. The following table indicates the average marks of students of two classes of a campus:

BBS class

MBS class

Average marks

60

65

Number of students

100

90

Find the combine mean marks of all students.

To find the combined mean marks of all students from both classes, we use the formula for the combined mean of two groups. The formula is:

\[ \bar{X} = \frac{n_1 \bar{X}_1 + n_2 \bar{X}_2}{n_1 + n_2} \]

Where:
- \( \bar{X} \) is the combined mean,
- \( n_1 \) is the number of students in the first class (BBS),
- \( \bar{X}_1 \) is the average marks of the first class,
- \( n_2 \) is the number of students in the second class (MBS),
- \( \bar{X}_2 \) is the average marks of the second class.

Given:
- \( n_1 = 100 \)
- \( \bar{X}_1 = 60 \)
- \( n_2 = 90 \)
- \( \bar{X}_2 = 65 \)

Substitute these values into the formula:

\[ \bar{X} = \frac{(100 \times 60) + (90 \times 65)}{100 + 90} \]

Calculate the numerator:

\[ (100 \times 60) + (90 \times 65) = 6000 + 5850 = 11850 \]

Calculate the denominator:

\[ 100 + 90 = 190 \]

Now, calculate the combined mean:

\[ \bar{X} = \frac{11850}{190} \]

\[ \bar{X} = 62.37 \]

Therefore, the combined mean marks of all students is 62.37.

Would you like any further details or have any questions?

Here are 5 questions you can ask:
1. How do you find the combined mean if the number of students in one class changes?
2. Can you explain the significance of using weighted averages in this context?
3. How would you calculate the combined variance of the marks?
4. Can you provide a similar example with different numbers?
5. How does the combined mean change if the average marks of one class increase?

Tip: Always ensure to correctly identify and use the weighted average formula when combining means from different groups to account for varying group sizes.

Learn how to calculate the combined mean marks of students from two classes, BBS and MBS. Given average marks of 60 and 65 for 100 and 90 students respectively, find the combined mean using the weighted average formula. Suitable for Grades 10-12.

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