histógrams

A histogram is a graphical representation of the distribution of a numerical variable. Data are grouped into a series of contiguous intervals, called bins, and the frequency (or relative frequency) of observations in each bin is shown as a bar. The bars touch to indicate the continuity of the data, distinguishing histograms from discrete bar charts.

To construct a histogram, select the variable, decide the number of bins or the bin width, assign each observation to a bin, and count the observations per bin. Common binning methods include Sturges’ rule, the Freedman–Diaconis rule, and Scott’s rule. The bin width affects interpretation: too few bins can hide features in the data, while too many bins can produce noise.

Histograms can display different measures: frequencies, relative frequencies, or densities. A relative-frequency histogram shows proportions, while a density histogram uses heights proportional to probability density, so the total area equals one. Cumulative histograms (ogives) plot cumulative frequency or probability.

Interpreting a histogram involves examining the shape: symmetry or skewness, modality (unimodal or multimodal), presence of gaps or outliers, and overall spread. They are useful for assessing distributional assumptions (such as normality), comparing distributions across groups, and identifying data quality issues. Limitations include sensitivity to bin choices and reduced precision for small samples, since individual values are not preserved.

Histograms are a foundational tool in exploratory data analysis, providing a concise view of where data are concentrated and how they are distributed.