Enter the number of data points, each individual data point, the mean of the data, and the standard deviation into the calculator to determine the Coefficient of Kurtosis.

## Coefficient Of Kurtosis Formula

The following formula is used to calculate the Coefficient of Kurtosis.

K = n(n+1)/((n-1)(n-2)(n-3)) * Σ((x_i – μ)^4/σ^4) – 3(n-1)^2/((n-2)(n-3))Variables:

- K is the Coefficient of Kurtosis
- n is the number of data points
- x_i is each individual data point
- μ is the mean of the data
- σ is the standard deviation of the data

## What is the Coefficient Of Kurtosis?

The Coefficient of Kurtosis is a statistical measure used to describe the distribution of observed data around the mean. It indicates the degree of peakedness or flatness in a distribution, and identifies the heaviness of the tails of the distribution. A high kurtosis value indicates a sharp peak with heavy tails, suggesting a large number of outliers. A low kurtosis value indicates a flat peak with light tails, suggesting a lack of outliers.

## How to Calculate Coefficient Of Kurtosis?

The following steps outline how to calculate the Coefficient of Kurtosis.

- First, determine the number of data points (n).
- Next, calculate the mean of the data (μ).
- Next, calculate the standard deviation of the data (σ).
- Next, calculate the sum of the fourth power of the difference between each data point and the mean divided by the fourth power of the standard deviation (∑((x_i – μ)^4/σ^4)).
- Next, calculate the numerator of the formula = n(n+1)/((n-1)(n-2)(n-3)) * ∑((x_i – μ)^4/σ^4).
- Finally, calculate the Coefficient of Kurtosis using the formula: K = numerator – 3(n-1)^2/((n-2)(n-3)).
- After inserting the variables and calculating the result, check your answer with the calculator above.

**Example Problem : **

Use the following variables as an example problem to test your knowledge.

Number of data points (n) = 10

Individual data point (x_i) = [5, 7, 9, 11, 13, 15, 17, 19, 21, 23]

Mean of the data (μ) = 15

Standard deviation of the data (σ) = 4