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Data & Analytics · Foundational

Interquartile Range (IQR)

The spread of the middle 50% of data: the third quartile minus the first quartile (Q3 - Q1).

Definition

The IQR is robust to outliers and underlies box plots and Tukey's outlier rule: values below Q1 - 1.5×IQR or above Q3 + 1.5×IQR are flagged as potential outliers.

Example

Q1 = 20, Q3 = 50, so IQR = 30, and the upper outlier fence = 50 + 45 = 95.

Exam tip

Memorize the 1.5 × IQR outlier fences.

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