What is the height of the class?

Calculation:

Given,

The frequency distribution of the height of students in the class is as follows:

Height (in cm) | Number of Students

Calculate the cumulative frequency.

Cumulative frequency for the 160–162 cm range: 12

Cumulative frequency for the 162–164 cm range: 12 + 15 = 27

Cumulative frequency for the 164–166 cm range: 27 + 24 = 51

Cumulative frequency for the 166–168 cm range: 51 + 13 = 64

The total number of students is 64, so the median class contains the 32nd student. The cumulative frequency before 32 is 27 (for the 162–164 cm class), and after 32 is 51 (for the 164–166 cm class). Therefore, the median class is 164–166 cm.

The formula for finding the median in a grouped frequency distribution is:

\( \text{Median} = L + \left( \frac{\frac{N}{2} - F}{f} \right) \times h \)

L = lower boundary of the median class = 164

N = total number of students = 64

F = cumulative frequency before the median class = 27

f = frequency of the median class = 24

h = class width = 2

Substituting the values:

\( \text{Median} = 164 + \left( \frac{32 - 27}{24} \right) \times 2 = 164 + \left( \frac{5}{24} \right) \times 2 = 164 + 0.42 = 164.42 \)

∴ The median height is approximately 164.41 cm.

Hence, the correct answer is Option 3.