The histogram below shows the heights, in cm, of male A-level students at a particular school - AQA - A-Level Maths Pure - Question 12 - 2018 - Paper 3

To determine which class interval contains the median height, we first need to find the total frequency represented by the histogram. The heights are categorized as follows:

• 155 to 160 cm: 1 student
• 160 to 170 cm: 3 students
• 170 to 180 cm: 2 students
• 180 to 190 cm: 1 student

Total number of students = 1 + 3 + 2 + 1 = 7 students.

Since there are 7 students, the median position is given by: $\text{Median position} = \frac{n + 1}{2} = \frac{7 + 1}{2} = 4$

This means the median falls at the 4th position when the heights are ordered. In this case, the cumulative frequency indicates that the first 4 students are accounted for in the 155-170 cm range. Therefore, the median lies within the class interval [170, 180]. Thus, the correct answer is:

Circle [170, 180].