1. **State the problem:** We are given the number of students in different mark intervals and need to calculate the mean mark. 2. **Formula for mean in grouped data:** $$\text{Mean} = \frac{\sum f_i x_i}{\sum f_i}$$ where $f_i$ is the frequency (number of students) in each class interval and $x_i$ is the midpoint of each class interval. 3. **Calculate midpoints ($x_i$) of each class interval:** - For 0-10: $\frac{0+10}{2} = 5$ - For 10-20: $\frac{10+20}{2} = 15$ - For 20-30: $\frac{20+30}{2} = 25$ - For 30-40: $\frac{30+40}{2} = 35$ - For 40-50: $\frac{40+50}{2} = 45$ - For 50-60: $\frac{50+60}{2} = 55$ - For 60-70: $\frac{60+70}{2} = 65$ 4. **List frequencies ($f_i$):** 4, 8, 11, 15, 12, 6, 2 5. **Calculate $f_i x_i$ for each interval:** - $4 \times 5 = 20$ - $8 \times 15 = 120$ - $11 \times 25 = 275$ - $15 \times 35 = 525$ - $12 \times 45 = 540$ - $6 \times 55 = 330$ - $2 \times 65 = 130$ 6. **Sum of frequencies:** $$\sum f_i = 4 + 8 + 11 + 15 + 12 + 6 + 2 = 58$$ 7. **Sum of $f_i x_i$:** $$\sum f_i x_i = 20 + 120 + 275 + 525 + 540 + 330 + 130 = 1940$$ 8. **Calculate mean:** $$\text{Mean} = \frac{1940}{58} = 33.45$$ **Final answer:** The mean mark of the 58 students is approximately **33.45**.