Matematika

Z-Score Calculator

📊Z-score Calculator

Value (x)

Mean (μ)

Stand. nuokrypis (σ)

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What is Z-Score Calculator?

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A z-score (standard score) expresses a value's distance from the population mean in standard deviation units. z = (x − μ) / σ. Positive z = above average; negative z = below average.

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How to Z-Score Calculator

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1z = (x − μ) / σ
2Percentile from z-score: use standard normal CDF
3z=1.96 → 97.5th percentile
4Enables comparison across different measurement scales

Worked Examples

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Example 1

Given:Score 85 · Mean 70 · SD 15

Rezultatas:z = 1.0 → 84th percentile

(85-70)/15=1.0; P(Z<1)=84.1%

Common z-score percentiles

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z-score	Percentile
-2.0	2.3%
-1.0	15.9%
0	50%
1.0	84.1%
1.96	97.5%
2.58	99.5%
3.0	99.9%

References

›Standard score — Wikipedia

Z-Score Calculator