Kurtosis Calculator

This function calculates the kurtosis of a data set

Kurtosis calculator


This function calculates the kurtosis of a data set. There are two results, one from calculating a sample and one from a full population.

To perform the calculation, enter a series of numbers. Then click the 'Calculate' button. The list can be entered unsorted.


Input format

The data can be entered as a series of numbers, separated by semicolons or spaces. You can enter the data as a list (one value per line). Or from a column from Excel spreadsheet by copy & paste


Kurtosis calculator

 Input
Decimal places
 Kurtosis Result
Sample
Population

Kurtosis formula

The kurtosis of a sample is determined by the following formula:

\(\displaystyle ω =\left[ \frac{1}{n} \sum^n_{i=1} \left( \frac{x_i - \overline{x}}{s}\right)^4\right]-3 \)

Sometimes the kurtosis is defined by another formula that omits the -3 term from the formula above. In this case, a normal distribution would give a kurtosis of 3.



The kurtosis of a full population is determined by the following formula:

\(\displaystyle ω =\left[ \frac{n(n-1)}{(n-1)(n-2)(n-3)} \sum^n_{i=1} \left( \frac{x_i - \overline{x}}{s}\right)^4\right]-\frac{3(n-1)^2}{(n-2)(n-3)} \)
\(x_i\)  Single data point
\(\overline{x}\)   Arithmetic mean
\(s\)   Standard deviation
\(n\)   Number of data points
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