Coefficient of Kurtosis Calculator

Formula

The formula to calculate the Coefficient of Kurtosis (K) is:

\[ K = \frac{n(n+1)}{(n-1)(n-2)(n-3)} \sum \left( \frac{(x_i - \mu)^4}{\sigma^4} \right) - \frac{3(n-1)^2}{(n-2)(n-3)} \]

Where:

Coefficient of Kurtosis (K): A statistical measure that describes the distribution of observed data around the mean, indicating the degree of peakedness or flatness in a distribution.
Number of Data Points (n): The total number of data points in the dataset.
Individual Data Point (x_i): Each specific value in the dataset.
Mean (μ): The average value of the dataset.
Standard Deviation (σ): A measure of the amount of variation or dispersion in the dataset.

Let's say the data points are 2, 4, 6, 8, and 10. Using the formula:

\[ K = \frac{5(5+1)}{(5-1)(5-2)(5-3)} \sum \left( \frac{(x_i - \mu)^4}{\sigma^4} \right) - \frac{3(5-1)^2}{(5-2)(5-3)} \]

We get:

\[ K \approx 2.62 \]

So, the coefficient of kurtosis is approximately 2.62.