Midinterval

Midinterval is a term used to denote the midpoint of a closed interval. For an interval [a, b], its midinterval is (a + b)/2. This point lies exactly halfway between the endpoints and is sometimes called the interval midpoint or class mark.

In mathematics and numerical methods, the midinterval serves as a central representative value for the interval. It is distinct from the endpoints and from statistical measures such as the mean of a data sample, though it shares the idea of central tendency within the interval. In interval arithmetic, the midpoint is used to approximate the value of a function over the interval.

In statistics, when data are grouped into classes or bins, the midinterval (or class mark) of a bin [L, U] is (L + U)/2. Frequencies are often associated with this representative value for the purpose of computing a histogram or an estimate of the data’s mean and density. The term midinterval is less common than midpoint or class mark, but it appears in some texts to emphasize the central position within a bin.

In data collection and measurement, if the exact time or value of an event is unknown but is known to lie within an interval, analysts may report the event as occurring at the midinterval of that window as a simple estimator. This approach assumes a roughly uniform distribution of the true value within the interval and is subject to bias if the distribution is skewed.

Other terms for this concept include interval midpoint and class mark, and the idea underlies practices in histogram construction, interval data analysis, and numerical approximation.