1. What is Coefficient of Skewness?

The coefficient of skewness measures the asymmetry of a probability distribution. It indicates whether the data is skewed to the left (negative skew), symmetric (zero skew), or skewed to the right (positive skew).

2. How Does the Calculator Work?

The calculator uses the Pearson's moment coefficient of skewness formula:

Where:

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

Explanation: This formula compares the mean and median to determine the direction and degree of skewness in the data distribution.

3. Interpretation of Skewness Values

Details:

• Skewness = 0: Symmetrical distribution (normal distribution)
• Skewness > 0: Positive skew (right-skewed, mean > median)
• Skewness < 0: Negative skew (left-skewed, mean < median)

Typically, values between -0.5 and 0.5 indicate approximately symmetric distribution.

4. Using the Calculator

Tips: Enter the mean, median, and standard deviation values. Standard deviation must be greater than zero for valid calculation.

5. Frequently Asked Questions (FAQ)

Q1: What does a skewness value of 1.5 indicate?
A: A skewness of 1.5 indicates moderate positive skewness, meaning the distribution is skewed to the right with a longer tail on the right side.

Q2: When is this skewness formula most appropriate?
A: This formula works best for unimodal distributions that are approximately symmetric and not too heavy-tailed.

Q3: What are the limitations of this skewness measure?
A: It can be sensitive to outliers and may not accurately represent skewness in multimodal distributions or distributions with extreme outliers.

Q4: How does skewness affect statistical analysis?
A: Skewness can affect the validity of parametric tests that assume normality. Highly skewed data may require transformation or non-parametric methods.

Q5: Can skewness be zero while the distribution is not symmetric?
A: While rare, it's possible for a distribution to have zero skewness but not be perfectly symmetric, especially in multimodal distributions.