3.12 : Skewness

The measures of central tendency calculated from a data set may not reveal much about its intrinsic distribution. If a plot is made of the data set’s values, the mean and the median may not only differ, but also the plot may have more values on one side of the central tendencies. Such a data set is said to be skewed towards that side.

The longer the tail of the plot on one side, the more skewed it is. The skewness of a data set’s values suggests that the measures of central tendency are somewhat crude, missing out on the finer details. In a symmetrical distribution, the mean, median, and mode are the same, while in an asymmetric distribution or skewed data set, the mean and median lie to the left or right of the mode.

For example, the mean income distribution of a country does not shed much light on its income inequality. While a few wealthiest individuals may earn a lot, the majority of the population may earn abysmally. Therefore, income distribution represents a skewed data set.