Geometric standard deviation

A dimensionless multiplicative spread factor obtained by exponentiating the standard deviation of logarithms.

Version

v1 · 2026-09-08 · History

Domain-specific #

4721

Origin domain

statistics

Subdomain

statistics

Core Idea

For positive data, GSD equals exp(sd(log X)); in a lognormal model, multiplying or dividing the geometric mean by powers of GSD describes symmetric intervals on the log scale. The logarithm converts ratios to differences, ordinary standard deviation measures log spread, and exponentiation restores a multiplicative factor. The abstraction is therefore identified by a declared carrier, a transformation or constraint over that carrier, and an invariant that tells an analyst whether the named structure is genuinely present.

The load-bearing residual is not the broad topic of statistics. It is the domain-specific identity determined by all observations are positive, the log base and dispersion convention are stated, and the result is interpreted multiplicatively.

Scope of Application

Geometric standard deviation belongs to statistics and is useful where the analyst can specify the typed statistics carrier, defining objects and relations, parameters, conventions, evidence, boundary cases and comparison targets, then evaluate all observations are positive, the log base and dispersion convention are stated, and the result is interpreted multiplicatively. The scope is broad within that domain but bounded by the need for all observations are positive, the log base and dispersion convention are stated, and the result is interpreted multiplicatively. The entry records a descriptive analytical identity; practical use requires the governing domain's evidence, standards, and safety obligations.

Clarity

The abstraction clarifies a crowded vocabulary by making all observations are positive, the log base and dispersion convention are stated, and the result is interpreted multiplicatively the center of the account. A claim should name the carrier, the governing operation or relation, the applicable assumptions, and the recognition test. A bare label is insufficient because the name Geometric standard deviation can be used for a formal identity, an implementation, or a neighboring result unless carrier and convention are stated.

Manages Complexity

Without the abstraction, an analyst must reason directly over many local details: the carrier roles, admissibility assumptions, competing conventions, derived invariants, boundary cases, and proof or validation obligations specific to Geometric standard deviation. Geometric standard deviation compresses them into the roles in the structural signature. That compression permits comparison across instances without erasing the variables that determine validity. It also exposes which details may be varied safely and which are constitutive.

Abstract Reasoning

1. Identify the carrier. State what the elements, states, objects, or observations are: the typed statistics carrier, defining objects and relations, parameters, conventions, evidence, boundary cases and comparison targets. Reject examples whose alleged carrier belongs to a different problem. 2. Lock the constitutive rule. Express all observations are positive, the log base and dispersion convention are stated, and the result is interpreted multiplicatively independently of one notation or implementation.

Knowledge Transfer

Knowledge transfers strongly among subfields of statistics because they reuse the typed statistics carrier, defining objects and relations, parameters, conventions, evidence, boundary cases and comparison targets, The logarithm converts ratios to differences, ordinary standard deviation measures log spread, and exponentiation restores a multiplicative factor., and type the carrier, state every parameter and convention in the definition, test that all observations are positive, the log base and dispersion convention are stated, and the result is interpreted multiplicatively, compare the nearest accepted identity, and report counterexamples, uncertainty, and limiting cases.

Relationships to Other Abstractions

Current abstraction Geometric standard deviation Domain-specific

Parents (1) — more general patterns this builds on

• Geometric standard deviation is a kind of Measurement Prime

  The proposed strict upward parent is prime:measurement.

Hierarchy path (1) — routes to 1 parentless root

• Geometric standard deviation → Measurement

Neighborhood in Abstraction Space

Geometric standard deviation sits in a crowded region of the domain-specific corpus (21^st percentile for distinctiveness): several abstractions share nearly its structure, so a description that fits it tends to fit its neighbors too.

Family — Logarithmic Information & Scale (9 abstractions)

Nearest neighbors

• Standard score — 0.92
• Coefficient of variation — 0.91
• Energy distance — 0.91
• Fisher information — 0.91
• Correlation ratio — 0.91

Computed from structural-signature embeddings · 2026-09-08