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Documentation/Calc Functions/KURT

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Function name:

KURT

Category:

Statistical Analysis

Summary:

Calculates the kurtosis of a supplied data set, which must comprise at least four numbers. There are several different formulas used to define kurtosis and KURT returns the sample excess kurtosis.

Kurtosis is a measure that can help a statistician to better understand the shape of a probability distribution. In particular, it quantifies the extent to which the tails of that distribution match those of a normal distribution. A negative sample excess kurtosis indicates that the distribution has fewer values in its tails than a normal distribution; a positive sample excess kurtosis indicates that the distribution has more values in its tails than a normal distribution. The expected sample excess kurtosis for a normal distribution would be 0.0.

Syntax:

KURT(Number 1 [; Number 2 [; … [; Number 255]]])

Returns:

Returns a real number, which is the sample excess kurtosis of the specified data set.

Arguments:

Number 1, Number 2, … , Number 255 give the set of real numbers for which the kurtosis is to be calculated. Each argument may take one of the following forms:

  • A real number, or an expression that evaluates to a real number.
  • A reference to a single cell containing a real number.
  • A simple reference to a cell range containing real numbers.
  • The name of a named range, comprising cells containing real numbers.
  • The name of a database range, comprising cells containing real numbers.
  • An inline array of real numbers (for example, {1.1, 2.2, 3.3, 4.4}).

Note that although KURT can accept up to 255 arguments, each argument could specify a range of cells. This means that the number of real numbers processed could be many more than 255.

The following conditions (including errors) may be encountered:

  • If any argument is a string in quotation marks, then KURT reports a parameter list error (Err:504).
  • Text in cells and empty cells are ignored.
  • If there are less than four supplied numbers, then KURT reports a #DIV/0! error.
  • If the standard deviation of the supplied numbers is zero, then KURT reports a #DIV/0! error.

Additional details:

  • The formula for the sample excess kurtosis returned by KURT is:
[math]\displaystyle{ \text{KURT}\:=\:\left(\frac{n(n+1)}{(n-1)(n-2)(n-3)}\displaystyle \sum_{i=1}^{n}\left(\frac{x_i-\bar{x}}{s}\right)^4\right)-\left(\frac{3(n-1)^2}{(n-2)(n-3)}\right) }[/math]
where
[math]\displaystyle{ s }[/math] is the sample standard deviation of the numbers in the data set.
[math]\displaystyle{ n }[/math] is the count of numbers in the data set.
[math]\displaystyle{ x_i }[/math] is the i-th number in the data set.
[math]\displaystyle{ \bar{x} }[/math] is the mean of the numbers in the data set.
  • For more information about kurtosis, visit Wikipedia's Kurtosis page.

Examples:

Note that the count of numbers in the following examples is too low to allow useful conclusions to be drawn.

Formula Description Returns
=KURT(A1; A2; A3; A4; A5; A6) where cells A1:A6 contain the numbers 1, 2, 3, 4, 5, and 6 respectively. Here the function calculates the sample excess kurtosis value for a set of six numbers. -1.2
=KURT({9, 7, 12, 15, 17}) Here the function calculates the sample excess kurtosis value for a set of five numbers expressed as an inline constant array. -1.89273356401384
=KURT(1; 3; 4; 5; 7) Here the function calculates the sample excess kurtosis value for a set of five numbers passed as individual arguments. 0.200000000000001

Related LibreOffice functions:

None

ODF standard:

Section 6.18.39, part 2

Related (or similar) Excel functions:

KURT