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

The cumulative frequencies for the given class intervals are calculated as follows:

Height $\le 162$ cm: $12$
Height $\le 164$ cm: $12 + 15 = 27$
Height $\le 166$ cm: $27 + 24 = 51$

To find the number of students with height less than or equal to $165$ cm, we use linear interpolation within the class interval $164$–$166$.

The number of students in the interval $164$–$166$ is $24$. Assuming a uniform distribution of frequencies within the class interval, the number of students with height between $164$ cm and $165$ cm is:

$\dfrac{165 - 164}{166 - 164} \times 24 = \dfrac{1}{2} \times 24 = 12$

The total number of students whose height is less than or equal to $165$ cm is the sum of students with height $\le 164$ cm and those between $164$ cm and $165$ cm:

$27 + 12 = 39$

Answer: $39$