histogramming

Histogramming is the process of constructing a histogram, a graphical or numerical representation of a dataset's distribution. Data are partitioned into discrete intervals, or bins, and the number of observations in each bin is counted. The histogram can be shown as counts or, when normalized, as a density or relative frequency. Histograms summarize shape, spread, and central tendency and help identify skewness, modality, and outliers.

Bin choices include the number of bins or the bin width. Fixed-width binning is common, with bin edges on a grid. Rules for selecting bin counts from data include Sturges', Scott's, and Freedman-Diaconis; each makes different assumptions about variability and sample size. The choice can substantially affect apparent features. Edge handling and outliers influence counts, and some implementations allow padding or clipping.

Normalizing yields distributions that sum to one, suitable for comparing datasets of different sizes. Cumulative histograms accumulate counts from the left and approximate the empirical distribution function. Multidimensional histograms extend binning to two or more variables, but they require more data and can be sparse.

Histogramming can be performed efficiently in a single pass: compute the bin index for each value and increment the counter. In streaming or large-scale data contexts, online algorithms update counts as new data arrive. Practical implementations must handle data outside the defined range, NaN values, and precision limits.

Beyond visualization, histogramming provides a simple summary for statistical analysis, data preprocessing (for example, scaling or histogram equalization in images), and as a surrogate for probability distributions in modeling and testing assumptions. It complements, rather than replaces, density estimation methods such as kernel density estimation.