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Skewness Calculator

Calculate Skewness of Data Distribution with Step-by-Step Derivation

Enter data values (comma separated)

Skewness Formulas

Sample Skewness = (n/[(n-1)(n-2)]) × Σ[(xᵢ - x̄)³/σ³]
Pearson Mode Skewness = (Mean - Mode) / σ
Pearson Median Skewness = 3(Mean - Median) / σ

Skewness measures the asymmetry of a distribution. Positive skew means the tail is on the right; negative skew means the tail is on the left.

Perfectly symmetric data has skewness = 0. Skewness > 1 or < -1 indicates substantial asymmetry.

What is Skewness?

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.

Positive Skew

Right tail longer, mean > median > mode

Negative Skew

Left tail longer, mean < median < mode

Symmetric

Zero skew, mean = median = mode

Distribution Shape

Complements mean and standard deviation

💡 Example: Data [2,4,6,8,10,12,14,16,18,20] is symmetric, skewness ≈ 0. If data is [1,2,3,4,5,6,7,8,9,100], it's right-skewed.

Applications

Statistics Finance Risk Analysis Quality Control Data Science

Frequently Asked Questions

What is skewness?
Skewness measures the asymmetry of a probability distribution. Positive skew means tail on right, negative skew means tail on left.
How to interpret skewness?
Skewness ≈ 0: symmetric. Skewness > 0: right-skewed. Skewness < 0: left-skewed. Values >1 or < -1 indicate substantial skewness.
What are the types of skewness?
Pearson mode skewness: (mean - mode)/σ. Pearson median: 3(mean - median)/σ. Sample skewness: third moment.
Why is skewness important?
Skewness affects statistical tests, indicates outliers, and helps understand data distribution shape beyond mean and standard deviation.

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