# Interquartile Range (IQR)

The interquartile range (IQR) is a measure of the spread of a distribution of a single quantitative variable. The IQR is a rather simple calculation and is merely the difference between (hence “range”) the upper quartile (Q3) and the lower quartile (Q1) (hence “inter” and “quartile”). For a better understanding of quartiles, here is a site with more in-depth information. There are two primary uses of the IQR (a more complete list of uses can be found on Wikipedia):

1. as a robust measure of spread
2. as a tool to determine possible outliers

Although seen less frequently than other measures of spread (standard deviation is much more common), IQR is useful in describing “messy” data; it, like the median, is uninfluenced by outliers. This is why the IQR is c0nsidered a robust measure (a more technical definition of “robust” can be found here). However, where the IQR excels at describing “messy” data, it provides significantly less information than other conventional measures when describing “nice” data.

The second primary use of IQR is a direct consequence of its robustness. The IQR-method of determining outliers involves solving a very simple series of calculations: x is a moderate outlier if, x<Q1-1.5*IQR or x>Q3+1.5*IQR; x is an extreme outlier if, x<Q1-3*IQR or x>Q3+3*IQR. Because quartiles and the IQR are not influenced by outliers, claims about how to define outliers can be made using these measures.

However, caution should be taken when using the IQR-method to determine outliers because it cannot account for skew.

Lastly, a helpful way to remember IQR is through analogy; that is, an IQR is to a median as a standard deviation is to a mean.