<p>A group of \(52\) students have their heights measured in cm. The cumulatuve frequency graph for the heights of the students is shown in the following diagram.</p>
<div class="content-block"><figure class="question-figure aligncenter" style="text-align: center;"><img src="https://vocwkpgapvksartxhhor.supabase.co/storage/v1/object/sign/question-images/pasted/1791205090293-v7l1zepyai.png?token=eyJraWQiOiJiZTM3ZjNhZS05OWM4LTQ5ZGQtYjRiNS1iMTBhYmJhNjY5MWYiLCJhbGciOiJIUzI1NiJ9.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvcGFzdGVkLzE3OTEyMDUwOTAyOTMtdjdsMXplcHlhaS5wbmciLCJzY29wZSI6ImRvd25sb2FkIiwiaWF0IjoxNzkxMjEyNjYxLCJleHAiOjE3OTEyMTI5NjF9.sv2Qd7c-lPZTXlKGTPdZKYI4R4yJvBYw1e4VjYiTQX0" style="max-width: min(400px, 100%); height: auto; display: block;" class="aligncenter custom-width" /></figure></div>
<ol class="abc-list"><li data-list-item-id="item-1791205094162-h9mfvdkky" data-list-item-path="item-1791205094162-h9mfvdkky"><div class="list-item-paragraph"><p>Use the graph to find an estimate of the median height.</p><span class="inline-marks">[2]</span></div></li></ol>
<p>The heights of the students are shown in the following frequency table where&nbsp;\(p, q \in \mathbb{N}\).</p>
<div class="content-block content-block--table"><div class="table-container"><table style="table-layout: fixed; width: 180px;"><colgroup><col style="width: 55.5556%;"><col style="width: 44.4444%;"></colgroup><thead><tr style="height: 40px;"><th style="height: 40px; min-height: 40px; text-align: center; --cell-justify: center"><strong>Height (\(h\) cm)</strong></th><th style="height: 40px; min-height: 40px; text-align: center; --cell-justify: center"><strong>Frequency</strong></th></tr></thead><tbody><tr style="height: 40px;"><td style="height: 40px; min-height: 40px; text-align: center; --cell-justify: center">\(155 \leq h &lt; 160\)</td><td style="height: 40px; min-height: 40px; text-align: center; --cell-justify: center">\(3\)</td></tr><tr style="height: 40px;"><td style="height: 40px; min-height: 40px; text-align: center; --cell-justify: center">\(160 \leq h &lt; 165\)</td><td style="height: 40px; min-height: 40px; text-align: center; --cell-justify: center">\(8\)</td></tr><tr style="height: 40px;"><td style="height: 40px; min-height: 40px; text-align: center; --cell-justify: center">\(165 \leq h &lt; 170\)</td><td style="height: 40px; min-height: 40px; text-align: center; --cell-justify: center">\(14\)</td></tr><tr style="height: 40px;"><td style="height: 40px; min-height: 40px; text-align: center; --cell-justify: center">\(170 \leq h &lt; 175\)</td><td style="height: 40px; min-height: 40px; text-align: center; --cell-justify: center">\(p\)</td></tr><tr style="height: 40px;"><td style="height: 40px; min-height: 40px; text-align: center; --cell-justify: center">\(175 \leq h &lt; 180\)</td><td style="height: 40px; min-height: 40px; text-align: center; --cell-justify: center">\(q\)</td></tr></tbody></table></div></div>
<ol class="abc-list" start="2"><li data-list-item-id="item-1791205332852-l1oefxnlr" data-list-item-path="item-1791205332852-l1oefxnlr"><div class="list-item-paragraph"><span class="inline-marks">[5]</span></div><ol class="i-list"><li data-list-item-id="subitem-1791205340745-h39jkgz24" data-list-item-path="item-1791205332852-l1oefxnlr/subitem-1791205340745-h39jkgz24"><div class="list-item-paragraph"><p>Find the value of \(p\) and the value of \(q\).</p></div></li><li data-list-item-id="subitem-1791205340888-uo2wp7ka7" data-list-item-path="item-1791205332852-l1oefxnlr/subitem-1791205340888-uo2wp7ka7"><div class="list-item-paragraph"><p>Use the frequency table to find an estimate of the mean height, giving your answer to four significant figures.</p></div></li></ol></li></ol>

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

<p>Use the graph to find an estimate of the median height.</p>

The heights of the students are shown in the following frequency table where \(p, q \in \mathbb{N}\).

Statistics

International Baccalaureate Mathematics: Analysis and Approaches Standard Level

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

2026 MAY TZA P2 Q1

2026 MAY TZA P2 Q1