What is "trimean"

In statistics the trimean (TM), or Tukey's trimean, is a measure of a probability distribution's location defined as a weighted average of the distribution's median and its two quartiles:

$TM= \frac{Q_1 + 2Q_2 + Q_3}{4}$

This is equivalent to the average of the median and the midhinge:

$TM= \frac{1}{2}\left(Q_2 + \frac{Q_1 + Q_3}{2}\right)$

The foundations of the trimean were part of Arthur Bowley's teachings, and later popularized by statistician John Tukey in his 1977 book which has given its name to a set of techniques called exploratory data analysis.

Like the median and the midhinge, but unlike the sample mean, it is a statistically resistant L-estimator with a breakdown point of 25%. This beneficial property has been described as follows: