1. What are Kurtosis and Skewness?

Kurtosis and skewness are statistical measures that describe the shape of a distribution. Skewness measures asymmetry, while kurtosis measures the "tailedness" of the distribution.

2. How Does the Calculator Work?

The calculator uses the following formulas:

Where:

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

Explanation: The formulas calculate the third and fourth standardized moments about the mean, which quantify the shape characteristics of the distribution.

3. Interpretation of Results

Skewness: Positive values indicate right-skewed distributions, negative values indicate left-skewed distributions, and zero indicates symmetry.

Kurtosis: Positive values indicate heavy tails (leptokurtic), negative values indicate light tails (platykurtic), and zero indicates normal distribution.

4. Using the Calculator

Tips: Enter your numerical data points separated by commas. The calculator will compute the mean, standard deviation, skewness, and kurtosis of your dataset.

5. Frequently Asked Questions (FAQ)

Q1: What is considered a "normal" skewness value?
A: For a normal distribution, skewness should be close to 0. Values between -0.5 and 0.5 are generally considered symmetrical.

Q2: What does high kurtosis indicate?
A: High kurtosis (>3) indicates more outliers than a normal distribution, while low kurtosis (<3) indicates fewer outliers.

Q3: How many data points do I need for reliable results?
A: At least 30 data points are recommended for stable estimates of skewness and kurtosis.

Q4: Why subtract 3 in the kurtosis formula?
A: This adjustment makes the kurtosis of a normal distribution equal to 0 (excess kurtosis).

Q5: Can these measures be used for non-normal distributions?
A: Yes, skewness and kurtosis can be calculated for any distribution, but interpretation may differ.