IP331.com | Online Tools
HomeStatisticsSkewness Calculator

Skewness Calculator

Calculate sample skewness and Pearson skewness with formulas and step-by-step work

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. This calculator helps answer common searches such as how to calculate skewness, calculating skewness from raw data, and interpreting whether a data set is right-skewed, left-skewed, or approximately symmetric.

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.

How to Calculate Skewness

To calculate skewness manually, list the data values, compute the mean, find each deviation from the mean, standardize those deviations by the standard deviation, cube them, and combine them with the sample skewness correction. The result is positive for a long right tail and negative for a long left tail.

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.

Skewness Interpretation Guide

Skewness ValueDistribution ShapeMeaning
-0.5 to 0.5Approximately symmetricMean and median are usually close.
0.5 to 1Moderately right-skewedThe right tail is longer; high outliers may pull the mean upward.
> 1Highly right-skewedLarge positive outliers strongly affect the distribution.
-1 to -0.5Moderately left-skewedThe left tail is longer; low outliers may pull the mean downward.
< -1Highly left-skewedLarge negative outliers strongly affect the distribution.

Related Statistics Tools

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.

More Statistics Tools

Free online calculators and tools covering mathematics, unit conversion, text processing, and daily life. Accurate, fast, mobile-friendly, and completely free to use.

© 2026 IP331.com - Free Online Tools. All rights reserved.

Privacy Policy | Cookie Policy | Terms of Use | Disclaimer