Histogrammet

Histogrammet is a graphical representation of the distribution of numerical data. It consists of adjacent rectangles, or bins, spanning the data range. The height of each bin reflects how many observations fall within that interval, or the corresponding density. The x-axis shows data values; the y-axis shows frequency, relative frequency, or probability density. By displaying the shape of the distribution, histogrammet helps reveal properties such as central tendency, variability, skewness, and multimodality.

Construction: To build histogrammet, collect the data and choose binning parameters—either a fixed number of bins or a fixed bin width. Observations are assigned to their bin; in a frequency histogram the bin height is a count, in a relative-frequency histogram it is a proportion, and in a density histogram it is scaled so that the total area under the histogram equals 1. Alternatives include stacked histograms for groups and normalized histograms for comparing datasets.

Interpretation and caveats: The appearance depends on bin width and edges, so different bin choices can emphasize or obscure features. Large samples tend to yield stable histograms; small samples may look noisy. Histograms illustrate distribution shape and support decisions about modeling, such as normality or skewness, but they do not provide exact probabilities for individual values.

History and context: The concept originates from Karl Pearson in statistics literature of the late 19th century, who popularized histogram as a tool for visualizing distributions. Today histograms are a standard element of data analysis, widely available in statistical software and programming libraries. Related plots include kernel density estimates, box plots, and empirical cumulative distribution functions.