interdecile range

{{Short description|Statistical measure}}

In statistics, the interdecile range is the difference between the first and the ninth deciles (10% and 90%). The interdecile range is a measure of statistical dispersion of the values in a set of data, similar to the range and the interquartile range, and can be computed from the (non-parametric) seven-number summary.

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|date=January 2017}} 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.{{sfn|Evans|1955|loc=Appendix G: Inefficient statistics, pp. [https://archive.org/stream/atomicnucleus032805mbp#page/n925/mode/2up 902–904]}} Analogous measures of location are given by the median, midhinge, and trimean (or statistics based on nearby points).