onesvaries

Onesvaries is a statistical descriptor used to quantify variability across features in a dataset. It is defined as the average of normalized per-feature ranges, intended to be simple and interpretable across diverse data domains.

Consider a dataset X with m observations and n features. For each feature j, let L_j and U_j be the known lower and upper bounds. The per-feature range is R_j = max_i x_i,j − min_i x_i,j. The onesvaries value of X is then onesvaries(X) = (1/n) sum_j (R_j / (U_j − L_j)).

This measure lies between 0 and 1 when all bounds are finite. It is invariant to translations and positive linear scaling of the data when bounds scale accordingly, and it does not reflect correlations between features.

Computation is straightforward and runs in O(mn) time. It can be implemented efficiently in streaming or batched settings by maintaining per-feature minima and maxima.

Applications include quick comparisons of dataset variability, pre-assessment in feature engineering, and quality control to detect unusually constrained features. It provides a simple, interpretable summary alongside variance-based metrics.

Onesvaries is a coined term in data analysis and is not a standard in statistical practice. Critics note that relying on ranges ignores distribution shape and outliers; as with any single metric, it should be used with complementary measures.