1. **Problem Statement:** Find the percentile rank for $X=18$ using interpolation from the given frequency distribution table. 2. **Given Data:** - Class intervals and cumulative percentages (c%): - $20-24$: 60% - $15-19$: 35% - $10-14$: 15% 3. **Step 1: Identify the class interval containing $X=18$** - $18$ lies in the class $15-19$. 4. **Step 2: Use the interpolation formula for percentile rank:** $$\text{Percentile rank} = L + \left(\frac{X - \text{Lower class boundary}}{\text{Class width}}\right) \times (U - L)$$ where: - $L$ = cumulative percentage before the class containing $X$ (here, 15%) - $U$ = cumulative percentage at the upper boundary of the class (here, 35%) - Class width = $19 - 15 + 1 = 5$ (assuming inclusive class intervals) - Lower class boundary = 14.5 (assuming continuous classes) 5. **Step 3: Calculate the percentile rank:** $$\text{Percentile rank} = 15 + \left(\frac{18 - 14.5}{5}\right) \times (35 - 15)$$ $$= 15 + \left(\frac{3.5}{5}\right) \times 20$$ $$= 15 + 0.7 \times 20$$ $$= 15 + 14 = 29$$ 6. **Answer:** The percentile rank for $X=18$ is 29%.