Interquartile Range (IQR)
Definition
The difference between the third quartile and the first quartile: IQR = Q3 - Q1. It measures the spread of the central 50 percent of the data and is the basis for identifying outliers in a box plot. Resistant to extreme values, unlike the standard deviation.
- Formula
- IQR = Q3 minus Q1
- Measures
- Spread of the central 50 percent of data
- Common use
- Outlier detection on a box plot
- Outlier resistance
- Resistant to extreme values, unlike SD
Common questions
How is IQR used to flag outliers?+
A common rule marks any value below Q1 minus 1.5 times IQR, or above Q3 plus 1.5 times IQR, as a potential outlier worth reviewing on a box plot.
Why prefer it over standard deviation for skewed forensic data?+
IQR is based only on the middle half of the data, so a few extreme measurements do not distort the reported spread the way they can inflate a standard deviation calculation.
Related terms
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- Box Plot (Box-and-Whisker Plot)
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- Histogram
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- Kernel Density Estimate (KDE)
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- Scatter Plot
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