
Answer-first summary for fast verification
Answer: 0.8.
## Explanation To calculate the interquartile range (IQR), we need to find the difference between the third quartile (Q3) and the first quartile (Q1). **Step 1: Arrange the data in ascending order** The Sharpe ratios are already sorted: 0.2, 0.6, 0.7, 0.9, 1.0, 1.4, 1.6 **Step 2: Find the position of Q1 (25th percentile)** For n = 7 observations: Position of Q1 = (n + 1) × 0.25 = 8 × 0.25 = 2 So Q1 is the 2nd observation: **0.6** **Step 3: Find the position of Q3 (75th percentile)** Position of Q3 = (n + 1) × 0.75 = 8 × 0.75 = 6 So Q3 is the 6th observation: **1.4** **Step 4: Calculate IQR** IQR = Q3 - Q1 = 1.4 - 0.6 = **0.8** **Step 5: Match with options** The IQR of 0.8 corresponds to option B. **Verification:** - Option A (0.6) would be incorrect - Option B (0.8) is correct - Option C (1.4) is the value of Q3, not the IQR Therefore, the interquartile range of the Sharpe ratios is closest to 0.8.
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