How this calculator works
The z-score is z=(x−μ)/σ.
Formula
z=(x−μ)/σStandardizes a value by its supplied mean and positive standard deviation.
Worked example
One SD above mean is a verified test case used by the calculation engine.
Assumptions and limitations
- The value and mean are finite real numbers.
- Standard deviation must be positive.
- The calculator standardizes the supplied values; it does not infer a probability distribution.
Methodology & sources
This calculator uses deterministic, versioned calculation logic. The formula and verified examples above are part of the calculation definition used by CalcuMint. Technical calculation version: 1.
- CalcuMint deterministic statistics engine
Frequently asked questions
What does a positive z-score mean?
The supplied value lies above the supplied mean by that many standard deviations.
Can standard deviation be zero?
No. Division by zero is undefined, so the calculator requires a positive standard deviation.