1. What is Pearson's Skewness Coefficient?

Pearson's skewness coefficient is a measure of the asymmetry of a probability distribution. It quantifies the extent to which a distribution differs from a symmetrical normal distribution, indicating whether data is skewed to the left or right.

2. How Does the Calculator Work?

The calculator uses Pearson's first skewness coefficient formula:

Where:

• \( Sk \) — Pearson's skewness coefficient (dimensionless)
• \( \text{Mean} \) — Arithmetic mean of the dataset
• \( \text{Median} \) — Middle value of the dataset
• \( \text{SD} \) — Standard deviation of the dataset

Interpretation:

• Sk = 0: Symmetrical distribution
• Sk > 0: Positive skew (right-skewed)
• Sk < 0: Negative skew (left-skewed)

3. Importance of Skewness Measurement

Details: Skewness measurement is crucial in statistics for understanding data distribution characteristics. It helps identify whether data transformation is needed, informs appropriate statistical tests, and provides insights into the underlying data generation process.

4. Using the Calculator

Tips: Enter the mean, median, and standard deviation of your dataset. All values must be valid numbers, with standard deviation greater than zero. The result is a dimensionless coefficient indicating the direction and degree of skewness.

5. Frequently Asked Questions (FAQ)

Q1: What does a skewness value of 0.5 mean?
A: A skewness coefficient of 0.5 indicates moderate positive skewness, meaning the distribution has a longer tail on the right side and most values 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 higher moments. This version is simpler and more intuitive for basic skewness assessment.

Q3: What range of values is considered normal for skewness?
A: For approximately normal distributions, skewness typically falls between -0.5 and +0.5. Values beyond ±1 indicate highly skewed distributions.

Q4: When should I be concerned about skewness?
A: Significant skewness (|Sk| > 1) may violate assumptions of parametric tests and could require data transformation or non-parametric methods for analysis.

Q5: Can skewness be zero in non-normal distributions?
A: Yes, some symmetrical non-normal distributions can have zero skewness. Skewness only measures asymmetry, not normality.