1. What is Pearson's Coefficient of Skewness?

Pearson's coefficient of skewness 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 coefficient of skewness formula:

Where:

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

Interpretation:

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

3. Importance of Skewness Calculation

Details: Skewness is crucial in statistics for understanding data distribution characteristics. It helps identify outliers, informs data transformation decisions, and ensures appropriate statistical method selection for analysis.

4. Using the Calculator

Tips: Enter the mean, median, and standard deviation values. Standard deviation must be greater than zero. 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 value 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 coefficient uses mean and median, while Fisher-Pearson standardized moment coefficient uses the third moment about the mean. Pearson's method is simpler but less sensitive to outliers.

Q3: What range of values is considered normal for skewness?
A: Generally, values between -0.5 and 0.5 indicate approximately symmetrical data. Values between -1 and -0.5 or 0.5 and 1 show moderate skewness, and values beyond ±1 indicate highly skewed distributions.

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

Q5: Can skewness be zero in non-normal distributions?
A: Yes, some symmetrical non-normal distributions (like uniform distribution) can have zero skewness, so additional tests like kurtosis should be used for complete distribution assessment.