Kurtosis Calculator
Calculate the kurtosis of your dataset to measure the tailedness and peakedness of its distribution. Enter your data as comma-separated values to determine the shape characteristics.
Sample Kurtosis (Excess):
Kurt = [n(n+1)/((n-1)(n-2)(n-3))] × Σ[(Xi-X̄)/s]⁴ - 3(n-1)²/((n-2)(n-3))
Interpretation:
• Kurt = 0: Normal distribution (mesokurtic)
• Kurt > 0: Heavy tails (leptokurtic)
• Kurt < 0: Light tails (platykurtic)
Kurt = [n(n+1)/((n-1)(n-2)(n-3))] × Σ[(Xi-X̄)/s]⁴ - 3(n-1)²/((n-2)(n-3))
Interpretation:
• Kurt = 0: Normal distribution (mesokurtic)
• Kurt > 0: Heavy tails (leptokurtic)
• Kurt < 0: Light tails (platykurtic)
Example: Data [1,2,3,4,5]
Mean = 3, SD = 1.58
Standardized values: [-1.27, -0.63, 0, 0.63, 1.27]
4th powers sum: 5.2
Kurtosis ≈ -1.2 (platykurtic, flatter than normal)
Mean = 3, SD = 1.58
Standardized values: [-1.27, -0.63, 0, 0.63, 1.27]
4th powers sum: 5.2
Kurtosis ≈ -1.2 (platykurtic, flatter than normal)
🔗 Related Calculators
📐 Formula
Sample Kurtosis (Excess):
Kurt = [n(n+1)/((n-1)(n-2)(n-3))] × Σ[(Xi-X̄)/s]⁴ - 3(n-1)²/((n-2)(n-3))
Interpretation:
• Kurt = 0: Normal distribution (mesokurtic)
• Kurt > 0: Heavy tails (leptokurtic)
• Kurt < 0: Light tails (platykurtic)
Kurt = [n(n+1)/((n-1)(n-2)(n-3))] × Σ[(Xi-X̄)/s]⁴ - 3(n-1)²/((n-2)(n-3))
Interpretation:
• Kurt = 0: Normal distribution (mesokurtic)
• Kurt > 0: Heavy tails (leptokurtic)
• Kurt < 0: Light tails (platykurtic)
📝 Example Calculation
Example: Data [1,2,3,4,5]
Mean = 3, SD = 1.58
Standardized values: [-1.27, -0.63, 0, 0.63, 1.27]
4th powers sum: 5.2
Kurtosis ≈ -1.2 (platykurtic, flatter than normal)
Mean = 3, SD = 1.58
Standardized values: [-1.27, -0.63, 0, 0.63, 1.27]
4th powers sum: 5.2
Kurtosis ≈ -1.2 (platykurtic, flatter than normal)