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 indicates whether the data is concentrated on one side.

2. How Does the Calculator Work?

The calculator uses the skewness formula:

Where:

• \( mean \) — Arithmetic mean of the data
• \( median \) — Middle value of the data
• \( sd \) — Standard deviation of the data

Explanation: The formula compares the mean and median to measure asymmetry. A positive value indicates right-skewed data, negative indicates left-skewed, and zero indicates symmetry.

3. Interpreting Skewness Values

Details:

• Skewness > 0: Right-skewed (mean > median)
• Skewness < 0: Left-skewed (mean < median)
• Skewness = 0: Symmetrical distribution (mean = median)

4. Using the Calculator

Tips: Enter the mean, median, and standard deviation of your dataset. Standard deviation must be greater than zero.

5. Frequently Asked Questions (FAQ)

Q1: What is considered a "large" skewness value?
A: Generally, skewness > |1| is considered substantial, but interpretation depends on context.

Q2: How is this different from Pearson's moment coefficient of skewness?
A: This is Pearson's second skewness coefficient. The first uses mode instead of median.

Q3: When is skewness important to consider?
A: Skewness is crucial when making statistical inferences that assume normality, as many tests are sensitive to skew.

Q4: What are limitations of this skewness measure?
A: It's less robust to outliers than other measures and doesn't capture multi-modal distributions well.

Q5: How can I fix skewed data?
A: Common approaches include transformations (log, square root), or using non-parametric methods.