1. What is Skewness?

Skewness is a measure of the asymmetry of the probability distribution of a real-valued random variable about its mean. It describes the extent to which a distribution differs from a normal distribution in terms of symmetry.

2. How Does the Calculator Work?

The calculator uses the skewness formula:

Where:

• \( \mu_3 \) — Third central moment of the distribution
• \( \sigma \) — Standard deviation of the distribution

Explanation: The formula calculates the standardized third moment about the mean, providing a dimensionless measure of distribution asymmetry.

3. Importance of Skewness Calculation

Details: Skewness is crucial in statistics for understanding the shape of data distribution. It helps identify whether data is symmetric, left-skewed (negative skew), or right-skewed (positive skew), which affects statistical analyses and modeling decisions.

4. Using the Calculator

Tips: Enter the third moment (μ₃) and standard deviation (σ) values. 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: Zero indicates perfect symmetry, positive values indicate right-skewed distribution, and negative values indicate left-skewed distribution.

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

Q3: How is the third moment calculated?
A: The third central moment is calculated as \( \mu_3 = \frac{\sum(x_i - \bar{x})^3}{n} \) for a sample, where \( \bar{x} \) is the mean and n is the sample size.

Q4: Are there alternative skewness formulas?
A: Yes, Pearson's first and second skewness coefficients and Fisher-Pearson standardized moment coefficient are alternative measures of skewness.

Q5: When is skewness most useful?
A: Skewness is particularly useful in finance for risk assessment, in quality control for process monitoring, and in social sciences for understanding population distributions.