Calculate sample skewness and Pearson skewness with formulas and step-by-step work
Skewness measures the asymmetry of a distribution. This calculator helps answer common searches such as how to calculate skewness, calculating skewness from raw data, and interpreting whether a data set is right-skewed, left-skewed, or approximately symmetric.
Skewness is a measure of the asymmetry of the probability distribution of a real-valued random variable about its mean. It tells us the direction and relative magnitude of the deviation from symmetry.
To calculate skewness manually, list the data values, compute the mean, find each deviation from the mean, standardize those deviations by the standard deviation, cube them, and combine them with the sample skewness correction. The result is positive for a long right tail and negative for a long left tail.
Right tail longer, mean > median > mode
Left tail longer, mean < median < mode
Zero skew, mean = median = mode
Complements mean and standard deviation
| Skewness Value | Distribution Shape | Meaning |
|---|---|---|
| -0.5 to 0.5 | Approximately symmetric | Mean and median are usually close. |
| 0.5 to 1 | Moderately right-skewed | The right tail is longer; high outliers may pull the mean upward. |
| > 1 | Highly right-skewed | Large positive outliers strongly affect the distribution. |
| -1 to -0.5 | Moderately left-skewed | The left tail is longer; low outliers may pull the mean downward. |
| < -1 | Highly left-skewed | Large negative outliers strongly affect the distribution. |
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