Definitions
In plain terms
It measures dispersion in the same units as the input series and supplies the distance scale for this project's Bollinger Bands.
Technical
The D07 contract applies it to the same n current-inclusive closes as the middle-band SMA and permits a legitimate zero value.
Scope
The word population describes the denominator convention here; it does not claim the price window is a statistical population for inference.
Formula
Population standard deviation = square root of population variance\sigma=\sqrt{\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: input units
Examples
- A reviewer traces Rolling Population Standard Deviation from aligned inputs through its first-ready row and edge cases before accepting a displayed value.
Common misconceptions
- The word population describes the denominator convention here; it does not claim the price window is a statistical population for inference.
Concept relationships
Prerequisites
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