Skewness Calculator
Calculate skewness and kurtosis to analyze distribution asymmetry
Data Input
Input Requirements
- • At least 3 data points are required to calculate skewness
- • At least 4 data points are required to calculate kurtosis
- • Only numeric values will be processed
- • Current data points: 0
Step-by-Step Calculation Example
Heights of 18 Children (cm)
Data: 140, 146, 146, 148, 152, 153, 154, 156, 156, 160, 162, 162, 163, 165, 166, 166, 168, 172
Sample Size (N): 18
Calculated Statistics
Mean (x̄): 157.5 cm
Standard Deviation (s): 8.833 cm
Skewness: -0.3212 (slight left skew)
Kurtosis: -0.7195 (flatter than normal)
Interpretation
Distribution: Slightly negatively skewed with more short children than tall ones
Shape: Flatter than normal distribution, suggesting uniform height distribution
Skewness Interpretation
-0.5 to 0.5 - Symmetric
Distribution is approximately normal
±0.5 to ±1.0 - Moderate
Noticeable asymmetry in distribution
±1.0+ - Highly Skewed
Strong asymmetry, far from normal
Positive: Right tail longer (right skew)
Negative: Left tail longer (left skew)
Kurtosis Interpretation
-1 to 1 - Normal
Similar peakedness to normal distribution
1+ - Leptokurtic
Heavy tails, sharp peak
-1- - Platykurtic
Light tails, flat peak
Understanding Skewness and Kurtosis
What is Skewness?
Skewness measures the asymmetry of a distribution. A normal distribution has zero skewness, while positive skewness indicates a longer right tail and negative skewness indicates a longer left tail.
Skewness Applications
- •Finance: Analyze return distributions and risk assessment
- •Quality Control: Detect manufacturing process deviations
- •Research: Test normality assumptions in statistical models
What is Kurtosis?
Kurtosis measures the "tailedness" or peakedness of a distribution relative to a normal distribution. It indicates whether data are concentrated around the center or in the tails.
Types of Kurtosis
Mesokurtic (≈0): Normal distribution-like
Leptokurtic (>0): Heavy tails, sharp peak
Platykurtic (<0): Light tails, flat peak
Practical Examples
Income Distribution
Typically right-skewed (positive skewness) due to high earners extending the right tail.
Test Scores
Often left-skewed (negative skewness) when most students perform well with few low scores.
Stock Returns
May show high kurtosis (fat tails) indicating higher probability of extreme events.