Definitions
In plain terms
It treats the n values in the selected window as the full set being described and therefore divides by n.
Technical
The window, center, denominator, current-row inclusion, missing-value policy, numerical algorithm, and first-ready row must be declared.
Scope
It differs from sample variance, which uses an n-minus-one denominator for an inferential estimate.
Formula
Population variance = sum((x_i - mean)^2) / n\sigma^2=\frac{1}{n}\sum_{i=1}^{n}(x_i-\bar{x})^2| Symbol | Meaning | Unit |
|---|---|---|
x_i | window value i | input units |
bar{x} | window arithmetic mean | input units |
n | window count | observations |
Output unit: squared input units
Examples
- A reviewer traces Rolling Population Variance from aligned inputs through its first-ready row and edge cases before accepting a displayed value.
Common misconceptions
- It differs from sample variance, which uses an n-minus-one denominator for an inferential estimate.
Concept relationships
Where this concept is used
Evidence and governance
- TA-Lib Bollinger Bands TA-Lib · first party technical publication
Supports: preferred label, short definition, technical definition, formula
Limits: TA-Lib permits moving-average variants beyond the local close-SMA and population-deviation contract.
- Measures of Scale NIST/SEMATECH · official standard
Supports: preferred label, short definition, technical definition, formula
Limits: The statistical reference does not define Bollinger Bands or validate financial forecasts from price dispersion.
- Reviewed by
- fintech-builder-batch-009
- Last reviewed
- 2026-07-30
- Next review
- 2027-07-30
- Record status
- published