Deciles > Interdecile Range

## What is the Interdecile Range?

The interdecile range (IDR) is the distance between the 9th decile and the 1st decile (or the 10th and 90th percentiles). It is a measure of dispersion or spread; Cutting off the top and bottom 10% of scores eliminates the very high scores and very low scores, leaving you with a measure of where the bulk of scores are.

The IDR is similar to:

- The
**range**, which measures from the smallest score to the largest score; It is wider than the IDR (by 10% in each direction). - The
**interquartile range**, which measures the middle 50% (trimming 25% off the top and bottom), compared to the middle 80% of the IDR (10% top and bottom trim).

The name “interdecile” comes from the fact that a decile is 10% of a set. When you find the interdecile range you’re basically cutting off the first and last deciles and then finding the range that’s left over.

## How to Calculate the Interdecile Range

You have several options for calculating the IDR:

- If you already have a non-parametric
**seven number summary**, you can use that to find the IDR. Just subtract the 10th percentile from the 90th. - Use the
(or OpenOffice, which is free) to find the 90th and 10th percentiles for your data. Then subtract the two.**PERCENTILE function in Excel** **By hand**: can be laborious, depending on the data, but you can find the steps to find percentiles*here*. Find the 90th and 10th percentiles, then subtract the two.

## Relative Interdecile Range (RIDR)

The RIDR, decribed by Lutz et. al, is the 80% predictive interval divided by the by the median. As a formula, that’s:

Or, in deciles:

_{90}– D

_{10}/ Median

Values for the RIDR are relative to the median. For example:

- RIDR = 0.5: the difference between the 90th and 10th percentiles is 1/2 the median.
- RIDR = 1.0: the difference between the 90th and 10th percentiles is exactly the same as the median.

Let’s say you have a data set for the median price of homes. The median home price in your area is $150,000, with a range of $25,000 to $500,000. The 90th percentile is $450,000 and the 10th percentile is $50,000.

- IDR = $500,000 – $25,000 = $475,000. This tells you that the bulk of the house prices are contained within a spread of $475,000 (excluding the top and bottom deciles).
- RIDR = ($500,000 – $25,000)/ $150,000 = $475,000/$150,000 = 3.16. This tells you that the difference between the 90th percentile house price and 10th percentile house price is 3.16 times the median value.

**References**:

Lutz, W., W. C. Sandserson, and S. Scherbov. (2004). “The End of World Population Growth.” In The End of World Population Growth in the 21st Century, 17–83, edited by W.Lutz, W. C.Sandserson, and S.Scherbov. London: Earthscan. Retrieved 1/12/2017 from here.

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