You can use the Kurtosis Calculator to derive the Kurtosis. Each value entered in the calculator should be separated by a comma. Example is included below.
How to use the Kurtosis Calculator
Let's review a simple example in order to see how to use the Kurtosis calculator.
Suppose that your goal is to derive the Kurtosis, given the following values:
2, 7, 15, 4, 8
To start, enter the above values in the Kurtosis calculator, and then press on the 'Calculate Kurtosis' button:
You'll then get the Kurtosis of 1.85954:
How to Manually Calculate the Kurtosis
You can use the formula below in order to manually calculate the Kurtosis:
Σ(xi - x̅)4
Kurtosis = (n-1)(SD4)
Where:
- x̅ = Mean (average of all data points)
- xi = Value of each data point
- n = Sample size
- SD = Standard Deviation
For example, let's say that you'd like to derive the Kurtosis, given the following values:
2, 7, 15, 4, 8
Here are the calculations to derive the Kurtosis:
- x̅ = (2+7+15+4+8) / 5 = 7.2
- Σ(xi - x̅)4 = (2-7.2)4 + (7-7.2)4 + (15-7.2)4 + (4-7.2)4 + (8-7.2)4 = 4537.936
- n = 5
- SD = [Σ(xi - x̅)2 ]0.5 / (n-1)0.5 = [98.8]0.5 / (5-1)0.5 = 4.970
Σ(xi - x̅)4 4537.936
Kurtosis = (n-1)(SD4) = (5-1)(4.9704) = 1.859
You'll then get the Kurtosis of 1.859.