What a z-score actually tells you
A z-score converts any value into how many standard deviations it sits from the mean. That strips away the original units, which is the point: a z of +2 means the same thing whether you are talking about exam marks, blood pressure or rainfall. Positive is above the mean, negative below, and zero is exactly average.
The shaded area on the curve is the percentile — the proportion of the distribution that falls below your value.
The familiar landmarks
- z = ±1 — about 68% of values fall inside this band
- z = ±1.96 — 95%, the line most statistical tests draw
- z = ±2.58 — 99%
- z = ±3 — 99.7%; beyond this, values are genuinely rare
These hold when the data is roughly normal. For strongly skewed data a z-score still tells you the distance from the mean, but the percentile it implies will be wrong.
Frequently asked questions
Can a z-score be bigger than 3?
Yes, and it is a signal worth taking seriously. Under a normal distribution only about 0.3% of values sit beyond ±3, so such a value is either genuinely exceptional or a data-entry error.
Can I rely on this for coursework or research?
The normal distribution values are verified against published tables. Some courses use the population standard deviation here and some the sample; the choice changes the score.
Is my data uploaded?
No. The score is worked out locally, so the underlying measurements stay yours.
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