Calculate Pearson’s second coefficient of skewness from mean, median, and standard deviation, or solve for the missing value with any three inputs.
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Coefficient of Skewness Formula
The calculator uses Pearson’s second coefficient of skewness, which estimates skewness from the mean, median, and standard deviation.
Rearranged formulas used to solve for the missing value:
- Sk = coefficient of skewness
- Mean = arithmetic average of the data set
- Median = middle value of the data set
- s = standard deviation
To use the calculator, enter any three values and leave exactly one field blank. If the skewness coefficient is blank, the calculator applies the main formula directly. If the mean, median, or standard deviation is blank, it rearranges the same formula to solve for that missing value.
The standard deviation must be greater than 0. When solving for standard deviation, the skewness coefficient cannot be 0 because that would require division by zero.
How to Interpret the Skewness Coefficient
| Skewness coefficient | Shape of distribution | What it usually means |
|---|---|---|
| Sk > 0 | Right-skewed | The mean is greater than the median. The right tail is longer. |
| Sk = 0 | Approximately symmetric | The mean and median are equal or very close. |
| Sk < 0 | Left-skewed | The mean is less than the median. The left tail is longer. |
Common Skewness Strength Guidelines
| Absolute value of skewness | Typical interpretation |
|---|---|
| 0 to 0.5 | Low skewness or roughly symmetric |
| 0.5 to 1 | Moderate skewness |
| Greater than 1 | High skewness |
Example Calculations
Example 1: Calculate the skewness coefficient
Suppose the mean is 72, the median is 68, and the standard deviation is 12.
The skewness coefficient is 1, so the distribution is positively skewed.
Example 2: Calculate the mean
Suppose the skewness coefficient is 0.6, the median is 50, and the standard deviation is 10.
The mean is 52.
FAQ
What does a positive coefficient of skewness mean?
A positive coefficient of skewness means the distribution is skewed to the right. In Pearson’s second coefficient, this happens when the mean is greater than the median. A few large values can pull the mean upward.
What does a negative coefficient of skewness mean?
A negative coefficient of skewness means the distribution is skewed to the left. In this formula, it happens when the mean is less than the median. A few small values can pull the mean downward.
Can standard deviation be zero in this formula?
No. Standard deviation is in the denominator of the skewness formula, so it must be greater than 0. If the standard deviation is 0, all values are the same, and this coefficient of skewness is not defined.
