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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.
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 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.
The top chart shows a list of elements with values indicated by height and the median element shown in red. The lower chart shows the same elements with weights as indicated by the width of the boxes. The weighted median is shown in red and is different than the ordinary median. In statistics, a weighted median of a sample is the 50% weighted ...
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the weighted arithmetic mean of the median and two quartiles. Winsorized mean an arithmetic mean in which extreme values are replaced by values closer to the median. Any of the above may be applied to each dimension of multi-dimensional data, but the results may not be invariant to rotations of the multi-dimensional space. Geometric median