Skewed Distribution


< Probability distributions

A skewed distribution is a type of distribution in which one tail is longer than the other. These distributions are sometimes called asymmetric or asymmetrical distributions as they don’t show any kind of symmetry. Symmetry means that one half of the distribution is a mirror image of the other half. For example, the normal distribution is a symmetric distribution with no skew; The tails are exactly the same.

skewed distribution
Rodolfo Hermans | Wikimedia Commons.

What is Skewness?

Skewness is a measure of the asymmetry of a distribution.

  • A left-skewed distribution (also called a negative skewed distribution) has a long left tail.
  • A right-skewed distribution (also called a positive skewed distribution) has a long right tail.

A left skewed distribution is sometimes called a negatively skewed distribution because it’s long tail is on the negative direction on a number line.

There are two main things that make a distribution skewed left:

  • The mean is to the left of the peak. This is the main definition behind “skewness”, which is technically a measure of the distribution of values around the mean.
  • The tail is longer on the left.

In most cases, the mean is to the left of the peak (or median). This isn’t a reliable test for skewness though, as some distributions (i.e. many multimodal distributions) violate this rule.

It’s important to note that skewness can also be in the positive direction, or to the right. This is called positive skew, or a right skewed distribution. However, this type of skewness is much less common than left skew.

Conclusion

Skewness is an important concept in statistics because it helps us understand data sets that may not appear “normal.” Next time you’re looking at data, see if you can identify any skew!

References

Image: (Godot) at en.wikipedia., CC BY-SA 3.0 https://creativecommons.org/licenses/by-sa/3.0, via Wikimedia Commons