1. What is Pearson's Coefficient of Skewness?

Pearson's coefficient of skewness is a statistical measure that quantifies the asymmetry of a probability distribution. It indicates whether data is skewed to the left (negative skew) or right (positive skew) relative to a normal distribution.

2. How Does the Calculator Work?

The calculator uses Pearson's first coefficient of skewness formula:

Where:

• \( Mean \) — Arithmetic average of the dataset
• \( Median \) — Middle value of the dataset
• \( Standard\ Deviation \) — Measure of data dispersion

Interpretation:

• Skewness = 0: Symmetrical distribution
• Skewness > 0: Right-skewed (positive skew)
• Skewness < 0: Left-skewed (negative skew)

3. Importance of Skewness Calculation

Details: Skewness measurement is crucial for understanding data distribution characteristics, identifying outliers, selecting appropriate statistical tests, and making informed decisions in data analysis and modeling.

4. Using the Calculator

Tips: Enter the mean, median, and standard deviation values. All values must be valid (standard deviation > 0). The result is dimensionless and indicates the direction and degree of skewness.

5. Frequently Asked Questions (FAQ)

Q1: What does a skewness value of 0.5 mean?
A: A skewness of 0.5 indicates moderate positive skewness, meaning the distribution has a longer tail on the right side and most data points are concentrated on the left.

Q2: How is this different from other skewness measures?
A: Pearson's first coefficient uses mean and median, while other measures like Fisher-Pearson standardized moment use third moments. Pearson's method is simpler but less robust to outliers.

Q3: What is considered significant skewness?
A: Generally, absolute values greater than 0.5 indicate moderate skewness, and values greater than 1.0 indicate high skewness. However, interpretation depends on the context and sample size.

Q4: When should I be concerned about skewness?
A: Significant skewness may violate assumptions of parametric tests, affect mean as a measure of central tendency, and require data transformation before analysis.

Q5: Can skewness be zero in real-world data?
A: Perfectly symmetrical distributions are rare in practice, but many datasets approximate symmetry with skewness values close to zero.