The height which occurs most frequently in the class is

Calculation:

Given the frequency distribution of height of students:

The class interval with the highest frequency is 164–166, with 24 students.

The formula for calculating the mode for grouped data is:

\( \text{Mode} = L + \left( \frac{f_1 - f_0}{2f_1 - f_0 - f_2} \right) \times h \)

Where:

L: Lower boundary of the modal class = 164

f₁: Frequency of the modal class = 24

f₀: Frequency of the class before the modal class = 15

f₂: Frequency of the class after the modal class = 13

h: Class width = 2

Substituting the values into the formula:

\( \text{Mode} = 164 + \left( \frac{24 - 15}{2(24) - 15 - 13} \right) \times 2 \)

\( = 164 + \left( \frac{9}{48 - 28} \right) \times 2 \)

\( = 164 + \left( \frac{9}{20} \right) \times 2 \)

\( = 164 + 0.9 \)

\( = 164.9 \)

∴ The mode is approximately 164.9 cm.

Hence, the correct answer is Option 4.