Definition Skewness

Skewness is a measure of the symmetry of a distribution. The highest point of a distribution is its mode. The mode marks the response value on the x-axis that occurs with the highest probability. A distribution is skewed if the tail on one side of the mode is fatter or longer than on the other: it is asymmetrical.

In an asymmetrical distribution a negative skew indicates that the tail on the left side is longer than on the right side (left-skewed), conversely a positive skew indicates the tail on the right side is longer than on the left (right-skewed). Asymmetric distributions can occur when extreme values lead to a distortion of the normal distribution.

An example: There a 100 families living in a small town in Spain. 90 families have a common family income, which lies around an average of €1,300. If we were to draw a distribution of these 90 incomes, the mode would also be at around €1,300. The interpretation of this would be that the income value of €1,300 occurs with the highest probability. Now we add 10 more families who are building a vacation home in our small Spanish town. Their monthly income lies between €8,000 and €15,000, which is significantly higher than the town average. In this case, the distribution of all 100 families would turn out to have a positive skew. The mean moves to the right, away from the mode and not stands around €2,200. The distribution is skewed to the right now.