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Median Quartile Percentile 9F2E35

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1. **State the problem:** We need to find the Median (Md), the first quartile (Q1), and the 43rd percentile (P43) for the data set: 60, 70, 50, 80, 90, 100, 110. 2. **Sort the data:** Arrange the data in ascending order: 50, 60, 70, 80, 90, 100, 110. 3. **Find the Median (Md):** The median is the middle value of the sorted data. Since there are 7 data points (odd number), the median is the 4th value. $$Md = 80$$ 4. **Find the first quartile (Q1):** Q1 is the median of the lower half of the data (not including the median if odd number of data points). Lower half: 50, 60, 70. Median of lower half is the 2nd value: $$Q1 = 60$$ 5. **Find the 43rd percentile (P43):** Use the formula for the percentile rank position: $$L = \frac{P}{100} \times (n + 1) = \frac{43}{100} \times (7 + 1) = 0.43 \times 8 = 3.44$$ This means P43 lies between the 3rd and 4th data points. Interpolate between 3rd (70) and 4th (80) values: $$P43 = 70 + 0.44 \times (80 - 70) = 70 + 4.4 = 74.4$$ **Final answers:** - Median (Md) = 80 - First quartile (Q1) = 60 - 43rd percentile (P43) = 74.4