Trimean
In statistics the trimean (TM), or Tukey's trimean, is a measure of a probability distribution's central tendency defined as a weighted average of the distribution's quartiles: T M = Q 1 + 2 Q 2 + Q 3 4 {\displaystyle TM={\frac {Q_{1}+2Q_{2}+Q_{3}}{4}}} It gives twice as much weight to the median or second quartile Q 2 {\displaystyle Q_{2}} than the first and third quartiles. This is equivalent to the arithmetic mean of the median and the midhinge: T M = 1 2 ( Q 2 + Q 1 + Q 3 2 ) {\displaystyle 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.