In statistics, the trimean (TM) is a measure of a probability distribution's location, defined as a weighted average of the distribution's median and its two quartiles:
It equals the average of the median and the midhinge:
Like the median and the midhinge, but unlike the sample mean, it is a statistically resistant L-estimator, having a breakdown point of 25%.
The trimean goes back to Arthur Bowley. It was discussed by statistician John Tukey in his 1977 book Exploratory Data Analysis.
The "statistical resistance" benefits of the trimean have been described as follows:
An advantage of the trimean as a measure of the center (of a distribution) is that it combines the median's emphasis on center values with the midhinge's attention to the extremes.
— Herbert F. Weisberg, Central Tendency and Variability[1]
See also
References
- ^ Weisberg, H. F. (1992). Central Tendency and Variability. Sage University. (p. 39)
External links
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