The mean weight of 21 students is 21 kg. If a student weighing 21 kg is removed from the group, then what is the mean weight of the remaining students ?

Options

A. 20 kg
B. 21 kg
C. 19 kg
D. 22 kg

Explanation

To find the mean weight of the remaining students after removing one student weighing 21 kg, we can follow these steps:

### Step 1: Calculate the total weight of the 21 students.
The mean weight of the 21 students is given as 21 kg. The mean is calculated using the formula:

\[ \text{Mean} = \frac{\text{Total Weight}}{\text{Number of Students}} \]

From this, we can rearrange the formula to find the total weight:

\[ \text{Total Weight} = \text{Mean} \times \text{Number of Students} \]

Substituting the values:

\[ \text{Total Weight} = 21 \, \text{kg} \times 21 = 441 \, \text{kg} \]

### Step 2: Subtract the weight of the removed student from the total weight.
Now, we need to remove the weight of the student who is leaving the group. The weight of the removed student is 21 kg.

\[ \text{New Total Weight} = \text{Total Weight} - \text{Weight of Removed Student} \]

Substituting the values:

\[ \text{New Total Weight} = 441 \, \text{kg} - 21 \, \text{kg} = 420 \, \text{kg} \]

### Step 3: Calculate the new number of students.
After removing one student, the number of remaining students is:

\[ \text{New Number of Students} = 21 - 1 = 20 \]

### Step 4: Calculate the new mean weight.
Now we can calculate the new mean weight using the new total weight and the new number of students:

\[ \text{New Mean} = \frac{\text{New Total Weight}}{\text{New Number of Students}} \]

Substituting the values:

\[ \text{New Mean} = \frac{420 \, \text{kg}}{20} = 21 \, \text{kg} \]

### Final Answer:
The mean weight of the remaining students is **21 kg**.

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