Descriptive Statistics

Skew

Skewness describes the extent to which a distribution is symmetrical or asymmetrical in its shape around the mean. This is best explained with some examples. Consider the histograms below that describe the number of previous purchases for customers of products A, B, and C. The mean and variance are identical for all three distributions. However, skewness is different for the three distributions.

For product A, there is no skew (i.e., the distribution is symmetrical around the mean). That is to say, the left side of the distribution is roughly the mirror image of the right side.

For product B, there is a negative skew. The tail on the left side is more pronounced.

For product C, there is a positive skew. The tail on the right side is more pronounced.

Skewness is quantitative property, and it can be calculated. The skew for product A is -0.06 (i.e., practically zero), the skew for product B is -1, and the skew for product C is 1. Frankly, I don't see these numerical expressions of skewness used very often. It's simply the sign (i.e., positive or negative) that's more often considered, and this conclusion is often reached based on a simple inspection of the histogram.

As I say, strictly speaking the skew of product B is negative and the skew for product C is positive. However, many people get this backwards, calling negative skew a positive skew. In my opinion, it's so common for people to get this backwards that it's difficult to be sure you're communicating accurately with someone. My personal reaction to that problem has been to move away from saying, "The distribution has a negative skew." Instead, I've started saying, "The distribution is skewed, with a longer tail in the lower values." That seems to avoid the problem.