Equalwidth

Equalwidth binning, also called uniform binning, partitions the numeric range of a dataset into a fixed number of intervals of identical width. If the data range is [min, max] and the chosen number of bins is k, then the bin width is w = (max − min) / k and the bin edges are min = e0 < e1 < … < ek = max, with each bin i spanning [ei, ei+1). Data values are assigned to the bin whose interval contains the value; in many implementations, the final bin is closed on both ends to include the maximum value.

Common uses include histograms and discretization for machine learning features. Equal-width binning provides a straightforward, interpretable way to summarize continuous data and to transform it into categorical-like inputs for certain algorithms.

Advantages of equal-width binning include its simplicity, speed, and the even coverage of the data range, which can be helpful for visualization and quick preprocessing. Disadvantages include sensitivity to outliers and the data distribution; bin boundaries may split dense regions or obscure important structure, especially in skewed or multimodal data. The choice of k (the number of bins) strongly influences the resulting representation, and the method does not adapt to varying data density.

Related approaches include equal-frequency binning (quantile binning), which uses variable widths to ensure roughly equal counts per bin, at the cost of uneven interval sizes. Rules such as Sturges’, Scott’s, and Freedman–Diaconis offer heuristics for selecting an appropriate number of bins or bin width based on sample size and dispersion.