The mean height of a group of 30 students is 150 cm. If a 150 cm tall student is included in the group , then the mean height of the new group is ___.

Options

A. 151 cm
B. 149 cm
C. 150 cm
D. 152 cm

Explanation

To solve the problem step by step, we will follow these calculations:

### Step 1: Calculate the total height of the original group of students.
- Given that the mean height of 30 students is 150 cm, we can calculate the total height using the formula:
\[ \text{Total Height} = \text{Mean Height} \times \text{Number of Students} \]
- So, substituting the values:
\[ \text{Total Height} = 150 \, \text{cm} \times 30 = 4500 \, \text{cm} \]

### Step 2: Add the height of the new student to the total height.
- A new student with a height of 150 cm is added to the group. Therefore, the new total height becomes:
\[ \text{New Total Height} = \text{Original Total Height} + \text{Height of New Student} \]
- Substituting the values:
\[ \text{New Total Height} = 4500 \, \text{cm} + 150 \, \text{cm} = 4650 \, \text{cm} \]

### Step 3: Calculate the new number of students.
- The original group had 30 students, and we are adding one more student:
\[ \text{New Number of Students} = 30 + 1 = 31 \]

### Step 4: Calculate the new mean height.
- The new mean height can be calculated using the formula:
\[ \text{New Mean Height} = \frac{\text{New Total Height}}{\text{New Number of Students}} \]
- Substituting the values:
\[ \text{New Mean Height} = \frac{4650 \, \text{cm}}{31} = 150 \, \text{cm} \]

### Final Answer:
The mean height of the new group is **150 cm**.

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