StATS: What is an interquartile range?

The interquartile range (IQR) is the distance between the 75^th percentile and the 25^th percentile. The IQR is essentially the range of the middle 50% of the data. Because it uses the middle 50%, the IQR is not affected by outliers or extreme values.

The IQR is also equal to the length of the box in a box plot.

Example

Compute the interquartile range for the sorted Cotinine data:

18, 33, 58, 67, 73, 93, 147

The 25^th and 75^th percentiles are the .25*(7+1) and .75*(7+1) = 2nd and 6th observations, respectively.

IQR = 93-33 = 60.

Compute the interquartile range of the LDL data.

1 84
2 96
3 84,68,72,49,84,73
4 80,41,14
5 57,85,26

.25*(14+1) and .75*(14+1) are 3.25 and 11.75 respectively. Select halfway between the 11th and 12th observations (4.80 and 5.26) and halfway between the 3rd and 4th observations (3.49 and 3.68). Remember to sort the appropriate stems!

IQR = 5.03-3.585 = 1.445.

This page was written by Steve Simon while working at Children's Mercy Hospital. Although I do not hold the copyright for this material, I am reproducing it here as a service, as it is no longer available on the Children's Mercy Hospital website. Need more information? I have a page with general help resources. You can also browse for pages similar to this one at Category: Definitions, Category: Descriptive statistics.