The mean weight of 120 students of a school is `52*75` kg. If the mean weight of 50 of them is 51 kg, find the mean weight of the remaining students.

Answer

To solve the problem step by step, we will follow the information provided in the question and apply the formula for mean.

### Step 1: Calculate the total weight of 120 students
The mean weight of 120 students is given as 52.75 kg. We can use the formula for mean:

\[ \text{Mean} = \frac{\text{Sum of observations}}{\text{Total number of observations}} \]

From this, we can derive the sum of weights of all 120 students:

\[ \text{Sum of weights of 120 students} = \text{Mean} \times \text{Total number of students} \]

Substituting the values:

\[ \text{Sum of weights of 120 students} = 52.75 \times 120 \]

Calculating this gives:

\[ \text{Sum of weights of 120 students} = 6330 \text{ kg} \]

### Step 2: Calculate the total weight of 50 students
The mean weight of 50 students is given as 51 kg. Again, we can use the formula for mean:

\[ \text{Sum of weights of 50 students} = \text{Mean} \times \text{Total number of students} \]

Substituting the values:

\[ \text{Sum of weights of 50 students} = 51 \times 50 \]

Calculating this gives:

\[ \text{Sum of weights of 50 students} = 2550 \text{ kg} \]

### Step 3: Calculate the total weight of the remaining 70 students
Now, we need to find the sum of weights of the remaining 70 students. We can do this by subtracting the sum of weights of the 50 students from the sum of weights of all 120 students:

\[ \text{Sum of weights of 70 students} = \text{Sum of weights of 120 students} - \text{Sum of weights of 50 students} \]

Substituting the values:

\[ \text{Sum of weights of 70 students} = 6330 - 2550 \]

Calculating this gives:

\[ \text{Sum of weights of 70 students} = 3780 \text{ kg} \]

### Step 4: Calculate the mean weight of the remaining 70 students
Now that we have the sum of weights of the 70 students, we can find their mean weight using the formula for mean:

\[ \text{Mean weight of 70 students} = \frac{\text{Sum of weights of 70 students}}{\text{Total number of students}} \]

Substituting the values:

\[ \text{Mean weight of 70 students} = \frac{3780}{70} \]

Calculating this gives:

\[ \text{Mean weight of 70 students} = 54 \text{ kg} \]

### Final Answer
The mean weight of the remaining 70 students is **54 kg**.

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