Skewness is a statistical measure that describes the asymmetry of a distribution. It indicates whether the data values are spread more to the left or right of the center. A perfectly symmetrical distribution, such as a normal distribution, has a skewness of zero.
Skewness helps you understand the shape of your data and whether the bulk of the values fall on one side of the mean. It’s especially useful when evaluating whether data meet the assumption of normality in statistical analyses.
Types of Skewness
You can generally identify the presence and type of skewness in a distribution by visually assessing a graph.
Right or Positive
The tail on the right side of the peak is longer. The mean is greater than the median.
Left or Negative
The tail on the left side is longer. The mean is less than the median.
Zero
The distribution is symmetric. The mean and median are roughly equal.
How to Calculate Skewness
There are several formulas to measure skewness. One of the simplest and most intuitive is Pearson’s median skewness. It takes advantage of the fact that the mean and median differ in a skewed distribution.
This formula tells you how many standard deviations separate the mean and the median. A positive value indicates right skew, while a negative value indicates left skew.
Real-world datasets rarely have a Pearson’s median skewness value of exactly zero. If your data has a value close to 0, you can generally consider it symmetric. There is no universal cutoff for “close enough,” but some researchers suggest that values between −0.4 and 0.4 indicate roughly symmetric distributions in large samples.
Skewness Example
A dataset of household incomes shows that most households earn between $30,000 and $70,000, but a few earn over $1 million. The distribution has a long right tail, making it positively skewed. In this case, the mean income is pulled higher than the median due to a few extreme values.
Understanding skewness helps analysts choose appropriate summary statistics and determine whether transformations or nonparametric methods are needed for further analysis.
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