Enter a raw value, mean and standard deviation to compute the z score (x - mu)/sigma, for standardisation and outlier detection.
| Item | Formula / Note | Source / Standard |
|---|---|---|
| Standard score | z = (x - mu) / sigma | NIST/SEMATECH e-Handbook of Statistical Methods §1.3.5 |
| Properties after standardization | The standardized variable has mean 0 and standard deviation 1 | NIST/SEMATECH e-Handbook of Statistical Methods §1.3.5 |
| Percentile conversion | Percentile = Phi(z), where Phi is the standard normal CDF | NIST/SEMATECH e-Handbook of Statistical Methods, normal quantiles |
| Outlier rule of thumb | |z| > 3 is commonly treated as an outlier (3-sigma rule) | Montgomery DC, Introduction to Statistical Quality Control (7th ed.) |