The average height of a group of 12 students is 170 cm. Four students of heights 154 cm. 157 cm, 165 cm and 172 cm left the group. What is the new average height (in cm) of the group?

Options

A. 165
B. 176
C. 170
D. 174

Answer

To find the new average height of the group after four students have left, we can follow these steps:

### Step 1: Calculate the total height of the original group
The average height of the group is given as 170 cm, and there are 12 students.

Total height = Average height × Number of students
Total height = 170 cm × 12 = 2040 cm

### Step 2: Calculate the total height of the students who left
The heights of the four students who left are 154 cm, 157 cm, 165 cm, and 172 cm.

Total height of students who left = 154 + 157 + 165 + 172
Total height of students who left = 648 cm

### Step 3: Calculate the new total height of the remaining students
New total height = Original total height - Total height of students who left
New total height = 2040 cm - 648 cm = 1392 cm

### Step 4: Calculate the number of remaining students
The number of students remaining after four students left is:
Remaining students = Original number of students - Number of students who left
Remaining students = 12 - 4 = 8

### Step 5: Calculate the new average height
New average height = New total height / Number of remaining students
New average height = 1392 cm / 8 = 174 cm

### Final Answer
The new average height of the group is **174 cm**.

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