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 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. 

Please note that the definitions in our statistics encyclopedia are simplified explanations of terms. Our goal is to make the definitions accessible for a broad audience; thus it is possible that some definitions do not adhere entirely to scientific standards.