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