To solve this problem, we need to calculate the mean mark for the girls in class 10R. Let's break down the information step by step:

Given:

• Total students in class 10R: 30
• Boys in class 10R: 20
• Girls in class 10R = $30 - 20 = 10$
• Mean mark for the whole class: 70%
• Mean mark for the boys: 62%

Step 1: Calculate the total marks for the whole class.

The total marks for the class can be calculated by multiplying the mean mark by the total number of students: $\text{Total marks for the class} = 70\% \times 30 = 0.7 \times 30 = 21 \text{ marks}.$

Step 2: Calculate the total marks for the boys.

The total marks for the boys is given by: $\text{Total marks for the boys} = 62\% \times 20 = 0.62 \times 20 = 12.4 \text{ marks}.$

Step 3: Calculate the total marks for the girls.

The total marks for the class is the sum of the total marks for the boys and the girls. Therefore, we can calculate the total marks for the girls by subtracting the total marks for the boys from the total marks for the whole class: $\text{Total marks for the girls} = 21 - 12.4 = 8.6 \text{ marks}.$

Step 4: Calculate the mean mark for the girls.

Now, to find the mean mark for the girls, divide the total marks for the girls by the number of girls: $\text{Mean mark for the girls} = \frac{8.6}{10} = 0.86 = 86\%.$

Conclusion:

The mean mark for the girls is 86%.

Would you like more details or do you have any further questions? Here are some related questions you might find helpful:

1. How do weighted averages work in other contexts?
2. How would the result change if there were more boys or girls in the class?
3. What is the importance of calculating mean scores in statistical analysis?
4. Can you calculate the range of scores if we know more data about individual performances?
5. How can this method be extended to handle more complex distributions of students and scores?

Tip: Always make sure to double-check units (percentages, scores, etc.) when calculating averages in mixed groups!