1. **State the problem:** We need to find the mean mass of a group of students given the frequency distribution of their masses in intervals. 2. **Formula for mean in grouped data:** $$\text{Mean} = \frac{\sum (f \times x)}{\sum f}$$ where $f$ is the frequency of each group and $x$ is the midpoint of each mass interval. 3. **Calculate midpoints ($x$) of each interval:** - For 40 - 44: $\frac{40 + 44}{2} = 42$ - For 45 - 49: $\frac{45 + 49}{2} = 47$ - For 50 - 54: $\frac{50 + 54}{2} = 52$ - For 55 - 59: $\frac{55 + 59}{2} = 57$ - For 60 - 64: $\frac{60 + 64}{2} = 62$ 4. **Multiply each midpoint by its frequency ($f \times x$):** - $5 \times 42 = 210$ - $8 \times 47 = 376$ - $12 \times 52 = 624$ - $12 \times 57 = 684$ - $3 \times 62 = 186$ 5. **Sum of frequencies:** $$\sum f = 5 + 8 + 12 + 12 + 3 = 40$$ 6. **Sum of $f \times x$ values:** $$\sum (f \times x) = 210 + 376 + 624 + 684 + 186 = 2080$$ 7. **Calculate the mean:** $$\text{Mean} = \frac{2080}{40}$$ Show canceling common factor: $$\text{Mean} = \frac{\cancel{2080}}{\cancel{40}} = 52$$ 8. **Interpretation:** The mean mass of the group of students is 52 kg. **Final answer:** 52 kg (option c)