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Weighted median

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 percentile.[1][2][3] It was first proposed by F. Y. Edgeworth in 1888.[4][5] Like the median, it is useful as an estimator of central tendency, robust against outliers. It allows for non-uniform statistical weights related to, e.g., varying precision measurements in the sample.

  1. ^ Cormen, Thomas H.; Leiserson, Charles E.; Rivest, Ronald L.; Stein, Clifford (2001). Introduction to Algorithms. MIT Press. ISBN 9780262032933.
  2. ^ Horowitz, Ellis; Sahni, Sartaj; Rajasekaran, Sanguthevar (1996-12-15). Computer Algorithms C++: C++ and Pseudocode Versions. Macmillan. ISBN 9780716783152.
  3. ^ Bovik, Alan C (2010-07-21). Handbook of Image and Video Processing. Academic Press. ISBN 9780080533612.
  4. ^ Edgeworth, F. Y. (1888). "On a New Method of Reducing Observations Relating to Several Quantities". Philosophical Magazine. 25 (154): 184–191. doi:10.1080/14786448808628170.
  5. ^ Edgeworth, F. Y. (1887). "On Observations Relating to Several Quantities". Hermathena. 6 (13). Trinity College Dublin: 279–285. JSTOR 23036355.

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