Step 1 :First, we need to find the midpoint of each interval. The midpoints are 125 cm, 135 cm, and 145 cm for the intervals 120 Step 2 :Next, we multiply each midpoint by the frequency of that interval. This gives us 250 cm, 1620 cm, and 870 cm respectively. Step 3 :We then sum these values to get the total height of all the students. This gives us 250 cm + 1620 cm + 870 cm = 2740 cm. Step 4 :Finally, we divide the total height by the total number of students to get the mean height. The total number of students is the sum of the frequencies, which is 2 + 12 + 6 = 20. So, the mean height is \(\frac{2740}{20} = \boxed{137}\) cm.