The mean of marks secured by 50 students in division A of class X is 61, 25 students of division B is 57 and that of 50 students of division C is 55. What will be the mean of marks of the students of three divisions of Class X?

Options

A. 57.1
B. 56.4
C. 59.2
D. 57.8

Answer

To find the mean of marks of the students from three divisions of Class X, we can follow these steps:

### Step 1: Calculate the total marks for each division.
- **Division A**: The mean marks are 61 and there are 50 students.
\[ \text{Total Marks for Division A} = \text{Number of Students} \times \text{Mean} = 50 \times 61 = 3050 \]

- **Division B**: The mean marks are 57 and there are 25 students.
\[ \text{Total Marks for Division B} = 25 \times 57 = 1425 \]

- **Division C**: The mean marks are 55 and there are 50 students.
\[ \text{Total Marks for Division C} = 50 \times 55 = 2750 \]

### Step 2: Calculate the total marks for all divisions combined.
\[ \text{Total Marks} = \text{Total Marks for Division A} + \text{Total Marks for Division B} + \text{Total Marks for Division C} \]
\[ \text{Total Marks} = 3050 + 1425 + 2750 = 7225 \]

### Step 3: Calculate the total number of students.
\[ \text{Total Students} = \text{Number of Students in Division A} + \text{Number of Students in Division B} + \text{Number of Students in Division C} \]
\[ \text{Total Students} = 50 + 25 + 50 = 125 \]

### Step 4: Calculate the mean marks for all students.
\[ \text{Mean} = \frac{\text{Total Marks}}{\text{Total Students}} = \frac{7225}{125} \]
\[ \text{Mean} = 57.8 \]

Thus, the mean of marks of the students of the three divisions of Class X is **57.8**.