8. The mean marks in statistics of 100 students in a class was 72 per cent. The mean marks of boys was 75 percent, while their number was 70 per cent. Find out the mean marks of girls in the class.

To find the mean marks of girls in the class, we can use a weighted average approach. The total number of students is 100, and we know the overall mean marks, as well as the mean marks of boys. Here’s the step-by-step breakdown:

Let’s define the following:
- \( N = 100 \) (total number of students)
- \( \mu_{\text{total}} = 72\% \) (mean marks of all students)
- \( \mu_{\text{boys}} = 75\% \) (mean marks of boys)
- \( P_{\text{boys}} = 70\% \) (percentage of boys in the class)

### Step 1: Determine the number of boys and girls
Since the boys make up 70% of the class, the number of boys is:
\[
N_{\text{boys}} = 0.70 \times 100 = 70
\]
Thus, the number of girls is:
\[
N_{\text{girls}} = 100 - 70 = 30
\]

### Step 2: Total marks for boys and girls
- The total marks for all 100 students is given by \( N \times \mu_{\text{total}} \):
\[
\text{Total marks for all students} = 100 \times 72 = 7200
\]

- The total marks for boys is given by \( N_{\text{boys}} \times \mu_{\text{boys}} \):
\[
\text{Total marks for boys} = 70 \times 75 = 5250
\]

### Step 3: Total marks for girls
The total marks for girls can be found by subtracting the total marks of boys from the total marks of the whole class:
\[
\text{Total marks for girls} = 7200 - 5250 = 1950
\]

### Step 4: Mean marks of girls
The mean marks for girls is the total marks for girls divided by the number of girls:
\[
\mu_{\text{girls}} = \frac{1950}{30} = 65\%
\]

Thus, the mean marks of the girls in the class is **65%**.

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Would you like more details on the calculations or clarifications?

Here are five related questions:
1. How would the result change if the percentage of boys was different?
2. How do weighted averages apply in other real-world scenarios?
3. Can we calculate the variance in marks given additional data?
4. What happens if we add more categories (e.g., different sections of students)?
5. How would this calculation change if the total number of students wasn't 100?

**Tip:** Always ensure that your total number of students matches the sum of boys and girls to avoid errors in weighted averages.

The mean marks in statistics of 100 students in a class was 72 per cent. The mean marks of boys was 75 percent, while their number was 70 per cent. Find out the mean marks of girls in the class.

Solve a class statistics problem where the mean marks of 100 students is 72%. The boys, making up 70% of the class, have an average of 75%. Learn how to calculate the mean marks for the girls using weighted averages. Suitable for Grades 8-10 students.

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