How to Calculate IQR
What is 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.
Step-by-Step Guide
- 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]
Worked Examples
Input
Data: 4,7,13,16,21,24,25,28 · Q1=10 · Q3=24.5
Result
IQR = 14.5 · Fences: [−11.75, 46.25] → no outliers
Tukey fences method
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