Z-Score Calculator
A z-score (standard score) measures how many standard deviations a data point is from the mean. Z-scores normalise different datasets to the same scale, enabling comparisons.
- 1z = (x − μ) / σ
- 2x is the data point, μ is the mean, σ is the standard deviation
- 3z = 0 means at the mean; z = 1 means one std dev above
x=85, μ=75, σ=10=z = 1.085 is 1 std dev above average
x=60, μ=75, σ=10=z = −1.560 is 1.5 std devs below average
| Z-score | Percentile (approx) | Interpretation |
|---|---|---|
| −3 | 0.1% | Extremely below average |
| −2 | 2.3% | Well below average |
| −1 | 15.9% | Below average |
| 0 | 50% | Average |
| 1 | 84.1% | Above average |
| 2 | 97.7% | Well above average |
| 3 | 99.9% | Extremely above average |
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