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Documentation/Calc Functions/NORMINV

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Function name:

NORMINV

Category:

Statistical Analysis

Summary:

Calculates the inverse of the cumulative distribution function for a normal distribution.

The normal distribution is also known as the Gaussian distribution. It is a family of continuous probability distributions used in many fields to represent independent, randomly generated variables. Each normal distribution has a curve with the same general bell shape that is symmetric about the mean (often denoted by the lowercase Greek letter mu (μ)), with a spread defined by the standard deviation (often denoted by the lowercase Greek letter sigma (σ)).

Using the nomenclature of the previous paragraph, NORMINV calculates the real number x such that [math]\displaystyle{ \text{NORMDIST}(x;\:\mu;\:\sigma;\:1)~=~p }[/math], where the given probability p lies in the range (0, 1).

Syntax:

NORMINV(Number; Mean; STDEV)

Returns:

Returns a real number, which is the value of the random variable that would give the specified probability in the cumulative distribution function for the specified normal distribution.

Arguments:

Number is a real number in the range (0, 1), or a reference to a cell containing that number, which is a probability in the cumulative distribution function of the normal distribution.

Mean is a real number, or a reference to a cell containing that number, which is the mean of the normal distribution.

STDEV is a positive real number, or a reference to a cell containing that number, which is the standard deviation of the normal distribution.

  • If any of Number, Mean, or STDEV is non-numeric, then NORMINV reports a #VALUE! error.
  • If Number is less than 0.0 or greater than 1.0, then NORMINV reports an invalid argument error (Err:502).
  • If Number is equal to either 0.0 or 1.0, then NORMINV reports a #VALUE! error.
  • If STDEV is less than or equal to 0.0, then NORMINV reports an invalid argument error (Err:502).

Additional details:

  • Calc's NORMINV and NORM.INV functions perform identical calculations. The requirements for NORMINV are specified in ODF 1.2; NORM.INV is provided for interoperability with Microsoft Excel.
  • The normal distribution with a mean of 0 and standard deviation of 1 is known as the standard normal distribution. This gives rise to the following relationship between relevant Calc functions:
[math]\displaystyle{ \text{NORMINV}(x;\:0;\:1)\:=\:\text{NORMSINV}(x) }[/math]

Examples:

Formula Description Returns
=NORMINV(A1; A2; A3) where cells A1:A3 contain the numbers 0.961007571808867, 1.5, and 3.2 respectively. Here the function calculates the inverse of the given value from the cumulative distribution function for the specified normal distribution. 7.14
=NORMINV(90%; 63; 5) Assuming that the average egg weighs 63 grams with a standard deviation of 5 grams, then the value returned indicates that there is a 90% probability that an individual egg will be lighter than 69.41 grams. 69.407757827723
=NORMINV(0.797671619036357; 0; 1.2) Here the function calculates the inverse of the given value from the cumulative distribution function for the specified normal distribution. 1
=NORMINV(0.691462461274013 ; 0; 1) Here the function calculates the inverse of the given value from the cumulative distribution function for the standard normal distribution. 0.5

Related LibreOffice functions:

NORM.DIST

NORM.INV

NORM.S.DIST

NORM.S.INV

NORMDIST

NORMSDIST

NORMSINV

PHI

ODF standard:

Section 6.18.53, part 2

Related (or similar) Excel functions:

NORMINV