1. What is Skewness?

Skewness is a statistical measure that describes the asymmetry of a probability distribution around its mean. It indicates whether the data is skewed to the left (negative skew), skewed to the right (positive skew), or symmetric (zero skew).

2. How Does the Calculator Work?

The calculator uses the population skewness formula:

Where:

• \( x_i \) — Individual data points
• \( \mu \) — Mean of the data
• \( \sigma \) — Standard deviation of the data
• \( n \) — Sample size

Explanation: The formula calculates the third standardized moment about the mean, normalized by the cube of the standard deviation.

3. Importance of Skewness

Details: Skewness is crucial in statistics for understanding data distribution characteristics. It helps identify outliers, assess normality assumptions, and informs appropriate statistical modeling approaches.

4. Using the Calculator

Tips: Enter numerical data points separated by commas. The calculator will compute skewness, mean, standard deviation, and sample size automatically.

5. Frequently Asked Questions (FAQ)

Q1: What does positive skewness indicate?
A: Positive skewness means the distribution has a longer right tail, with most data concentrated on the left side.

Q2: What does negative skewness indicate?
A: Negative skewness means the distribution has a longer left tail, with most data concentrated on the right side.

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

Q4: How does skewness affect statistical analysis?
A: Skewed data may violate normality assumptions, requiring transformations or non-parametric tests for valid statistical inference.

Q5: What's the difference between population and sample skewness?
A: This calculator uses population skewness. Sample skewness typically uses n-1 in the denominator for unbiased estimation.