The common method for calculation of the trimean is adding the 25th percentile plus twice the 50th percentile plus the 75th percentile and dividing the sum by four. The trimean is almost as resistant to extreme scores as the median and does not wobble as much from sample to sample as does the average in a skewed distribution. The trimean is a good measure of central tendency. The trimean requires more information than the median because it includes the upper and lower quartiles.
trimean = (quartile1 + 2*median + quartile3) / 4
Tukey's method (which used upper and lower hinge instead of the 25th percentile and the 75th percentile) produces a very similar answer. The lower hinge is the median of the lower half of the data up to and including the median. The upper hinge is the median of the upper half of the data up to and including the median. The hinges are the same as the quartiles unless the remainder when dividing the sample size by four is three.
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