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Firstly, computing median of an odd list is faster and simpler; while one could use an even list, this requires taking the average of the two middle elements, which is slower than simply selecting the single exact middle element. Secondly, five is the smallest odd number such that median of medians works.
[3] [4] In any of these cases, the use of these or other symbols for the median needs to be explicitly defined when they are introduced. The median is a special case of other ways of summarizing the typical values associated with a statistical distribution: it is the 2nd quartile, 5th decile, and 50th percentile.
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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.
The median of medians method partitions the input into sets of five elements, and uses some other non-recursive method to find the median of each of these sets in constant time per set. It then recursively calls itself to find the median of these n / 5 {\displaystyle n/5} medians.
A variation of the Theil–Sen estimator, the repeated median regression of Siegel (1982), determines for each sample point (x i, y i), the median m i of the slopes (y j − y i)/(x j − x i) of lines through that point, and then determines the overall estimator as the median of these medians. It can tolerate a greater number of outliers than ...
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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.