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.

2. How Does the Calculator Work?

The calculator uses Pearson's first skewness coefficient formula:

Where:

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

Explanation: This formula compares the mean and median to assess distribution symmetry. Positive values indicate right skew, negative values indicate left skew, and zero indicates symmetry.

3. Importance of Skewness Calculation

Details: Skewness is crucial in statistics for understanding data distribution characteristics, identifying outliers, and selecting appropriate statistical methods. Many statistical tests assume normal distribution, and skewness helps verify this assumption.

4. Using the Calculator

Tips: Enter the mean, median, and standard deviation of your dataset. Standard deviation must be greater than zero. The result is a dimensionless measure of skewness.

5. Frequently Asked Questions (FAQ)

Q1: What do different skewness values indicate?
A: Positive skewness (>0) means right-tailed distribution, negative (<0) means left-tailed, and zero indicates symmetrical distribution.

Q2: What is considered significant skewness?
A: Generally, values between -0.5 and 0.5 indicate approximately symmetric distribution, while values beyond ±1 indicate highly skewed distribution.

Q3: How does Pearson's skewness differ from other measures?
A: Pearson's first coefficient uses mean and median, while other methods like Fisher-Pearson standardized moment use third moments about the mean.

Q4: When is this formula most appropriate?
A: This formula works well for unimodal distributions and is particularly useful when the mean and median are readily available.

Q5: What are limitations of Pearson's skewness coefficient?
A: It may be sensitive to outliers and less reliable for small sample sizes. For multimodal distributions, other measures might be more appropriate.