interdecile

Interdecile refers to the interval between the first and ninth deciles of a data distribution. The interdecile range (IDR) is defined as D9 minus D1, where D1 is the 10th percentile and D9 is the 90th percentile. Deciles partition data into ten equal parts; the 1st decile marks the value below which 10% of observations fall, and the 9th decile marks the value below which 90% fall.

Calculation: For a sorted sample x(1) ≤ x(2) ≤ ... ≤ x(n), D1 and D9 are estimated as the 10th and 90th percentiles. Many methods use interpolation between order statistics. As a simple illustration, consider the dataset 1, 2, ..., 20. Using a nearest-rank approach, D1 is the 2nd value (2) and D9 is the 18th value (18), giving an interdecile range of 16.

Interpretation: The IDR measures the spread of the central 80% of observations. By excluding the outer 10% tails on each end, it is less affected by extreme values than the full range, while still reflecting the overall dispersion. The IDR is typically larger than the interquartile range, since it covers a wider portion of the data.

Relation to other measures: The IDR complements the interquartile range (IQR), which covers the central 50% (Q3 − Q1). Like IQR, the IDR provides a robust summary of dispersion relative to the full range, with exact values depending on the percentile estimation method and sample size. Applications include economic income dispersion, meteorological variability, education testing, and quality-control summaries.