How to calculate skewness
Pearson's second skewness coefficient measures asymmetry using 3 × (mean − median) ÷ standard deviation. For a mean of 5, median of 4 and standard deviation of 2, the skewness is 3 × (5 − 4) ÷ 2 = 1.5. Because the mean is above the median, the distribution has a longer right tail — a positive, or right, skew. The cubed deviations are scaled by the standard deviation, which is what makes skewness unitless.
How to use this calculator
Enter the mean, the median and the standard deviation. The standard deviation must be non-zero. The result shows the skewness coefficient and whether the distribution leans left, right or is symmetric. You can get the mean and median from the mean, median, mode calculator.
All three inputs must come from the same data set and the same units, otherwise the coefficient is meaningless. Dividing by the standard deviation is what makes the result unit-free, so the same figure is comparable across data sets measured on completely different scales.
Reading the sign of skewness
A positive value means a right-skewed distribution with a longer right tail and the mean above the median. A negative value means a left skew, and zero means symmetry. Values typically fall between −3 and 3. Skew often signals outliers — check for them with the outlier calculator.
Frequently asked questions
- How do I calculate skewness?
- Use Pearson's second coefficient: 3 × (mean − median) ÷ standard deviation. For mean 5, median 4 and SD 2 the result is 1.5.
- What does positive skewness mean?
- The distribution has a longer right tail and the mean is greater than the median. Negative skew is the mirror image.
- What does a skewness of zero mean?
- It indicates a symmetric distribution where the mean and median coincide.
- Why must the standard deviation be non-zero?
- The formula divides by the standard deviation, so a value of zero would make the calculation undefined.
- When should I use a moment-based skewness instead?
- Use the third-moment formula when you have the raw data and need the figure most statistical software reports. Pearson's second coefficient is a quick estimate that needs only three summary numbers, which makes it ideal when the underlying observations are not available.