Z-Score Calculator
Calculate the z-score (standard score) that indicates how many standard deviations a value is from the mean.
Escore Z
1.500000
Z-Score vs Value (x)
Formula
## How to Calculate a Z-Score ### Formula **Z = (X - mu) / sigma** The z-score expresses how far a data point is from the population mean in units of standard deviations. A positive z-score means the value is above the mean; a negative z-score means below. Z-scores allow comparison across different scales and distributions.
Exemplo Resolvido
A student scores 85 on a test where the class mean is 70 and SD is 10.
- 01Z = (X - mu) / sigma
- 02Z = (85 - 70) / 10
- 03Z = 15 / 10 = 1.5
- 04The score is 1.5 standard deviations above the mean
Perguntas Frequentes
What is a "good" z-score?
It depends on context. In testing, z > 0 means above average. A z-score beyond 2 or -2 is unusual (roughly top/bottom 2.5%). Beyond 3 or -3 is very rare (about 0.1%).
Can z-scores be used with non-normal data?
You can always compute a z-score, but its probabilistic interpretation (using normal tables) is only valid when the data is approximately normally distributed.
How do I convert a z-score back to the original value?
Use X = mu + Z * sigma. For example, z = 1.5 with mean 70 and SD 10 gives X = 70 + 1.5*10 = 85.
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