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
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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
More statistics functions
Arithmetic Mean • Contraharmonic Mean • Covariance • Empirical distribution CDF • Deviation • Five-Number Summary • Geometric Mean • Harmonic Mean • Inverse Empirical distribution CDF • Kurtosis • Log Geometric Mean • Lower Quartile • Median • Pooled Standard Deviation • Pooled Variance • Skewness (Statistische Schiefe) • Upper Quartile • Variance
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