Skewness Calculator
Skewness measures how asymmetric a distribution is around its mean. A skewness of 0 means the data is symmetric; positive skewness means a longer tail stretches to the right, toward higher values; negative skewness means the tail stretches left. Enter your values, comma-separated, to get both the population skewness (g₁) and the sample-adjusted version (G₁) that spreadsheet software typically reports.
The Skewness Formula
Population skewness is g₁ = m₃/m₂^1.5, where m₂ and m₃ are the second and third central moments: the average of (x−mean)² and (x−mean)³ across all values. The sample-adjusted G₁ corrects for the bias that creeps in with small samples, and is the figure most spreadsheet software reports.
Worked Example: Symmetric vs. Skewed Data
The values 1, 2, 3, 4, 5 are perfectly symmetric around their mean of 3, giving a skewness of exactly 0. Compare that to 1, 2, 2, 3, 10: the mean is pulled up by the outlier 10, but most values sit below it, producing a positive skewness around 1.36 (g₁), a clear right-skew signature.
Population vs. Sample-Adjusted: Which to Report
For large samples the two measures converge and the difference barely matters. For small samples, G₁ is the more honest figure to report since it corrects for the systematic bias g₁ carries, this is also why Excel's SKEW() function returns G₁, not g₁, by default.
Frequently Asked Questions
What's the difference between g₁ and G₁?
g₁ is the population (biased) moment coefficient of skewness: g₁ = m₃/m₂^1.5, using the raw third and second central moments. G₁ applies a small-sample correction factor and is what Excel's SKEW function and most statistical software report by default.
What does a skewness near 0 mean?
A skewness between roughly −0.5 and 0.5 is usually called approximately symmetric, the data's spread above and below the mean is roughly balanced. Perfectly symmetric data, like a normal distribution, has a true skewness of exactly 0.
What does positive (right) skewness look like?
A right-skewed distribution has most values clustered on the lower end with a longer tail stretching toward higher values, household income is a classic example, where most people earn a moderate amount but a few earn very high amounts, pulling the tail right.
How many values do I need to calculate skewness?
At least 3, since the sample-adjusted formula divides by (n−2). With very small samples, skewness estimates are unstable and should be treated as a rough indication, not a precise measurement.
Why does skewness matter for statistical tests?
Many common tests assume roughly normal, symmetric data. Strong skewness is a signal that a nonparametric alternative, like the Kruskal-Wallis or Mann-Whitney U test on this site, may be more appropriate than a mean-based test.