Interdecile range

---

title: "Interdecile range" type: doc version: 1 created: 2026-02-28 author: "Wikipedia contributors" status: active scope: public tags: ["scale-statistics"] description: "Statistical measure" topic_path: "science/mathematics" source: "https://en.wikipedia.org/wiki/Interdecile_range" license: "CC BY-SA 4.0" wikipedia_page_id: 0 wikipedia_revision_id: 0

::summary 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 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. Analogous measures of location are given by the median, midhinge, and trimean (or statistics based on nearby points).

References

::callout[type=info title="Wikipedia Source"] This article was imported from Wikipedia and is available under the Creative Commons Attribution-ShareAlike 4.0 License. Content has been adapted to SurfDoc format. Original contributors can be found on the article history page. ::