klassintervall

Klassintervall (class interval) is a term in statistics that refers to a contiguous range of values used to group a data set into a frequency distribution. Each interval is defined by a lower bound and an upper bound, and the collection of intervals covers the range of the data. The interval width, also called the class width, is the difference between consecutive bounds and is typically constant in a grouped data set. Boundaries are commonly defined so that the lower bound is inclusive and the upper bound exclusive, for example 10–19 means values 10 up to but not including 20. Some conventions use closed intervals for all endpoints, provided the intervals do not overlap.

Klassintervall are used to compute frequencies (how many observations fall into each interval), relative frequencies, and frequency densities. They form the basis of histograms, where the height of a bar reflects frequency or density and the width reflects the class interval.

Choosing the number and width of intervals affects the readability and interpretability of the distribution. A common approach to determine the number of intervals is Sturges’ rule: k ≈ 1 + log2(n), where n is the sample size; alternative rules include Scott’s and Freedman–Diaconis, which take data spread into account. When class widths are unequal, one often reports frequencies and uses density values to allow comparison.

Example: for data ranging from 3 to 29, one might use class intervals 0–9, 10–19, 20–29. Count observations in each interval to obtain a frequency distribution and, if needed, plot a histogram.

Klassintervall is a fundamental concept in descriptive statistics, especially for summarizing and visualizing large data sets.