Kurtosis Calculator

Online calculator to calculate the kurtosis of a data series


On this page the kurtosis of a series of numbers is calculated.

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 Results
Sample
Population

Kurtosis is a measure of the relative "flatness" of a distribution. A positive kurtosis shows a tapered distribution (leptokurtic distribution); a negative kurtosis indicates a flat distribution (platykurtic distribution). Normal peak distributions are also referred to as mesokurtic.


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