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>A class of students took a Mathematics test. Their scores are represented in the stem-and-leaf diagram as shown.</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/1767953771817-j6yj3lfba9.png?token=eyJraWQiOiJiZTM3ZjNhZS05OWM4LTQ5ZGQtYjRiNS1iMTBhYmJhNjY5MWYiLCJhbGciOiJIUzI1NiJ9.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvcGFzdGVkLzE3Njc5NTM3NzE4MTctajZ5ajNsZmJhOS5wbmciLCJzY29wZSI6ImRvd25sb2FkIiwiaWF0IjoxNzkyNjk1NzMwLCJleHAiOjE3OTI2OTYwMzB9.v2VtWvIYL2iEgCzFre8UE0aZy4M_XiviukNFx_E8DJI" style="max-width: min(350px, 100%); height: auto; display: block;" class="aligncenter custom-width" /></figure></div>
<p>Find</p>
<ol class="abc-list"><li><div class="list-item-content"><span class="list-item-text">the modal score,</span></div></li><li><div class="list-item-content"><span class="list-item-text">the median score,</span></div></li><li><div class="list-item-content"><span class="list-item-text">the mean score,</span></div></li><li><div class="list-item-content"><span class="list-item-text">the standard deviation of the scores, correct to $3$ significant figures.</span></div></li></ol>

A class of students took a Mathematics test. Their scores are represented in the stem-and-leaf diagram as shown.

the standard deviation of the scores, correct to $3$ significant figures.

Median

Mean and Standard Deviation for Ungrouped Data

Mode

Stem-and-Leaf Diagrams

Evaluating Modal, Median, and Mean Values in Discrete Distributions

Statistics

<p>The stem-and-leaf diagram shows the masses of $21$ students.</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/1767946990179-hnrcvplxvzg.png?token=eyJraWQiOiJiZTM3ZjNhZS05OWM4LTQ5ZGQtYjRiNS1iMTBhYmJhNjY5MWYiLCJhbGciOiJIUzI1NiJ9.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvcGFzdGVkLzE3Njc5NDY5OTAxNzktaG5yY3ZwbHh2emcucG5nIiwic2NvcGUiOiJkb3dubG9hZCIsImlhdCI6MTc5MjY5NTczMCwiZXhwIjoxNzkyNjk2MDMwfQ.1DstngYpLJ06aSJPUaLjviJuMmSicaBoetL2x3dLDJw" style="max-width: min(300px, 100%); height: auto; display: block;" class="aligncenter custom-width" /></figure></div>
<ol class="abc-list"><li><div class="list-item-content"><span class="list-item-text">Write down the modal mass.</span></div></li><li><div class="list-item-content"><span class="list-item-text">Calculate the percentage of the students who weigh at least $55\text{ kg}$.</span></div></li><li><div class="list-item-content"><span class="list-item-text">The box-and-whisker plot for the above distribution is shown below. Write down the value of $a$ and of $b$.</span></div></li></ol>
<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/1767947005432-ow0zbltnxla.png?token=eyJraWQiOiJiZTM3ZjNhZS05OWM4LTQ5ZGQtYjRiNS1iMTBhYmJhNjY5MWYiLCJhbGciOiJIUzI1NiJ9.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvcGFzdGVkLzE3Njc5NDcwMDU0MzItb3cwemJsdG54bGEucG5nIiwic2NvcGUiOiJkb3dubG9hZCIsImlhdCI6MTc5MjY5NTczMCwiZXhwIjoxNzkyNjk2MDMwfQ.JzfpgOe--m-P7BVysTyUpqJP7QzEW_j_wPl02o6Qf_Q" style="max-width: min(350px, 100%); height: auto; display: block;" alt="Box-and-whisker plot for mass distribution" class="aligncenter custom-width" /></figure></div>

The stem-and-leaf diagram shows the masses of $21$ students.

Calculate the percentage of the students who weigh at least $55\text{ kg}$.

