Skewness Calculator
Calculate skewness online for free. Understand data distribution asymmetry with our skewness calculator. Enter your dataset and get instant results and interactive histogram visualization.
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Data Distribution Visualization
Understanding Skewness
Skewness is a measure of the asymmetry of the probability distribution of a real-valued random variable about its mean. The skewness value can be positive, negative, or zero.
- Positive Skewness (Right-skewed): The right tail is longer; the mass of the distribution is concentrated on the left. Mean > Median > Mode.
- Negative Skewness (Left-skewed): The left tail is longer; the mass of the distribution is concentrated on the right. Mean < Median < Mode.
- Zero Skewness: The distribution is symmetric. Mean = Median = Mode.
This calculator uses the adjusted Fisher-Pearson standardized moment coefficient (G1) to calculate skewness, which is often preferred for sample skewness calculation. Understanding skewness helps in data analysis to interpret the distribution and choose appropriate statistical methods.
Formula
The formula for sample skewness (adjusted Fisher-Pearson coefficient of skewness) is:
$$ G_1 = \frac{\frac{1}{n} \sum_{i=1}^{n} (x_i - \bar{x})^3}{s^3} \times \frac{n}{\left(n-1\right) \left(n-2\right)} $$Where: \( n \) is the number of data points, \( x_i \) are the data points, \( \bar{x} \) is the sample mean, and \( s \) is the sample standard deviation.