Trimean

The trimean, also known as Tukey's trimean, or best easy systematic (BES) estimate is a statistically resistant measure of a distribution's central tendency. A seldom used weighted average of the quartiles, it was discussed by statistician John Tukey in his 1977 book Exploratory Data Analysis. The "statistical resistance" benefits of the trimean has been desribed 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

The formula to calculate the trimean is trivial, given the availability of other common statistical summaries:


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