Z-Score

Updated 02 Oct 2026

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What it is
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  expresses a value's distance from a mean in standard-deviation units
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Formula
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  population form: $z=(x-\mu)/\sigma$ .
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  sample-standardized form: $z=(x-\bar x)/s$ , provided $s>0$ .
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Interpretation
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  positive values lie above the mean; negative values lie below it.
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  a threshold such as $|z|>3$ is a screening heuristic, not a universal definition of an error.
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Limitations
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  Skewness and extreme observations can make mean/standard-deviation screening misleading.
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Related
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  Unavailable reference
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  Standard Deviation
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  K-Means Clustering

Linked references 1