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
