IQR fence (1.5 IQR rule)

An IQR fence is a boundary set 1.5 IQRs below the first quartile or above the third quartile, and values outside the fences count as outliers.

The fences mark how far the data can reasonably reach before a value is worth flagging. You place the lower fence at Q11.5×IQRQ_1 - 1.5 \times \text{IQR} and the upper fence at Q3+1.5×IQRQ_3 + 1.5 \times \text{IQR}, finding the quartiles by the median-excluded (TI-84) rule this site uses. If Q1=12Q_1 = 12 and Q3=20Q_3 = 20, then the IQR is 8, 1.5×8=121.5 \times 8 = 12, and the fences sit at 1212=012 - 12 = 0 and 20+12=3220 + 12 = 32, so a value of 35 is an outlier by this rule while 31 is not. The fences are a convention for identifying points that deserve a second look, not proof that anything is wrong with those points.

Where this comes up

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