Hist

Hist, short for histogram, is a graphical representation of the distribution of a numerical dataset. A histogram partitions the data into a series of contiguous bins and tallies the number of observations whose values fall within each bin. The height of each bar corresponds to the count, relative frequency, or probability density, depending on how the histogram is configured. Histograms are widely used in exploratory data analysis to assess features such as central tendency, skew, modality, and spread.

Constructing a histogram requires choosing the bin boundaries, associated bin width, and whether to normalize. Common approaches to selecting the number or width of bins include Sturges' rule, Scott's rule, and the Freedman–Diaconis rule. The choice can influence the perceived shape of the distribution, leading to phenomena such as over-smoothing or fragmentation.

Variants include two-dimensional histograms for bivariate data, and cumulative histograms that show the cumulative distribution function. Histograms can be normalized to yield relative frequencies or densities, facilitating comparisons across data sets with different sizes. In image processing, histogram equalization is a technique that redistributes the intensity values to enhance contrast.

In programming and statistics software, hist is a common function name. In Python, libraries such as numpy, matplotlib, and pandas provide histogram-related functions (for example, numpy.histogram and matplotlib.pyplot.hist). In R, the hist() function creates a histogram object; MATLAB and Octave include histogram utilities as well. The concept is language-agnostic and appears in many data analysis toolchains.

Histogram-based visualization has limitations: histograms do not reveal the precise distribution of values within bins and are sensitive to data range and binning. Kernel density estimation provides a smooth alternative for estimating a distribution without discretizing into bins.