The KURT function returns the kurtosis of a data set.

Syntax

=KURT(num_1,[num_2], … )

Note: Beginning with Excel 2007, you can enter up to 255 number arguments to the function. Excel 2003 would only accept up to 30 number arguments.

Arguments

Argument Description
num_1 The first number, cell reference, or range for which you want the kurtosis
[num_2], … Optional. Additional numbers, cell references or ranges for which you want the kurtosis, up to a maximum of 255

Note: Logical values and text representations of numbers, typed directly into the KURT function, are included in the calculation. However, logical values and any text values, including text representations of numbers,  stored within an array of cells are ignored.

Examples

  A B C D
1 Array1 Array2    
2 12 15    
3 17 18    
4 14 27    
5 13 16    
6 5 28    
7        
8 Formula Result Notes
9 =KURT(A2:A6,B2:B6) 2.400732 Kurtosis of the data set A2:A6
10 =KURT(A2:A6,B2:B6) 0.479978 Kurtosis of the data set A2:A6 and B2:B6

Common Function Error(s)

Problem What went wrong
#VALUE Occurs if any of the supplied number arguments that are supplied directly to the function are not recognized as numeric values

  If the KURT function is provided with a reference to a range of cells, any text values within this cell range are simply ignored and do not cause the function to return an error
#DIV/0! Occurs if either:

  there are fewer than 4 data points in the supplied data set
  the sample standard deviation of the supplied data set is 0

Kurtosis characterizes the relative peakedness or flatness of a distribution compared with the normal distribution. Positive kurtosis indicates a relatively peaked distribution. Negative kurtosis indicates a relatively flat distribution.

Kurtosis is defined as:    

    \[    \begin{split}\left\{ \frac {n(n+1)} {(n-1)(n-2)(n-3)} \sum \left( \frac {x_i - \bar{x}}{s} \right)^4 \right\}  \\- \frac {3(n-1)^2}{(n-2)(n-3)}\end{split}   \]

where s is the sample standard deviation.

See Wikipedia for more information on kurtosis.