Subjects statistics

Interquartile Range 561Fa9

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1. **Problem:** Find the interquartile range (IQR) of the number of viewers over 9 days: 50, 42, 66, 120, 48, 170, 110, 40, 35. 2. **Step 1: Sort the data in ascending order:** $$35, 40, 42, 48, 50, 66, 110, 120, 170$$ 3. **Step 2: Identify quartiles:** - Median (Q2) is the middle value since there are 9 data points: 5th value = 50. - Lower half (below median): $$35, 40, 42, 48$$ - Upper half (above median): $$66, 110, 120, 170$$ 4. **Step 3: Find Q1 (median of lower half):** Since 4 values, median is average of 2nd and 3rd values: $$Q1 = \frac{40 + 42}{2} = \frac{82}{2} = 41$$ 5. **Step 4: Find Q3 (median of upper half):** Median of $$66, 110, 120, 170$$ is average of 2nd and 3rd values: $$Q3 = \frac{110 + 120}{2} = \frac{230}{2} = 115$$ 6. **Step 5: Calculate interquartile range (IQR):** $$IQR = Q3 - Q1 = 115 - 41 = 74$$ **Final answer:** The interquartile range is **74**. Answer choice: D) 74