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 skewed to the left or right of the mean.

2. How Does the Calculator Work?

The calculator uses the skewness formula:

Where:

• \( x \) — Individual data values
• \( \text{mean} \) — Mean of the data values
• \( n \) — Number of data values
• \( \text{SD} \) — Standard deviation of the data

Explanation: The formula calculates the third standardized moment, measuring the degree of asymmetry in the distribution.

3. Importance of Skewness Calculation

Details: Skewness helps identify the direction and degree of asymmetry in data distributions, which is crucial for statistical analysis, data transformation decisions, and understanding underlying patterns.

4. Using the Calculator

Tips: Enter comma-separated values. The calculator can automatically compute mean and standard deviation if not provided. All values must be numeric.

5. Frequently Asked Questions (FAQ)

Q1: What does positive skewness indicate?
A: Positive skewness indicates a distribution with an asymmetric tail extending toward more positive values (right-skewed).

Q2: What does negative skewness indicate?
A: Negative skewness indicates a distribution with an asymmetric tail extending toward more negative values (left-skewed).

Q3: What is considered a significant skewness value?
A: Generally, skewness values between -0.5 and 0.5 are considered approximately symmetric, while values beyond this range indicate significant skewness.

Q4: Can skewness be zero?
A: Yes, skewness of zero indicates a perfectly symmetric distribution, though this is rare in real-world data.

Q5: How does skewness relate to mean and median?
A: In right-skewed distributions, mean > median; in left-skewed distributions, mean < median; in symmetric distributions, mean ≈ median.