Measures of Spread

Interquartile Range

The interquartile range is the difference between the Q3 and Q1, and it is abbreviated IQR. Thus, IQR=Q3−Q1. The IQR gives information about how the middle 50% of the data are spread. Fifty percent of the data values are always between Q3 and Q1. 


Example: A recent study proclaimed Mobile, Alabama the wettest city in America. (Source: http://www.livescience.com/environment/070518_rainy_cities.html.) The following table lists measurements of the approximate annual rainfall in Mobile over a 10 year period. 

Find the range and IQR for this data.


First, place the data in order from smallest to largest. 

To find the IQR, first identify the quartiles, and then compute Q3−Q1.

The IQR shows that there is a difference of 22 inches of rainfall for the middle 50% of the data. It appears that Mobile experiences wide fluctuations in yearly rainfall totals, which might be explained by its position near the Gulf of Mexico and its exposure to tropical storms and hurricanes.