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In geometry, a median of a triangle is a line segment joining a vertex to the midpoint of the opposite side, thus bisecting that side. Every triangle has exactly three medians, one from each vertex, and they all intersect at the triangle's centroid .
In geometry, the geometric median of a discrete point set in a Euclidean space is the point minimizing the sum of distances to the sample points. This generalizes the median , which has the property of minimizing the sum of distances or absolute differences for one-dimensional data.
The median of a normal distribution with mean μ and variance σ 2 is μ. In fact, for a normal distribution, mean = median = mode. The median of a uniform distribution in the interval [a, b] is (a + b) / 2, which is also the mean. The median of a Cauchy distribution with location parameter x 0 and scale parameter y is x 0, the location parameter.
A median of a triangle is a straight line through a vertex and the midpoint of the opposite side, and divides the triangle into two equal areas. The three medians intersect in a single point, the triangle's centroid or geometric barycenter.
Median (geometry), in geometry, a line joining a vertex of a triangle to the midpoint of the opposite side; Median (graph theory), a vertex m(a,b,c) that belongs to shortest paths between each pair of a, b, and c; Median algebra, an algebraic triple product generalising the algebraic properties of the majority function
The median triangle of a given (reference) triangle is a triangle, the sides of which are equal and parallel to the medians of its reference triangle.
The medial triangle is not the same thing as the median triangle, which is the triangle whose sides have the same lengths as the medians of ABC. Each side of the medial triangle is called a midsegment (or midline). In general, a midsegment of a triangle is a line segment which joins the midpoints of two sides of the triangle.
The median is also a Fréchet mean, if the definition of the function Ψ is generalized to the non-quadratic = = (,), where =, and the Euclidean distance is the distance function d. [3] In higher-dimensional spaces, this becomes the geometric median.