IB AA HL May 2026 P2 TZA Q1

A group of \(52\) students have their heights measured in cm. The cumulative frequency graph for the heights of the students is shown in the following diagram.

1. Use the graph to find an estimate of the median height.[2]
2. The heights of the students are shown in the following frequency table where \(p,q\in\mathbb{N}\).

   Height (\(h\text{ cm}\))	Frequency
   \(155\leq h<160\)	\(3\)
   \(160\leq h<165\)	\(8\)
   \(165\leq h<170\)	\(14\)
   \(170\leq h<175\)	\(p\)
   \(175\leq h<180\)	\(q\)

   1. Find the value of \(p\) and the value of \(q\).
   2. Use the frequency table to find an estimate of the mean height, giving your answer to four significant figures.[5]