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The median of a power law distribution x −a, with exponent a > 1 is 2 1/(a − 1) x min, where x min is the minimum value for which the power law holds [10] The median of an exponential distribution with rate parameter λ is the natural logarithm of 2 divided by the rate parameter: λ −1 ln 2.
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.
Conversely, in any median algebra, one may define an interval [,] to be the set of elements such that ,, =. One may define a graph from a median algebra by creating a vertex for each algebra element and an edge for each pair ( x , z ) {\displaystyle (x,z)} such that the interval [ x , z ] {\displaystyle [x,z]} contains no other elements.
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 mathematics, concentration of measure (about a median) is a principle that is applied in measure theory, probability and combinatorics, and has consequences for other fields such as Banach space theory.
For the 1-dimensional case, the geometric median coincides with the median.This is because the univariate median also minimizes the sum of distances from the points. (More precisely, if the points are p 1, ..., p n, in that order, the geometric median is the middle point (+) / if n is odd, but is not uniquely determined if n is even, when it can be any point in the line segment between the two ...
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.
It allows to link multiple representations dynamically. For example, changing a formula can instantly change the graph, the table of values, and the text read-out for the function represented in all these ways. Technology use can increase accuracy and speed of data collection and allow real-time visualization and experimentation. [14]
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