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 (measure of the lopsidedness of the distribution)
• \( \sigma \) — Standard deviation (measure of dispersion)

Interpretation:

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

3. Importance of Skewness Calculation

Details: Skewness is crucial in statistics for understanding the shape of data distribution. It helps identify whether data is normally distributed or has asymmetric tendencies, which is important for selecting appropriate statistical methods and making accurate inferences.

4. Using the Calculator

Tips: Enter the third moment (μ₃) and standard deviation (σ). Standard deviation must be greater than zero. The result is a unitless measure of distribution asymmetry.

5. Frequently Asked Questions (FAQ)

Q1: What does positive skewness indicate?
A: Positive skewness indicates that the right tail of the distribution is longer or fatter than the left tail, with most data points concentrated on the left.

Q2: What does negative skewness indicate?
A: Negative skewness indicates that the left tail is longer or fatter than the right tail, with most data points concentrated on the right.

Q3: What is considered a significant skewness value?
A: Generally, skewness values between -0.5 and 0.5 are considered approximately symmetrical, while values beyond ±1 indicate highly skewed distributions.

Q4: How is the third moment calculated?
A: The third central moment is calculated as: μ₃ = E[(X - μ)³], where E is the expected value operator and μ is the mean of the distribution.

Q5: Are there other measures of skewness?
A: Yes, other measures include Pearson's first and second skewness coefficients, and Bowley's measure of skewness, each with different applications and interpretations.