📊Interquartile Range (IQR)
The interquartile range (IQR = Q3 − Q1) covers the middle 50% of data. It is robust to outliers and used to identify them: values outside Q1−1.5×IQR or Q3+1.5×IQR are flagged as outliers.
- 1Sort data ascending
- 2Q1 = median of lower half · Q3 = median of upper half
- 3IQR = Q3 − Q1
- 4Outlier fences: [Q1−1.5×IQR, Q3+1.5×IQR]
Data: 4,7,13,16,21,24,25,28 · Q1=10 · Q3=24.5=IQR = 14.5 · Fences: [−11.75, 46.25] → no outliersTukey fences method
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Fun Fact
The box plot (IQR visualised), invented by John Tukey in 1970, remains one of the most effective displays for comparing distributions.
References
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