Enter a raw score, population mean and population standard deviation to standardise the score as z = (x - mu)/sigma and get its percentile rank, comparing values across distributions.
Z>0 表示高于均值，Z<0 表示低于均值。
| Item | Formula / Note | Source / Standard |
|---|---|---|
| Z score | z = (x - mu)/sigma, where mu is the population mean and sigma the population SD | NIST/SEMATECH e-Handbook of Statistical Methods §1.3.5 |
| Percentile rank | Percentile = Phi(z) × 100%, where Phi is the standard normal CDF | NIST/SEMATECH e-Handbook of Statistical Methods, normal quantiles |
| Direction | z > 0 means above the mean; z < 0 means below; z = 0 is exactly the mean | NIST/SEMATECH e-Handbook of Statistical Methods §1.3.5 |
| Cross-distribution comparison | Being dimensionless after standardization, z allows comparison across distributions | NIST/SEMATECH e-Handbook of Statistical Methods §1.3.5 |