Binbreite

Binbreite, or bin width, is the width of each interval (bin) in a histogram. It determines how data values are grouped along the horizontal axis and, together with the data range, influences how much detail the histogram conveys about the underlying distribution. A histogram with equal-width bins uses the same bin width for all intervals.

In a simple, equal-width histogram, the bin width w is related to the data range and the number of bins k by w = (max(X) - min(X)) / k, where max(X) and min(X) are the largest and smallest data values. Alternatively, given a desired bin width, the number of bins is approximately k = (max(X) - min(X)) / w. The choice of bin width affects the visualization: small widths reveal more detail but can introduce noise, while large widths smooth over features and may obscure important structure.

Selecting an appropriate bin width involves a bias–variance trade-off and depends on the data set and the purpose of the visualization. Common rules of thumb include Sturges’ formula, which recommends a number of bins based on sample size, and density-based rules such as Scott’s rule and the Freedman–Diage rule, which prescribe widths using the data’s standard deviation or interquartile range, respectively. Many software tools allow either setting the number of bins or fixing the bin width directly.

In practice, analysts may experiment with different bin widths to assess the robustness of observed features. It is important to consider data characteristics, such as the presence of outliers or skewness, and to be aware that the bin width can influence interpretation as much as the data itself.