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 are symmetric or skewed to one side.

2. How Does the Calculator Work?

The calculator uses the 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, measuring the degree and direction of asymmetry in the data distribution.

3. Importance of Skewness Calculation

Details: Skewness helps identify distribution patterns. Positive skew indicates a longer right tail, negative skew indicates a longer left tail, and zero skew suggests symmetry.

4. Using the Calculator

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

5. Frequently Asked Questions (FAQ)

Q1: What do different skewness values mean?
A: Positive skewness (>0) means right-skewed distribution, negative (<0) means left-skewed, and zero indicates symmetric distribution.

Q2: What is considered significant skewness?
A: Generally, skewness values between -0.5 and 0.5 indicate approximately symmetric data, while values beyond ±1 show highly skewed distributions.

Q3: How does skewness affect statistical analysis?
A: High skewness may violate normality assumptions, requiring data transformation or non-parametric tests for accurate analysis.

Q4: What's the difference between skewness and kurtosis?
A: Skewness measures asymmetry, while kurtosis measures the "tailedness" or peakiness of the distribution.

Q5: When is skewness most useful?
A: Skewness is particularly valuable in finance, quality control, and social sciences where distribution shape impacts decision-making.