Skewness Calculator
Written by Thierno Sadou Diallo, formula verified per our methodology • Last checked on 9/10/2026
Skewness is calculated with g₁ = m₃ ÷ m₂^1.5, the ratio of the third to the second central moment of the sample. For the values 1, 2, 3, 4, 10, g₁ is about 1.14, signaling a distribution stretched to the right by the extreme value 10.
Explanation
Skewness complements the variance and standard deviation: where those only measure the magnitude of the data's dispersion around the mean, skewness reveals whether that dispersion is balanced or leaning to one side. A positive g₁ signals a distribution with a long "tail" of high values to the right (the mean is then pulled upward by a few extreme values, staying above the median); a negative g₁ signals the reverse, a long tail to the left; and g₁ exactly equal to 0 signals a perfectly symmetric distribution, like (1, 2, 3, 4, 5), where each value has an exact mirror on the other side of the mean. This measure is particularly useful for spotting income or price distributions (often strongly right-skewed, with a majority of modest values and a minority of very high ones) or for checking, ahead of a statistical analysis, whether the normality assumption for the data — often needed to apply a confidence interval or a classic parametric test — is reasonable: a normal distribution always has a theoretical skewness of 0.
Example: the values 1, 2, 3, 4, 10
Inputs
Values: 1, 2, 3, 4, 10.
Calculation
Mean = (1+2+3+4+10) ÷ 5 = 4. m₂ = average of (xᵢ−4)² = (9+4+1+0+36) ÷ 5 = 10. m₃ = average of (xᵢ−4)³ = (−27−8−1+0+216) ÷ 5 = 36. g₁ = 36 ÷ 10^1.5 ≈ 36 ÷ 31.62 ≈ 1.1384.
Result
This sample has a skewness of about 1.14, a distribution stretched to the right.
Frequently asked questions
What is the difference between positive and negative skewness?
Positive skewness (g₁ > 0) means the distribution has a long tail of high values to the right, while most values stay grouped to the left — the typical profile of incomes or real estate prices. Negative skewness (g₁ < 0) is the mirror image: a long tail of low values to the left, with most values grouped to the right, a rarer profile in practice.
Does this calculator use the only possible formula for skewness?
No: several conventions coexist in the statistical literature, including an adjusted coefficient (called Fisher-Pearson) that applies a bias correction for small samples, similar in spirit to the Bessel's correction used for the sample standard deviation. This calculator uses the simplest formula, the Pearson moment without correction — the values obtained may differ slightly from those of a statistical software using another convention, without either being more "correct" than the other.
Does a skewness close to 0 mean the data follows a normal distribution?
Not necessarily: a g₁ close to 0 is a necessary but not sufficient condition, because other symmetric distributions (such as the uniform distribution) also have zero skewness without being normal distributions. Checking skewness is a useful first step, but it must be complemented by other indicators, such as kurtosis, to more fully assess the normality of a sample.