A robust measure of location equal to 1/4(Q1+2Q2+Q3), where Q2 is the median of the data and Q1 and Q3 are, respectively, the lower and upper quartiles. It is an example of a L-estimate.
Trimean
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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[1] which has given its name to a set of techniques called 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[2]
See also
- Gastwirth's estimate
- L-estimator
References
- ^ Tukey, John Wilder (1977). Exploratory Data Analysis. Addison-Wesley. ISBN 0-201-07616-0.
- ^ Weisberg, H. F. (1992). Central Tendency and Variability. Sage University. ISBN 0803940076 (p. 39)
External links
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 | Statistics Dictionary. A Dictionary of Statistics. Second edition revised. Copyright © Oxford University Press, 2008. All rights reserved. Read more |
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