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It is also known as the spatial median, [1] Euclidean minisum point, [1] Torricelli point, [2] or 1-median. The geometric median is an important estimator of location in statistics, [3] because it minimizes the sum of the L2 distances of the samples. [4] It is to be compared to the mean, which minimizes the sum of the squared L2 distances, and ...
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 the case of isosceles and equilateral triangles, a median bisects any angle at a vertex whose ...
Median. Finding the median in sets of data with an odd and even number of values. The median of a set of numbers is the value separating the higher half from the lower half of a data sample, a population, or a probability distribution. For a data set, it may be thought of as the “middle" value.
Apollonius's theorem. In geometry, Apollonius's theorem is a theorem relating the length of a median of a triangle to the lengths of its sides. It states that the sum of the squares of any two sides of any triangle equals twice the square on half the third side, together with twice the square on the median bisecting the third side.
The geometric mean can be understood in terms of geometry. The geometric mean of two numbers, and , is the length of one side of a square whose area is equal to the area of a rectangle with sides of lengths and . Similarly, the geometric mean of three numbers, , , and , is the length of one edge of a cube whose volume is the same as that of a ...
The geometric distribution is the discrete probability distribution that describes when the first success in an infinite sequence of independent and identically distributed Bernoulli trials occurs. Its probability mass function depends on its parameterization and support.
Diagram of Stewart's theorem. Let a, b, c be the lengths of the sides of a triangle. Let d be the length of a cevian to the side of length a.If the cevian divides the side of length a into two segments of length m and n, with m adjacent to c and n adjacent to b, then Stewart's theorem states that + = (+).
The median of three vertices in a tree, showing the subtree formed by the union of shortest paths between the vertices. Every tree is a median graph. To see this, observe that in a tree, the union of the three shortest paths between pairs of the three vertices a, b, and c is either itself a path, or a subtree formed by three paths meeting at a single central node with degree three.