The problem in the image is as follows:

• The mean marks obtained by 25 students in a class is 35.
• The mean marks obtained by 35 students is 25.
• We are asked to find the mean marks obtained by all the students.

Solution:

First, we calculate the total marks obtained by each group of students.

1. Total marks for 25 students: $\text{Total marks} = 25 \times 35 = 875$

2. Total marks for 35 students: $\text{Total marks} = 35 \times 25 = 875$

Now, we calculate the combined total marks for all the students: $\text{Combined total marks} = 875 + 875 = 1750$

The total number of students is: $\text{Total students} = 25 + 35 = 60$

Finally, we calculate the mean marks for all the students: $\text{Mean marks} = \frac{\text{Combined total marks}}{\text{Total students}} = \frac{1750}{60} \approx 29.17$

So, the mean marks obtained by all the students is approximately 29.17.

Would you like a more detailed explanation or have any further questions?

Here are 5 related questions to expand your understanding:

1. What would happen to the mean if 5 students scored zero marks?
2. How would you calculate the median of this data if you had individual marks?
3. What is the effect of outliers on the mean compared to the median?
4. How would you calculate the weighted average if the two groups had different importance?
5. How does the harmonic mean differ from the arithmetic mean in similar problems?

Tip: When combining averages from different groups, it's essential to use the total counts and sums, not just the averages.