Free Z-Score Calculator
Calculate the z-score (standard score) that indicates how many standard deviations a value is from the mean.
Z-Score
1.500000
Absolute Distance (in SDs)1.5000
Raw Deviation15.0000
Z-Score vs Value (x)
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.
Example Calculation
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
Frequently Asked Questions
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