A Math

A Math (IGCSE)

E Math

E Math (IGCSE)

H1 Math

H2 Math

IB AA HL Math

IB AA SL Math

IB AI HL Math

IB AI SL Math

IP Math

N(A) A Math

N(A) E Math

PSLE

PSLE Foundation Mathematics

<p>\(16\) pupils sat for a test. The sum of their marks is \(504\). The sum of the squares of their marks is \(16855\).</p>
<ol class="abc-list"><li data-list-item-id="item-a" data-list-item-path="item-a"><div class="list-item-paragraph">Calculate</div><ol class="i-list"><li data-list-item-id="item-a-i" data-list-item-path="item-a/item-a-i"><div class="list-item-paragraph">the mean,</div></li><li data-list-item-id="item-a-ii" data-list-item-path="item-a/item-a-ii"><div class="list-item-paragraph">the standard deviation, of these test marks.</div></li></ol></li><li data-list-item-id="item-b" data-list-item-path="item-b"><div class="list-item-paragraph">One of the marks was \(43\) but was incorrectly recorded as&nbsp;\(25\). Calculate the correct mean and standard deviation of these test marks.</div></li><li data-list-item-id="item-c" data-list-item-path="item-c"><div class="list-item-paragraph">Explain, stating your reasons clearly,</div><ol class="i-list"><li data-list-item-id="item-c-i" data-list-item-path="item-c/item-c-i"><div class="list-item-paragraph">why the mean has increased,</div></li><li data-list-item-id="item-c-ii" data-list-item-path="item-c/item-c-ii"><div class="list-item-paragraph">why the standard deviation has increased.</div></li></ol></li></ol>

\(16\) pupils sat for a test. The sum of their marks is \(504\). The sum of the squares of their marks is \(16855\).

One of the marks was \(43\) but was incorrectly recorded as \(25\). Calculate the correct mean and standard deviation of these test marks.

Mean and Standard Deviation for Ungrouped Data

Effects of Changing Data on Statistical Measures

IP2U15 HOT Q2

Statistics

<p>The height of students at a school is shown as a cumulative frequency graph below.</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/1769331137120-oubtwaa4dlf.png?token=eyJraWQiOiJiZTM3ZjNhZS05OWM4LTQ5ZGQtYjRiNS1iMTBhYmJhNjY5MWYiLCJhbGciOiJIUzI1NiJ9.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvcGFzdGVkLzE3NjkzMzExMzcxMjAtb3VidHdhYTRkbGYucG5nIiwic2NvcGUiOiJkb3dubG9hZCIsImlhdCI6MTc5MjY5NTc3NywiZXhwIjoxNzkyNjk2MDc3fQ.3iqlUw2L7C0MugTDb-zhlsSpOpCBPdgkIPy8g8pxXBg" style="max-width: min(400px, 100%); height: auto; display: block;" alt="Cumulative frequency graph showing Number of students vs Height (cm)" class="aligncenter custom-width" /></figure></div>
<ol class="abc-list"><li><div class="list-item-content"><span class="list-item-text">Use the graph to estimate</span></div><ol class="i-list"><li><div class="list-item-content"><span class="list-item-text">the median,</span></div></li><li><div class="list-item-content"><span class="list-item-text">the inter-quartile range.</span></div></li></ol></li><li><div class="list-item-content"><span class="list-item-text">If&nbsp;\(20\)% of the students are taller than \(h\) cm, find the value of \(h\).</span></div></li><li><div class="list-item-content"><span class="list-item-text">Copy and complete the grouped frequency table of students' heights.</span></div></li></ol>
<div class="content-block content-block--table"><div class="table-container"><table><thead><tr style="height: 23px;"><th style="height: 23px; min-height: 23px; text-align: center; --cell-justify: center">Heights (cm)</th><th style="height: 23px; min-height: 23px; text-align: center; --cell-justify: center">No. of students</th></tr></thead><tbody><tr style="height: 23px;"><td style="height: 23px; min-height: 23px; text-align: center; --cell-justify: center">\(120 \le x &lt; 130\)</td><td style="height: 23px; min-height: 23px; text-align: left; --cell-justify: flex-start"></td></tr><tr style="height: 23px;"><td style="height: 23px; min-height: 23px; text-align: center; --cell-justify: center">\(130 \le x &lt; 140\)</td><td style="height: 23px; min-height: 23px; text-align: left; --cell-justify: flex-start"></td></tr><tr style="height: 23px;"><td style="height: 23px; min-height: 23px; text-align: center; --cell-justify: center">\(140 \le x &lt; 150\)</td><td style="height: 23px; min-height: 23px; text-align: left; --cell-justify: flex-start"></td></tr><tr style="height: 23px;"><td style="height: 23px; min-height: 23px; text-align: center; --cell-justify: center">\(150 \le x &lt; 160\)</td><td style="height: 23px; min-height: 23px; text-align: left; --cell-justify: flex-start"></td></tr><tr style="height: 23px;"><td style="height: 23px; min-height: 23px; text-align: center; --cell-justify: center">\(160 \le x &lt; 170\)</td><td style="height: 23px; min-height: 23px; text-align: left; --cell-justify: flex-start"></td></tr><tr style="height: 23px;"><td style="height: 23px; min-height: 23px; text-align: center; --cell-justify: center">\(170 \le x &lt; 180\)</td><td style="height: 23px; min-height: 23px; text-align: left; --cell-justify: flex-start"></td></tr></tbody></table></div></div>
<ol class="abc-list" start="4"><li><div class="list-item-paragraph">Using your grouped frequency table, calculate an estimate of the standard deviation.</div></li><li><div class="list-item-paragraph">The students at the school took measurements of their weights using a faulty weighing machine. The box and whisker graph below shows the students' weights (in kg) measured by the faulty weight machine.</div><div class="content-block list-item-image" style="text-align: center;"><img src="https://vocwkpgapvksartxhhor.supabase.co/storage/v1/object/sign/question-images/pasted/1769331223446-mab2gukchu8.png?token=eyJraWQiOiJiZTM3ZjNhZS05OWM4LTQ5ZGQtYjRiNS1iMTBhYmJhNjY5MWYiLCJhbGciOiJIUzI1NiJ9.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvcGFzdGVkLzE3NjkzMzEyMjM0NDYtbWFiMmd1a2NodTgucG5nIiwic2NvcGUiOiJkb3dubG9hZCIsImlhdCI6MTc5MjY5NTc3NywiZXhwIjoxNzkyNjk2MDc3fQ.nFWEpcD6s5ZSiV9JT8wkadhduYJMD92O_Gi63kridog" alt="List item image" class="aligncenter" style="max-width: 100%; height: auto;" /></div><ol class="i-list"><li><div class="list-item-paragraph">If every student's true weight was actually \(5\) kg lower, describe briefly how the box and whisker graph will differ from the given graph.</div></li><li><div class="list-item-paragraph">State the correct value of the median weight.</div></li></ol></li></ol>

The height of students at a school is shown as a cumulative frequency graph below.

If \(20\)% of the students are taller than \(h\) cm, find the value of \(h\).

Copy and complete the grouped frequency table of students' heights.

Using your grouped frequency table, calculate an estimate of the standard deviation.

The students at the school took measurements of their weights using a faulty weighing machine. The box and whisker graph below shows the students' weights (in kg) measured by the faulty weight machine.

Math Question Bank