Interquartile Range (IQR)

Definition

The interquartile range is the difference between the 75th percentile (upper quartile) and the 25th percentile (lower quartile) of a dataset. It captures the spread of the middle 50% of the data and is robust to outliers, making it a preferred dispersion measure for skewed distributions.

Why It Matters

Unlike the standard deviation or range, the IQR is unaffected by extreme values. This robustness makes it the standard measure of spread when data are skewed or contain outliers — common situations in income data, response times, or environmental measurements. The IQR also forms the basis of the box plot, where it defines the box height and the 1.5-times-IQR rule identifies potential outliers. In data cleaning, the IQR rule is one of the most widely used methods for flagging extreme observations.

Example

A dataset of house prices has a 25th percentile of 150,000 and a 75th percentile of 450,000, yielding an IQR of 300,000. A few multimillion-pound properties exist in the dataset and would dramatically inflate the range and standard deviation, but the IQR remains stable because it depends only on the central portion of the data. Any price below 150,000 - 1.5 x 300,000 = 0 or above 450,000 + 1.5 x 300,000 = 900,000 would be flagged as a potential outlier by the IQR rule.

Related Terms

• Box Plot
• Quartile
• Median
• Standard Deviation

Software Notes

• SPSS: Analyze > Descriptive Statistics > Explore; IQR is reported as "Interquartile Range" in the statistics table
• R: IQR(x) for the interquartile range; quantile(x, c(0.25, 0.75)) for the quartiles themselves
• Stata: summarize varname, detail — IQR is reported as the difference between the 75th and 25th percentiles