The average height of a group of 16 students was 164 cm. Four students of height 153 cm, 158 cm, 166 cm and 145 cm left the group. Nine new students of average height 167 cm joined the remaining group. What is the new average (in cm, to the nearest whole number) of the students in the group?

Step 1: Calculate the initial total sum of heights
Initial total students = 16
Initial average height = 164 cm

Initial Sum=16×164=2624 cm
Step 2: Account for students who left
Total height of 4 students who left = 153+158+166+145=622 cm

Remaining sum after departure=2624−622=2002 cm
Remaining number of students = 16−4=12

Step 3: Account for new students who joined
Number of new students = 9
Average height of new students = 167 cm

Total height of new students=9×167=1503 cm
Step 4: Compute final average

Final Sum=2002+1503=3505 cm
Total number of students now = 12+9=21

New Average=
21
3505
​
≈166.904 cm
Rounding to the nearest whole number gives 167 cm.