1. What are Skewness and Kurtosis?

Skewness measures the asymmetry of the data distribution, while kurtosis measures the "tailedness" (peakedness and tail thickness) of the distribution. Together they help assess whether data follows a normal distribution.

2. How Does the Calculator Work?

The calculator uses standard formulas for sample skewness and kurtosis:

Where:

• \( n \) — Sample size
• \( x_i \) — Individual data points
• \( \bar{x} \) — Sample mean
• \( s \) — Sample standard deviation

Interpretation: For normal distribution, skewness ≈ 0 and kurtosis ≈ 0 (excess kurtosis).

3. Importance of Normality Testing

Details: Many statistical tests assume normally distributed data. Checking skewness and kurtosis helps determine if parametric tests are appropriate or if data transformation is needed.

4. Using the Calculator

Tips: Enter numeric values separated by commas. At least 4 data points are recommended for meaningful results. The calculator automatically excludes non-numeric entries.

5. Frequently Asked Questions (FAQ)

Q1: What values indicate normal distribution?
A: For normality, skewness should be between -0.5 and +0.5, and kurtosis between -0.5 and +0.5 (excess kurtosis).

Q2: What does positive skewness mean?
A: Positive skewness indicates a longer right tail (mean > median > mode).

Q3: What does high kurtosis indicate?
A: High kurtosis (>0) indicates heavy tails and sharp peak, while low kurtosis (<0) indicates light tails and flat distribution.

Q4: Are there alternative normality tests?
A: Yes, Shapiro-Wilk, Anderson-Darling, and Kolmogorov-Smirnov tests are other common normality tests.

Q5: How many data points are needed?
A: At least 20-30 points are recommended for reliable normality assessment, though the calculator works with as few as 4.