Documentation/Calc Functions/GAUSS

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    Function name:

    GAUSS

    Category:

    Statistical Analysis

    Summary:

    Calculates a value from the cumulative distribution function of the standard normal distribution and returns that value minus 0.5. The value returned represents the probability that a sample of a normally distributed random variable lies between the mean and a specified number of standard deviations above (positive) or below (negative) the mean.

    The standard normal distribution is a special case of the normal distribution, with a mean of 0 and a standard deviation of 1.

    Syntax:

    GAUSS(Number)

    Returns:

    Returns a real number in the range [-0.5, 0.5].

    Arguments:

    Number is a real number, or a reference to a cell containing that number, which is the value that is to be used in the calculation.

    • If Number is non-numeric, then GAUSS reports a #VALUE! error.

    Additional details:

    • The relationship between the GAUSS function and the NORM.S.DIST function is:
    [math]\displaystyle{ \text{GAUSS}(x)~=~\text{NORM.S.DIST}(x; 1)\:-\:0.5 }[/math]
    • The relationship between the GAUSS function and the NORM.DIST function is:
    [math]\displaystyle{ \text{GAUSS}(x)~=~\text{NORM.DIST}(x; 0; 1; 1)\:-\:0.5 }[/math]
    • The following figure shows a plot of the GAUSS function.
    Gauss function plot.png
    • For more information on the normal and standard normal distributions, visit Wikipedia's Normal distribution page.

    Examples:

    Formula Description Returns
    =GAUSS(A1) where cell A1 contains the value 2. Here the function calculates the probability that a value from a normal population will fall between the mean and two standard deviations above the mean. Note that the formulas =NORM.S.DIST(2; 1)-0.5 and =NORM.DIST(2; 0; 1; 1)-0.5 return the same value. 0.477249868051821
    =GAUSS(-2) Here the function calculates the probability that a value from a normal population will fall between the mean and two standard deviations below the mean. -0.477249868051821
    =GAUSS(0.0375) Here the function calculates the probability that a value from a normal population will fall between the mean and 0.0375 standard deviations above the mean. 0.0149568299259098

    Related LibreOffice functions:

    NORM.DIST

    NORM.S.DIST

    NORMDIST

    ODF standard:

    Section 6.18.33, part 2

    Related (or similar) Excel functions:

    GAUSS since v.2013.