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Documentation/Calc Functions/STANDARDIZE

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Function name:

STANDARDIZE

Category:

Statistical Analysis

Summary:

Calculates a normalized value that represents the number of standard deviations by which the value of a random variable is above or below the mean of the distribution. This statistical measure is often known as a standard score or a z-score.

A positive z-score indicates that the raw value is greater than the mean, while a negative z-score indicates that the raw value is less than the mean. A z-score of 0 indicates that the raw value is equal to the mean. The larger the absolute value of the z-score, the further the raw value from the mean.

Syntax:

STANDARDIZE(Number; Mean; STDEV)

Returns:

Returns a real number, which is the z-score for the specified raw value, given the specified mean and standard deviation.

Arguments:

Number is a real number, or a reference to a cell containing that number, which is the value of the random variable to be standardized.

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

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

  • If any of Number, Mean, or STDEV is non-numeric, then STANDARDIZE reports a #VALUE! error.
  • If STDEV is less than 0, then STANDARDIZE reports an invalid argument error (Err:502).
  • If STDEV is equal to 0, then STANDARDIZE reports a #DIV/0! error.

Additional details:

  • STANDARDIZE calculates the z-score ([math]\displaystyle{ z }[/math]) using the formula:
[math]\displaystyle{ z\:=\:\frac{x-\mu}{\sigma} }[/math]
where
  • [math]\displaystyle{ x }[/math] is the raw value of the random variable
  • [math]\displaystyle{ \mu }[/math] is the mean
  • [math]\displaystyle{ \sigma }[/math] is the standard deviation
  • For more information on standard scores / z-scores, visit Wikipedia's Standard score page.

Examples:

Formula Description Returns
=STANDARDIZE(A1; A2; A3) where cells A1:A3 contain the values 1, 5, and 2 respectively. Here the function calculates a negative z-score because the raw value is less than the mean. -2
=STANDARDIZE(5; 5; 3) Here the function calculates a zero z-score because the raw value is equal to the mean. 0
=STANDARDIZE(11.3; 6.5; 1.4) Here the function calculates a positive z-score because the raw value is greater than the mean. 3.42857142857143

Related LibreOffice functions:

GAUSS

ODF standard:

Section 6.18.71, part 2

Related (or similar) Excel functions:

STANDARDIZE