1. What is Pearson's Coefficient of Skewness?

Pearson's first skewness coefficient is a measure of the asymmetry of a probability distribution. It quantifies the extent to which a distribution differs from a symmetrical bell curve, 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:

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

Interpretation:

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

3. Importance of Skewness Measurement

Details: Skewness measurement is crucial in statistics for understanding data distribution characteristics. It helps identify whether data follows a normal distribution, which is important for many statistical tests and analyses.

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 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.

Q2: How is this different from other skewness measures?
A: Pearson's first coefficient uses mean and median, while other measures like Fisher-Pearson use moments. This version is simpler but equally effective for many applications.

Q3: What range of values is considered normal?
A: Values between -0.5 and 0.5 are generally considered approximately symmetrical. 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 statistical tests and require data transformation or non-parametric methods.

Q5: Can skewness be zero in non-normal distributions?
A: Yes, some symmetrical non-normal distributions can have zero skewness. Additional tests like kurtosis may be needed for complete distribution analysis.