The Interdecile Mean (IDM) is, like the
Interquartile Mean, a
statistical measure of
central tendency. Whereas the
mean, or
average of a collection of datapoints is determined by selecting all of the points in the set, the IDM is calculated by discarding everything below the 10th
%ile (below the first
decile), and everything above the 90th
%ile (above the ninth
decile). The central 80% of the dataset will be measured.
Consider the following ordered dataset:
1, 3, 3, 6, 6, 7, 7, 8, 8, 38
There are 10 observations (datapoints) in the dataset, thus we have 10 deciles of 1
number each. Discard the lowest and the highest values:
1, 3, 3, 6, 6, 7, 7, 8, 8, 38
We now have 8 of the 10 observations remaining; we can easily calculate the mean of these numbers:
IDM = (3+3+6+6+7+7+8+8) / 8 = 6
The Interdecile Mean shares many properties with the Interquartile Mean. In difference, it is more resistant to manipulation - shifting a measured point (up or down) is only .625 times as effective as in IQM. Also, IDM is more responsive to non-Gaussian distributions, capturing skew more effectively.
For more discussion on sampled means and their relationships, see Professor Pi's excellent writeup in Interquartile Mean.
There are two options for dealing with sample sizes that do not easily divide into tenths. The simplest is to simply shrink/enlarge the center sampling area to an integer size. The more accurate is to include partial samples (for instance, adding 30% of each edge sample, and increasing sample size by .6).