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:
ODF standard:
Related (or similar) Excel functions:
STANDARDIZE