ClarityHow to use this tool
- Enter observation, mean, standard deviation.
- Select Calculate to view the result.
- Check the method and assumptions below before using the result.
Input reference and sample values
Use the units and choices shown for each field. Sample values are provided for practice, not as recommendations.
| Input | Format and units | Sample |
|---|---|---|
| Observation | Numeric value. | 85 |
| Mean | Numeric value. | 70 |
| Standard deviation | Numeric value. Must be greater than zero. | 10 |
Result for these sample inputs
1.5
- Interpretation
- Standard deviations from the mean
Select Try the example in the form to load these values and calculate them again. This replaces the current form inputs. Compare the result with the method and worked explanation below.
The method, explained
z = (observation − mean) ÷ standard deviation. A positive score is above the mean and a negative score below it.
An observation of 85 with mean 70 and standard deviation 10 has a z-score of 1.5.
What to keep in mind
Standard deviation must be positive. A z-score alone does not justify a normal-distribution probability or identify an outlier without context.
Common questions
What does z = 0 mean?
The observation equals the supplied mean.
Does z = 2 always imply a percentile?
No. Percentile interpretation requires a distributional model; this tool only standardizes the value.
Methodology maintained by ClarityKit. How these tools are built and checked.