Consider the following for the four (04) items that follow: The...

The height which occurs most frequently corresponds to the mode of the given frequency distribution.

The maximum frequency is $24$, which corresponds to the class interval $164-166$. Thus, the modal class is $164-166$.

The lower limit of the modal class, $l = 164$
Frequency of the modal class, $f_1 = 24$
Frequency of the class preceding the modal class, $f_0 = 15$
Frequency of the class succeeding the modal class, $f_2 = 13$
Class size, $h = 2$

The mode is calculated using the formula:
$\text{Mode} = l + \left( \dfrac{f_1 - f_0}{2f_1 - f_0 - f_2} \right) \times h$

Substituting the values:
$\text{Mode} = 164 + \left( \dfrac{24 - 15}{2(24) - 15 - 13} \right) \times 2$

$\text{Mode} = 164 + \left( \dfrac{9}{48 - 28} \right) \times 2$

$\text{Mode} = 164 + \left( \dfrac{9}{20} \right) \times 2$

$\text{Mode} = 164 + \dfrac{9}{10} = 164 + 0.9 = 164.9$

The height which occurs most frequently is $164.9$ cm.

Answer: $164.9$ cm