How to Calculate Skewness Calc
What is Skewness Calc?
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.
Formula
Skewness = E[(X − μ)³] / σ³ = (Σ(xᵢ − x̄)³) / (n × s³)
- X
- data set
- μ
- mean
- σ
- standard deviation
- s
- sample standard deviation
Step-by-Step Guide
- 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
Input
Income data with a few very high earners
Result
Positively skewed (right tail); mean > median
Input
Test scores where most are near the top
Result
Negatively skewed (left tail)
Frequently Asked Questions
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).