Types of Skewness

Skewness is classified by the side on which the longer tail lies and, equivalently, by the relative positions of the mean, median and mode.

Symmetric distribution (zero skewness). The two halves balance, the single peak sits at the centre, and the three averages fall at the same point: $\text{Mean} = \text{Median} = \text{Mode}.$ There is no longer tail on either side, so the skewness is $0$.

Positively skewed distribution (right-skewed). A few unusually large values stretch the right tail out. The bulk of the data sits at the lower end, so the mode (the peak) is smallest; the median lies above it; and the mean, pulled up by the large extreme values, is the largest of the three: $\text{Mean} > \text{Median} > \text{Mode}.$ Here the skewness is a positive number. Wage data, where most employees earn modest amounts and a few earn a great deal, are a classic example.

Negatively skewed distribution (left-skewed). A few unusually small values stretch the left tail out. Now the large values are common and the small ones are rare, so the order of the averages reverses: $\text{Mean} < \text{Median} < \text{Mode}.$ The skewness is a negative number. The marks in a very easy test, where most students score high and only a few score low, are typically negatively skewed.

In every skewed distribution the median lies between the mean and the mode, and — as a useful working guide — it lies roughly one-third of the way from the mean to the mode. This is captured by the empirical relationship $\text{Mode} = 3\,\text{Median} - 2\,\text{Mean},$ which holds approximately for a moderately skewed distribution and is used later to recover a value of the mode when only the mean and median are known.

The three shapes can be summarised side by side by the side on which the longer tail lies and the resulting order of the three averages (read left-to-right along the horizontal axis):

| Shape of distribution | Longer tail | Position of the peak (mode) | Order of averages (left → right) | …