1. What is Pearson's Skewness Coefficient?

Pearson's Skewness Coefficient (γ₁) is a measure of the asymmetry of the probability distribution of a real-valued random variable about its mean. It describes the degree and direction of skew in a dataset.

2. How Does the Calculator Work?

The calculator uses Pearson's Skewness Coefficient formula:

Where:

• \( \gamma_1 \) — Pearson's Skewness Coefficient (dimensionless)
• \( \mu_3 \) — Third central moment (unit³)
• \( \sigma \) — Standard deviation (unit)

Explanation: The third moment measures the asymmetry of the distribution, while dividing by the cube of standard deviation makes the coefficient dimensionless and scale-invariant.

3. Importance of Skewness Calculation

Details: Skewness is crucial in statistics for understanding the shape of data distribution. It helps identify whether data is symmetric, left-skewed (negative skew), or right-skewed (positive skew), which affects statistical analyses and modeling approaches.

4. Using the Calculator

Tips: Enter the third central moment (μ₃) and standard deviation (σ) in consistent units. Standard deviation must be positive and non-zero. The result is dimensionless.

5. Frequently Asked Questions (FAQ)

Q1: What do different skewness values indicate?
A: γ₁ = 0: symmetric distribution; γ₁ > 0: right-skewed (tail on right); γ₁ < 0: left-skewed (tail on left).

Q2: What is the range of Pearson's Skewness Coefficient?
A: Theoretically unbounded, but typically ranges from -2 to +2 for most practical datasets.

Q3: How is the third moment calculated?
A: μ₃ = E[(X-μ)³], where E is expected value, X is random variable, and μ is mean.

Q4: When is skewness analysis important?
A: Crucial in finance (return distributions), quality control, social sciences, and any field dealing with asymmetric data distributions.

Q5: Are there other measures of skewness?
A: Yes, including Fisher-Pearson coefficient, Bowley's measure, and moment-based measures, but Pearson's is most commonly used.