Z-Score Calculator
Calculate z-scores for the standard normal distribution.
Calculate Z-Score
Z to Probability
Result
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Enter values and calculate
Z-Score
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Probability
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Percentile
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Interpretation
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Understanding Z-Scores
A z-score measures how many standard deviations a data point is from the mean. It standardizes scores for comparison across different distributions.
Z = (x - μ) / σ
Interpreting Z-Scores
- Z = 0: Score equals the mean
- Z > 0: Score is above the mean
- Z < 0: Score is below the mean
- |Z| > 2: Unusual score (beyond 95% of data)
- |Z| > 3: Very unusual (outlier candidate)
Z-Score Properties
| Range | % of Data |
|---|---|
| ±1σ (Z between -1 and 1) | 68.27% |
| ±2σ (Z between -2 and 2) | 95.45% |
| ±3σ (Z between -3 and 3) | 99.73% |
Frequently Asked Questions
Why use z-scores instead of raw scores?
Z-scores allow comparison across different distributions by standardizing to a common scale. A z-score of 1.5 means the same thing regardless of the original units.
Can z-scores be negative?
Yes, negative z-scores indicate values below the mean. A z-score of -1 means one standard deviation below the mean.