STA007 · Probability & statistics · Classes 9–11
Interquartile range
The interquartile range (IQR) is Q₃ − Q₁, the spread of the middle half of the data. It ignores extreme values.
Q₃ − Q₁Interquartile range
📐 Formula
IQR = Q₃ − Q₁; outlier if beyond 1.5 × IQR from the box
✏️ Worked example
Q₁ = 3, Q₃ = 8: IQR = 5 (the green box).
🌍 Where it is used
Comparing consistency of two cricketers' scores.
❓ Quick check
Q₁ = 12, Q₃ = 20. IQR?
🏋️ Practice
EasyQ₁ = 40, Q₃ = 70. IQR?
Answer: 30
MediumIs the IQR affected by one huge value?
Answer: Hardly
ChallengeOutlier fences for Q₁ = 10, Q₃ = 20?
Answer: Below −5 or above 35