1. **State the problem:** We need to compute the mean marks from the given cumulative frequency data. 2. **Understand the data:** The table shows cumulative frequencies for marks "More than" certain values. To find the mean, we first find the frequency for each class interval by subtracting consecutive cumulative frequencies. 3. **Calculate frequencies:** - Frequency for marks 10-20: $75 - 67 = 8$ - Frequency for marks 20-30: $67 - 58 = 9$ - Frequency for marks 30-40: $58 - 37 = 21$ - Frequency for marks 40-50: $37 - 22 = 15$ - Frequency for marks 50-60: $22 - 14 = 8$ - Frequency for marks above 60: $14$ 4. **Determine class midpoints:** - For 10-20: midpoint $= \frac{10 + 20}{2} = 15$ - For 20-30: midpoint $= 25$ - For 30-40: midpoint $= 35$ - For 40-50: midpoint $= 45$ - For 50-60: midpoint $= 55$ - For above 60, assume midpoint $= 65$ 5. **Calculate total frequency:** $$ \text{Total frequency} = 8 + 9 + 21 + 15 + 8 + 14 = 75 $$ 6. **Calculate mean using formula:** $$ \text{Mean} = \frac{\sum (f \times x)}{\sum f} $$ where $f$ is frequency and $x$ is midpoint. 7. **Calculate $\sum (f \times x)$:** $$ 8 \times 15 + 9 \times 25 + 21 \times 35 + 15 \times 45 + 8 \times 55 + 14 \times 65 = 120 + 225 + 735 + 675 + 440 + 910 = 3105 $$ 8. **Calculate mean:** $$ \text{Mean} = \frac{3105}{75} = \frac{\cancel{3105}}{\cancel{75}} = 41.4 $$ **Final answer:** The mean marks obtained is **41.4**.