In statistics, the interdecile range is the difference between the first and the ninth deciles (10% and 90%).
Despite its simplicity, the interdecile range of a sample drawn from a normal distribution can be divided by 2.56 to give a reasonably efficient estimator[citation needed] of the standard deviation of a normal distribution.
This is derived from the fact that the lower (respectively upper) decile of a normal distribution with arbitrary variance is equal to the mean minus (respectively, plus) 1.28 times the standard deviation.
A more efficient estimator is given by instead taking the 7% trimmed range (the difference between the 7th and 93rd percentiles) and dividing by 3 (corresponding to 86% of the data falling within ±1.5 standard deviations of the mean in a normal distribution); this yields an estimator having about 65% efficiency.
[1] Analogous measures of location are given by the median, midhinge, and trimean (or statistics based on nearby points).