# Interdecile Range: Definition, How to Calculate

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 interdecile range is a measure of spread.

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 PERCENTILE function in Excel (or OpenOffice, which is free) to find the 90th and 10th percentiles for your data. Then subtract the two.
• 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:

RIDR = (90th percentile – 10th percentile) / median.

Or, in deciles:
RIDR = D90 – D10 / 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.

------------------------------------------------------------------------------

Need help with a homework or test question? With Chegg Study, you can get step-by-step solutions to your questions from an expert in the field. Your first 30 minutes with a Chegg tutor is free!

Statistical concepts explained visually - Includes many concepts such as sample size, hypothesis tests, or logistic regression, explained by Stephanie Glen, founder of StatisticsHowTo.