Z-Score, Explained
A z-score (standard score) tells you how many standard deviations a value sits from the mean. It converts any normal measurement — test scores, heights, response times — onto one universal scale, which is what makes the z table possible.
Interpreting z-scores
| z-score | Meaning |
|---|---|
| 0 | Exactly at the mean |
| +1 | One standard deviation above — beats ~84% of values |
| −1 | One below — beats only ~16% |
| +2 | Well above — top ~2.3% |
| ±1.96 | The 95% boundary used in confidence intervals |
Worked example
Your exam score is 82; the class mean is 74 with σ = 5. Then z = (82 − 74) / 5 = 1.6. The positive z table gives 0.94520 — you outscored about 94.5% of the class. That single conversion — raw number → z → percentile — is most of what introductory statistics asks you to do.
Why z-scores matter
They make different scales comparable (SAT vs ACT, cm vs inches), they power z-tests for hypothesis checking, they flag outliers (|z| > 3 is a common screen), and in finance a related idea drives the Altman Z-Score. The prerequisite is a roughly normal distribution — z-scores can be computed for any data, but their percentile meaning comes from normality.