Question 1

How do I interpret skewness values?

Accepted Answer

A perfectly symmetric distribution has skewness = 0. Positive skewness (> 0): the right tail is longer — data is pulled toward higher values. Mean > median. Common in income, wealth, and house prices. Negative skewness (< 0): the left tail is longer — data is pulled toward lower values. Mean < median. Common in test scores after an easy exam. Rule of thumb: |skewness| < 0.5 ≈ approximately symmetric; 0.5–1.0 = moderately skewed; > 1.0 = highly skewed.

Question 2

What is excess kurtosis and how do I interpret it?

Accepted Answer

Excess kurtosis = kurtosis − 3, so that a normal distribution has excess kurtosis = 0. Positive excess kurtosis (leptokurtic): heavier tails and a sharper peak than normal — extreme values occur more often than expected. Examples: financial returns, insurance claims. Negative excess kurtosis (platykurtic): lighter tails and a flatter peak — extreme values are rarer than in a normal distribution. Examples: bounded data, uniform distributions.

Question 3

What skewness and kurtosis values indicate normality?

Accepted Answer

For a perfectly normal distribution: skewness = 0, excess kurtosis = 0. In practice, sample data will deviate from these values due to sampling error. A common rule of thumb: |skewness| < 2 and |excess kurtosis| < 7 are acceptable for parametric tests with n ≥ 30 (the CLT provides robustness). For small samples (n < 30), even mild skewness can violate normality assumptions.

Question 4

How is skewness calculated for a sample vs population?

Accepted Answer

This calculator uses the adjusted Fisher-Pearson standardised moment coefficient: G₁ = [n/((n−1)(n−2))] × Σ[(xᵢ−x̄)/s]³. This is the formula used by Excel's SKEW() function and most statistical software. The population skewness formula omits the correction factor and divides simply by n. For large samples (n > 100), both formulas give nearly identical results.

Question 5

When should I transform data with high skewness?

Accepted Answer

If |skewness| > 1.0 and you plan to use parametric tests that assume normality (t-test with small n, ANOVA), consider a transformation. Log transformation (log(x) or log(x+1)) works well for right-skewed positive data (income, house prices, biological concentrations). Square root transformation reduces moderate right skew. After transformation, recheck skewness and kurtosis, then verify the Q-Q plot.

Question 6

Are skewness and kurtosis affected by outliers?

Accepted Answer

Yes — both statistics are highly sensitive to outliers, especially for small samples. A single extreme value can dramatically change both measures because they involve cubing or raising to the 4th power the standardised deviations. Before interpreting skewness and kurtosis, check for outliers using the IQR method or z-scores. If outliers are genuine data errors, consider removing them. If they are real, use robust alternatives like the median-based skewness measure: 3(mean − median)/SD.

Value range	Skewness interpretation	Excess kurtosis interpretation
\|value\| < 0.5	Approximately symmetric	Near-normal tail weight (mesokurtic)
0.5 – 1.0	Moderately skewed	Mild deviation from normal tails
1.0 – 2.0	Highly skewed — consider log transform	Noticeably heavy or light tails
> 2.0	Severely skewed — transform before parametric tests	Very heavy tails — outliers likely
< 0 (negative)	Left tail is longer (left-skewed)	Lighter tails than normal (platykurtic)
> 0 (positive)	Right tail is longer (right-skewed)	Heavier tails than normal (leptokurtic)

Skewness and Kurtosis Calculator

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Interpreting Skewness and Kurtosis

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