Enter a complete data set to compute the population variance as the average squared deviation from the mean, measuring dispersion with results computed locally.
| Item | Formula / Note | Source / Standard |
|---|---|---|
| Population variance | sigma^2 = (1/N) · sum(x_i - mu)^2 | ISO 3534-1:2006, Statistics - Vocabulary and symbols |
| Population standard deviation | sigma = sqrt(sigma^2) | ISO 3534-1:2006, Statistics - Vocabulary and symbols |
| Distinction from sample variance | Population divides by N; sample divides by n - 1 (Bessel correction) | ISO 3534-1:2006; Cramer H., Mathematical Methods of Statistics (1946) |
| Linear transformation | Var(aX + b) = a^2 · Var(X) | NIST/SEMATECH e-Handbook of Statistical Methods §1.3.5.1 |