A Unified Scale for Interpreting Quantitative Measurements Across Distributions

Quantitative measurements are commonly interpreted using raw values, standardised scores, or interval-based summaries. However, these approaches do not provide a unified and directly interpretable representation of how observations relate to their underlying variability, particularly across variables with different scales and distributional forms.

This paper introduces a dispersion-based transformation, termed the Dispersion-Based Value (DBV), which expresses observed values on a continuous and direction-sensitive scale relative to their dispersion structure. Building on standardised deviation, the DBV framework maps values onto a bounded interpretive scale defined by a reference dispersion limit, enabling consistent classification of deviation magnitude across variables and analytical contexts.

Through illustrative and data-informed examples, the proposed representation is shown to preserve the structure of standardised deviation while enhancing interpretability, particularly for extreme observations. The framework is compatible with classical statistical practice and can be implemented using standard measures of central tendency and dispersion, including mean-standard deviation, median-interquartile range and transformation-based approaches.

By embedding deviation within a unified and scalable interpretive space, the DBV framework provides a structured tool for improving clarity, comparability and communication of quantitative measurements. While the formulation is general and potentially applicable across diverse domains, its use depends on appropriate specification of reference parameters and context-specific validation.