Mittelpunktswert

Mittelpunktswert, or central value, is a German mathematical term that denotes a central or representative value of a quantity. The exact meaning of the term varies by context, and it is not a single standardized concept in modern mathematics. In many texts it is used informally to refer to a value that serves as a center or reference point.

In geometry and interval arithmetic, the Mittelpunktswert of a closed interval [a, b] is the midpoint m = (a + b) / 2. This point lies at the center of the interval and often plays a role in symmetry considerations or in defining central measures for the interval.

In numerical analysis, the Mittelpunktswert can refer to the function value at the midpoint, f(m), especially in relation to the midpoint rule for numerical integration. The midpoint rule estimates an integral by multiplying the interval length by the function value at the midpoint, (b − a) f((a + b) / 2). Here, the Mittelpunktswert serves as the central sample value used in the approximation.

In statistics and probability, Mittelpunktswert is not a standard technical term. Central tendency is typically described using established terms such as Mittelwert (arithmetic mean) or Erwartungswert (expected value). The term may be encountered in older literature or informal explanations to describe a central or representative value, particularly in discussions of symmetry.

See also: Mittelpunkt, Mittelwert, Erwartungswert, Median, Mittelpunktsregel.