Statistics

Kurtosis Formula - Statistics

Learn the kurtosis formula with examples, step-by-step guide, and calculator tools. Measure the tailedness of a probability distribution

The kurtosis formula is a fundamental concept in statistics. Measure the tailedness of a probability distribution. This page provides a comprehensive guide with worked examples and practical applications.

The Formula

\[\text{Kurt} = \frac{n(n+1)}{(n-1)(n-2)(n-3)} \sum_{i=1}^{n} \left(\frac{x_i - \bar{x}}{\sigma}\right)^4 - \frac{3(n-1)^2}{(n-2)(n-3)}\]

Variables

Kurt
Kurtosis coefficient
n
Number of values
xᵢ
Individual values
Mean
σ
Standard deviation

Step-by-Step Guide

  1. 1

    Step 1: Gather your data values

  2. 2

    Step 2: Apply the formula

  3. 3

    Step 3: Perform the calculations

  4. 4

    Step 4: Interpret the result

Examples

Example 1

Example 1: [1,2,3,4,5] → Excess kurtosis ≈ 0 for normal distribution

Example 2

Example 2: -1.3 (platykurtic)

Frequently Asked Questions

What is the kurtosis formula?

Measure the tailedness of a probability distribution

How do I calculate kurtosis formula?

Use the formula: \text{Kurt} = \frac{n(n+1)}{(n-1)(n-2)(n-3)} \sum_{i=1}^{n} \left(\frac{x_i - \bar{x}}{\sigma}\right)^4 - \frac{3(n-1)^2}{(n-2)(n-3)}. Follow the steps provided above.

What tools can help with kurtosis formula?

We provide online calculators: statistics-calculator

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