Class 10R sat a test.

The mean mark for the class was 70%.

There are 30 students in class 10R, 20 of whom are boys.

The mean mark for the boys in the test was 62%.

Work out the mean mark for the girls.

We can solve this problem using the concept of weighted averages.

### Step-by-Step Breakdown:

1. **Total number of students**:  
   There are 30 students in total, consisting of 20 boys and \(30 - 20 = 10\) girls.

2. **Mean mark for the class**:  
   The mean mark for the class is 70%, so the total marks scored by the class is:
   \[
   \text{Total marks for class} = \text{mean mark} \times \text{number of students} = 70\% \times 30 = 0.70 \times 30 = 21 \text{ total marks (in terms of percent)}.
   \]

3. **Mean mark for the boys**:  
   The mean mark for the boys is 62%, so the total marks scored by the boys is:
   \[
   \text{Total marks for boys} = 62\% \times 20 = 0.62 \times 20 = 12.4 \text{ total marks (in terms of percent)}.
   \]

4. **Total marks for the girls**:  
   Since the total marks for the class is 21 and the total marks for the boys is 12.4, the total marks for the girls is:
   \[
   \text{Total marks for girls} = 21 - 12.4 = 8.6 \text{ total marks (in terms of percent)}.
   \]

5. **Mean mark for the girls**:  
   There are 10 girls, so the mean mark for the girls is:
   \[
   \text{Mean mark for girls} = \frac{\text{Total marks for girls}}{\text{Number of girls}} = \frac{8.6}{10} = 0.86 = 86\%.
   \]

### Final Answer:
The mean mark for the girls is **86%**.

Would you like more details or have any questions?

Here are some related questions to explore:

1. What is the difference in the mean mark between boys and girls?
2. How would the mean mark for the class change if one student scored 100%?
3. What if the class size was different but the mean mark for the class remained the same?
4. How would the total marks change if the boys’ mean score increased by 5%?
5. What if a new student joined the class? How would that affect the mean score?

**Tip:** Remember, the mean is sensitive to extreme values. Adding a very high or low score can change the mean significantly.

Class 10R sat a test. The mean mark for the class was 70%. There are 30 students in class 10R, 20 of whom are boys. The mean mark for the boys in the test was 62%. Work out the mean mark for the girls.

Work out the mean mark for the girls in Class 10R given the overall class average of 70% and the boys' mean score of 62%. This problem covers weighted averages, including calculating the total marks for boys and girls. Suitable for students in Grades 9-10.

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