Thomas measured the height, $x$, of each of the students in his class. He recorded the heights in the table below.
Calculate an estimate of the mean height of the students. Give your answer in centimetres $(\mathrm{cm})$.
Height (cm) $\quad 120< x \leq 130 \quad 130< x \leq 140 \quad 140< x \leq 150$
Frequency
2
12
6

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.