Interdecile range

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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, for estimating the standard deviation of a normal distribution, the scaled interdecile range gives a reasonably efficient estimator. More precisely, 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 of a normal distribution falling within 1.5 standard deviations of the mean) yields an estimate of about 65% efficiency.[1] Analogous measures of location are given by the median, midhinge, and trimean (or statistics based on nearby points).

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  1. ^ Evans 1955, Appendix G: Inefficient statistics, pp. 902–904.