is longest to the left of the central axis. For this very reason, negative skewness is also called left skewness. Negative asymmetry: Mean<Median<Mode.

A first simple empirical method to detect the presence of skewness is to check whether the median lies approximately in the middle between the first and third quartile values.

A second simple method to detect the presence of skewness is to compare the mean and median values of the variable. In fact, the arithmetic mean always coincides with the median when the center of gravity of the distribution (determined by the mean) corresponds with its central value (determined by the median).

Thus, if the mean value is different from the median value surely there is skewness. However, the fact that the mean coincides with the median is a necessary but not sufficient condition for defining a symmetric distribution.