A look at skewed distributions

Skew (1 of 3)

A distribution is skewed if one of its tails is longer than the other. The first distribution shown has a positive skew. This means that it has a long tail in the positive direction.

 

The distribution below it has a negative skew since it has a long tail in the negative direction. Finally, the third distribution is symmetric and has no skew.


Skew (2 of 3)

Distributions with positive skews are more common than distributions with negative skews. One example is the distribution of income. Most people make under $40,000 a year, but some make quite a bit more with a small number making many millions of dollars per year. The positive tail therefore extends out quite a long way whereas the negative tail stops at zero.

For a more psychological example, a distribution with a positive skew typically results if the time it takes to make a response is measured. The longest response times are usually much longer than typical response times whereas the shortest response times are seldom much less than the typical response time.

Negatively skewed distributions do occur, however. Consider this plot of actual test grades on a statistics test where most students did very well but a few did poorly. It has a large negative skew.

 


Skew (3 of 3)

The effect of skew on the mean and median
skew6a.GIF (2296 bytes)

This distribution has a positive skew. Note that the mean is larger than the median.

skew6b.GIF (2278 bytes)

This distribution has a negative skew. The median is larger than the mean.

Note that the tail of the distribution pulls the mean, as extreme values have a more pronounced effect on the mean than they do on the median.