Z-Score Calculator
Inputs
Enter a value, mean, and standard deviation to calculate the z-score.
What is a Z-Score?
A z-score (or standard score) indicates how many standard deviations a data point is from the mean. It standardizes data, allowing comparisons across different distributions.
A z-score of 0 means the value equals the mean. Positive z-scores are above the mean; negative z-scores are below.
The Z-Score Formula
z = (x - μ) / σ- x = Raw value
- μ (mu) = Population mean
- σ (sigma) = Population standard deviation
Interpreting Z-Scores
| Z-Score Range | Interpretation | % of Data (Normal) |
|---|---|---|
| -1 to +1 | Typical | ~68% |
| -2 to +2 | Common | ~95% |
| -3 to +3 | Almost all | ~99.7% |
| Beyond ±3 | Outlier | <0.3% |
Example
Test Score Example
Mean = 75, Std Dev = 10. A student scored 85.
- z = (85 - 75) / 10 = 10 / 10 = 1.0
- The student is 1 standard deviation above the mean (top ~16%).
Frequently Asked Questions
Can z-scores be negative?
Yes. A negative z-score means the value is below the mean.
What is the z-score used for?
Comparing values from different distributions, identifying outliers, hypothesis testing, and calculating probabilities.