Mathematics

Skewness Calculator

Data (space/comma separated)

✓Skewness

Skewness

0.7594

Mean

5.9091

3.1130

Positively skewed (right tail)

What is Skewness Calculator?

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Skewness measures the asymmetry of a probability distribution. Positive skew (right tail) means a few large values pull the mean up; negative skew (left tail) means a few small values pull it down.

Calkulon makes complex calculations simple — built for students and everyday problem-solvers.

Formula

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f(x)Skewness = E[(X − μ)³] / σ³ = (Σ(xᵢ − x̄)³) / (n × s³)

Variable Legend

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Symbol	Name	Unit	Description
X	data set	—	—
μ	mean	—	—
σ	standard deviation	—	—
s	sample standard deviation	—	—

How to Skewness Calculator

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1Sample skewness = (n/((n−1)(n−2))) × Σ((xᵢ−x̄)/s)³
2Symmetric: skewness ≈ 0
3Right-skewed: mean > median > mode
4Left-skewed: mean < median < mode

Worked Examples

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Example 1

Given:Income data with a few very high earners

Result:Positively skewed (right tail); mean > median

Example 2

Given:Test scores where most are near the top

Result:Negatively skewed (left tail)

Real-World Applications

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🏗️

Data analysis and exploratory statistics

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Income and wealth distribution analysis

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Financial risk assessment

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Quality control limits

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Hypothesis testing

Skewness Interpretation

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Skewness	Description	Example
< −1	Highly left-skewed	Retirement ages
−1 to −0.5	Moderately left-skewed	Top exam scores
−0.5 to 0.5	Approximately symmetric	Heights
0.5 to 1	Moderately right-skewed	House prices
> 1	Highly right-skewed	Wealth distribution

Frequently Asked Questions

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What does skewness tell us?

Positive skewness: tail on right (long right tail). Negative: tail on left. Zero: symmetric.

When is data considered skewed?

Typically, |skewness| > 0.5 indicates noticeable skew. > 1 is highly skewed.

How is skewness different from kurtosis?

Skewness measures asymmetry. Kurtosis measures tail weight (how extreme the values are).

References

›Skewness — Wikipedia

Formula-verified for precision

Reviewed October 2026

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Skewness Calculator