histogrammi

A histogram is a graphical representation of the distribution of a numeric data set. It consists of adjacent bars whose widths correspond to intervals, called bins, of data values. The height of each bar reflects the number of observations in the corresponding bin, typically expressed as frequency, relative frequency, or density.

Construction involves selecting the data range, choosing bin edges, counting observations in each bin, and choosing a vertical scale. A frequency histogram uses counts; a relative-frequency histogram uses proportions; a density histogram uses densities so that the area of a bar is proportional to the proportion of observations. For continuous data, bin width and the number of bins influence the visual impression of the distribution.

Bin selection is important and there are methods to guide it. Sturges’ formula suggests a number of bins based on sample size, while the Freedman–Diaconis rule and Scott’s rule provide bin widths based on data dispersion. Too many bins can overfit noise; too few can obscure features such as skewness or multiple modes.

Interpretation focuses on the shape of the distribution: symmetry, skewness, modality, tails, and potential outliers. Histograms are primarily exploratory tools and do not provide exact probabilities; they approximate the underlying distribution and depend on sample size and binning choices. They are often used to compare distributions across groups by overlaying histograms or displaying side-by-side.

Variants include stacked or normalized histograms for comparing categories, and the histogram is related to kernel density estimates, which produce a smooth approximation of the distribution.