What is the interquartile range (IQR) of the dataset {3, 5, 7, 8, 9, 11, 15, 16, 20}?
Answer and explanation
Correct answer: C. 9.5
- Step 1: Median is 9 (5th value). Step 2. Lower half {3, 5, 7, 8} has median Q1 = (5 + 7)/2 = 6. Step 3. Upper half {11, 15, 16, 20} has median Q3 = (15 + 16)/2 = 15.5. Step 4. IQR = Q3 - Q1 = 15.5 - 6 = 9.5. Answer: 9.5. Why not the others: 17 is the full range 20 - 3.
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