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The lower weighted median is 2 with partition sums of 0.49 and 0.5, and the upper weighted median is 3 with partition sums of 0.5 and 0.25. In the case of working with integers or non-interval measures, the lower weighted median would be accepted since it is the lower weight of the pair and therefore keeps the partitions most equal. However, it ...
A weighting curve is a graph of a set of factors, that are used to 'weight' measured values of a variable according to their importance in relation to some outcome. An important example is frequency weighting in sound level measurement where a specific set of weighting curves known as A-, B-, C-, and D-weighting as defined in IEC 61672 [1] are used.
A weight function is a mathematical device used when performing a sum, integral, or average to give some elements more "weight" or influence on the result than other elements in the same set. The result of this application of a weight function is a weighted sum or weighted average.
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.
A practical application of this occurs for example for random walks, since the probability for the time of the last visit to the origin in a random walk is distributed as the arcsine distribution Beta(1/2, 1/2): [5] [12] the mean of a number of realizations of a random walk is a much more robust estimator than the median (which is an ...
In another usage in statistics, normalization refers to the creation of shifted and scaled versions of statistics, where the intention is that these normalized values allow the comparison of corresponding normalized values for different datasets in a way that eliminates the effects of certain gross influences, as in an anomaly time series. Some ...
For example: If L = (2, 2, 2, 3, 3, 4, 8, 8), then L' consists of six 2's, six 3's, four 4's, and sixteen 8's. That is, L' has twice as many 2s as L; it has three times as many 3s as L; it has four times as many 4s; etc. The median of the 32-element set L' is the average of the 16th smallest element, 4, and 17th smallest element, 8, so the N50 is
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 ...