Enter values to see results
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Enter values to see results
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The Skewness Calculator measures the asymmetry of a dataset's distribution. Skewness tells you whether data values tend to be concentrated more on one side of the mean, with a longer tail extending in the opposite direction.
Enter up to 10 data values and the count to compute the adjusted Fisher-Pearson sample skewness coefficient.
Skewness quantifies the degree and direction of asymmetry in a frequency distribution. This calculator uses the adjusted Fisher-Pearson standardized moment coefficient, which is the most commonly used skewness formula in statistical software:
$$G_1 = \frac{n}{(n-1)(n-2)} \sum_{i=1}^{n} \left(\frac{x_i - \bar{x}}{s}\right)^3$$
Where:
The interpretation of skewness values:
Practical rules of thumb:
Skewness is important because many statistical procedures (t-tests, ANOVA, regression) assume normally distributed data. Significant skewness violates this assumption and may require data transformation (such as log or square root transforms) or the use of non-parametric methods.
In finance, skewness of return distributions is crucial. Investors generally prefer positive skewness (potential for large gains) and avoid negative skewness (risk of large losses). Income distributions are typically right-skewed, with a long tail of high earners pulling the mean above the median.
The adjustment factor n/((n-1)(n-2)) corrects for bias in the raw third moment estimator, making this the preferred formula for sample data. A minimum of 3 data points is required since the denominator includes (n-2).
A positive skewness indicates a right-skewed distribution with a longer right tail. A negative skewness indicates a left-skewed distribution. Values near zero suggest approximate symmetry. The mean and standard deviation are also provided for context.
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The value 20 pulls the right tail, creating a positive (right) skew of about 1.47.
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This nearly symmetric dataset has a skewness close to 0.
Skewness measures asymmetry (whether data leans left or right), while kurtosis measures the heaviness of the tails (how prone the distribution is to outliers). Both are higher-order moments of the distribution.
The adjusted Fisher-Pearson formula has (n-2) in the denominator. With fewer than 3 values, the formula is undefined. Additionally, skewness is meaningless for very small samples.
In a right-skewed distribution, the mean is typically greater than the median. In a left-skewed distribution, the mean is typically less than the median. For symmetric distributions, they are approximately equal.
Consider applying a transformation (log, square root, Box-Cox) to normalize the data before performing parametric tests. Alternatively, use non-parametric tests that do not assume normality.
Yes. The adjusted formula corrects for small-sample bias, but skewness estimates are more reliable with larger samples. For very small samples (n < 20), skewness estimates can be quite variable.
Yes. Even data drawn from a perfectly symmetric population will have some sample skewness due to random variation. Only with infinite data would the sample skewness exactly equal zero.
Roboculator Team
The Roboculator Team explains calculations, planning tools, and practical formulas in clear language for real-life situations.
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