The average weight of 16 students in a class is 50.25 kg, and that of the remaining 8 students is 45.15 kg. Find the average weight of all the students in the class.

Options

A. 31.44
B. 48.55
C. 56.23
D. 34.56

Answer

To find the average weight of all the students in the class, we can follow these steps:

### Step 1: Calculate the total weight of the first group of students.
The average weight of the first group of 16 students is given as 50.25 kg. To find the total weight of these students, we multiply the average weight by the number of students:

\[ \text{Total weight of 16 students} = \text{Average weight} \times \text{Number of students} = 50.25 \, \text{kg} \times 16 = 804 \, \text{kg} \]

### Step 2: Calculate the total weight of the second group of students.
The average weight of the second group of 8 students is given as 45.15 kg. Similarly, we find the total weight of these students:

\[ \text{Total weight of 8 students} = \text{Average weight} \times \text{Number of students} = 45.15 \, \text{kg} \times 8 = 361.2 \, \text{kg} \]

### Step 3: Calculate the total weight of all students.
Now, we add the total weights of both groups to find the total weight of all students in the class:

\[ \text{Total weight of all students} = \text{Total weight of 16 students} + \text{Total weight of 8 students} = 804 \, \text{kg} + 361.2 \, \text{kg} = 1165.2 \, \text{kg} \]

### Step 4: Calculate the total number of students.
The total number of students in the class is the sum of the two groups:

\[ \text{Total number of students} = 16 + 8 = 24 \]

### Step 5: Calculate the average weight of all students.
Finally, we can find the average weight of all the students by dividing the total weight by the total number of students:

\[ \text{Average weight of all students} = \frac{\text{Total weight of all students}}{\text{Total number of students}} = \frac{1165.2 \, \text{kg}}{24} = 48.55 \, \text{kg} \]

Thus, the average weight of all the students in the class is **48.55 kg**.

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