Z-score
Z-score (Standard Score)
The number of standard deviations a value is from the mean — standardizes values from different distributions to a common scale.
When you'd see it: Fraud detection (a transaction with a Z-score of 4 is 4 standard deviations from the typical transaction), quality control, outlier detection, and as the test statistic in Z-tests (hypothesis testing used with large samples or known population variance).
Why it matters: Z-scores let you compare values across different distributions: how unusual is a 95°F day in Seattle vs Phoenix? Each city has a different mean and standard deviation; the Z-score normalizes both to the same scale. A Z-score above 3 is generally considered an outlier in a normal distribution.
Common mistakes: Using Z-scores as if they carry meaning without knowing the underlying distribution. The 'how many standard deviations from the mean' framing assumes roughly normal data. For highly skewed distributions, Z-scores can be misleading because the tails are asymmetric.
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