1. **Problem Statement:** Find the missing values in the frequency distribution table (Part A) and answer questions about the data (Part B). 2. **Given Table (Part A):** | Classes | f | Xm | f Xm | Class boundaries | %f | cf | |---------|---|----|-------|------------------|----|-----|-----| | 10-14 | 2 | 12 | ? | 9.5 - 14.5 | 4 | 2 | 50 | | 15-19 | 5 | 17 | ? | 14.5 - 19.5 | 10 | ? | 48 | | 20-24 | 12| 22 | ? | 19.5 - 24.5 | 24 | 19 | 43 | | 25-29 | 15| 27 | ? | 24.5 - 29.5 | 30 | 34 | 31 | | 30-34 | 10| 32 | ? | 29.5 - 34.5 | 20 | 44 | 16 | | 35-39 | 4 | 37 | ? | 34.5 - 39.5 | 8 | 48 | 6 | | 40-44 | 2 | 42 | ? | 39.5 - 44.5 | 4 | 50 | 2 | | Total | 50| | ? | | | | | 3. **Step 1: Calculate missing f Xm values** Formula: $f \times Xm$ - For class 10-14: $2 \times 12 = 24$ - For class 15-19: $5 \times 17 = 85$ - For class 20-24: $12 \times 22 = 264$ - For class 25-29: $15 \times 27 = 405$ - For class 30-34: $10 \times 32 = 320$ - For class 35-39: $4 \times 37 = 148$ - For class 40-44: $2 \times 42 = 84$ 4. **Step 2: Calculate total f Xm** Sum all $f Xm$ values: $$24 + 85 + 264 + 405 + 320 + 148 + 84 = 1330$$ 5. **Step 3: Calculate missing cumulative frequencies (cf values** - For class 15-19: $>cf = 50 - 7 = 43$ 7. **Step 5: Calculate missing %f values** Formula: $\%f = \frac{f}{50} \times 100$ - For class 10-14: $\frac{2}{50} \times 100 = 4$% - For class 15-19: $\frac{5}{50} \times 100 = 10$% - For class 20-24: $\frac{12}{50} \times 100 = 24$% - For class 25-29: $\frac{15}{50} \times 100 = 30$% - For class 30-34: $\frac{10}{50} \times 100 = 20$% - For class 35-39: $\frac{4}{50} \times 100 = 8$% - For class 40-44: $\frac{2}{50} \times 100 = 4$% 8. **Step 6: Answer Part B questions** 9. Range = highest upper limit - lowest lower limit = $44 - 10 = 34$ 10. Class size = difference between lower limits or upper limits = $15 - 10 = 5$ 11. Midpoint of 4th class = $27$ 12. Lower limit of 5th class = $30$ 13. Upper class boundary of 3rd class = $24.5$ 14. Class interval with highest frequency = 25-29 (f=15) 15. Lowest upper-class limit = $14$ 16. Highest upper-class boundary = $44.5$ 17. Class interval with lowest frequency = 10-14 and 40-44 (f=2) 18. Upper limit of 5th class = $34$ 19. Number of students in lowest class = $2$ 20. Lower class boundary of 3rd class = $19.5$ **Final answers for missing values in Part A:** - f Xm: 24, 85, 264, 405, 320, 148, 84 - %f: 4, 10, 24, 30, 20, 8, 4 - cf: 50, 43, 31, 31, 16, 6, 2