1. What is Kurtosis?

Kurtosis is a statistical measure that describes the tailedness of a probability distribution. It indicates how much of the data's variance comes from extreme deviations versus moderate deviations from the mean.

2. How Does the Calculator Work?

The calculator uses the kurtosis formula:

Where:

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

Explanation: Kurtosis measures the "tailedness" of the distribution. Higher kurtosis indicates more data in the tails, while lower kurtosis indicates less data in the tails.

3. Types of Kurtosis

Mesokurtic (Kurtosis ≈ 3): Normal distribution - moderate tails
Leptokurtic (Kurtosis > 3): Heavy tails and sharp peak - more outliers
Platykurtic (Kurtosis < 3): Light tails and flat peak - fewer outliers

4. Using the Calculator

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

5. Frequently Asked Questions (FAQ)

Q1: What does kurtosis tell us about a distribution?
A: Kurtosis indicates the presence of outliers. High kurtosis suggests more outliers, while low kurtosis suggests fewer outliers.

Q2: What is the difference between kurtosis and skewness?
A: Skewness measures asymmetry, while kurtosis measures tail heaviness. Skewness is about the direction of the tail, kurtosis is about the weight of the tail.

Q3: What is considered a normal kurtosis value?
A: For a normal distribution, kurtosis is exactly 3. However, many statistical packages subtract 3 to make the normal distribution have kurtosis of 0 (excess kurtosis).

Q4: When is high kurtosis problematic?
A: High kurtosis can indicate potential issues with statistical models that assume normality, as it suggests more extreme values than expected.

Q5: Can kurtosis be negative?
A: Yes, kurtosis can be negative for platykurtic distributions that have lighter tails than a normal distribution.