The box-and-whisker plot for the above distribution is shown below. Write down the value of $a$ and of $b$.

Box-and-Whisker Plots

Expressing One Quantity as a Percentage of Another

Descriptive Statistics: Box Plot Construction and Interpretation

Percentages

<p>Twenty boys took a Mathematics test. The marks are shown in the stem-and-leaf 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/1767939934439-2kxx1nlb6tn.png?token=eyJraWQiOiJiZTM3ZjNhZS05OWM4LTQ5ZGQtYjRiNS1iMTBhYmJhNjY5MWYiLCJhbGciOiJIUzI1NiJ9.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvcGFzdGVkLzE3Njc5Mzk5MzQ0MzktMmt4eDFubGI2dG4ucG5nIiwic2NvcGUiOiJkb3dubG9hZCIsImlhdCI6MTc5MjY5NTczMCwiZXhwIjoxNzkyNjk2MDMwfQ.KwW82OPtzv-9MzabVWKPzN4e-O_Mz5FmvgB5FH4BGrA" style="max-width: min(200px, 100%); height: auto; display: block;" class="aligncenter custom-width" /></figure></div>
<ol class="abc-list"><li><div class="list-item-content"><span class="list-item-text">Write down the median of the boy's marks.</span></div></li><li><div class="list-item-content"><span class="list-item-text">Calculate the interquartile range of the boys' marks.</span></div></li></ol>

Twenty boys took a Mathematics test. The marks are shown in the stem-and-leaf diagram.

Write down the median of the boy's marks.

Calculate the interquartile range of the boys' marks.

Median, Quartiles, Range and Interquartile Range

Statistical Profiling of Student Commute Patterns

<p>The stem-and-leaf diagram below shows the pulse rates of $20$ students measured after a PE lesson.</p>
<div class="content-block content-block--columns"><div class="question-columns question-columns--1-2" data-layout="1-2"><div class="question-column" style="flex: 1; align-self: flex-start;"><ol class="abc-list"><li data-list-item-id="item-1779011958049-qhuqlqjaw"><div class="list-item-paragraph">State the median and mode of the distribution.</div></li><li data-list-item-id="item-1779011958773-fauza5kmv"><div class="list-item-paragraph">What percentage of the students has pulse rates greater than $107$ beats per minute?</div></li></ol></div><div class="question-column" style="flex: 2; align-self: flex-start;"><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/1765432766439-2yusam5e1tv.png?token=eyJraWQiOiJiZTM3ZjNhZS05OWM4LTQ5ZGQtYjRiNS1iMTBhYmJhNjY5MWYiLCJhbGciOiJIUzI1NiJ9.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvcGFzdGVkLzE3NjU0MzI3NjY0MzktMnl1c2FtNWUxdHYucG5nIiwic2NvcGUiOiJkb3dubG9hZCIsImlhdCI6MTc5MjY5NTczMCwiZXhwIjoxNzkyNjk2MDMwfQ.vVufJV-ddwPI-9ztjaqAHpkOmzcyunpkJZpqYS3Ykg8" style="max-width: min(400px, 100%); height: auto; display: block;" class="aligncenter custom-width" /></figure></div></div></div></div>

The stem-and-leaf diagram below shows the pulse rates of $20$ students measured after a PE lesson.

Pulse Rate Data: Median, Mode, and Percentage Analysis

<div class="content-block content-block--table"><div class="table-container"><table style="table-layout: fixed; width: 500px;"><colgroup><col style="width: 50px;"><col style="width: 50px;"><col style="width: 50px;"><col style="width: 50px;"><col style="width: 50px;"><col style="width: 50px;"><col style="width: 50px;"><col style="width: 50px;"><col style="width: 50px;"><col style="width: 50px;"></colgroup><thead><tr><th style="text-align: center; --cell-justify: center"><p>$157$</p></th><th style="text-align: center; --cell-justify: center"><p>$171$</p></th><th style="text-align: center; --cell-justify: center"><p>$194$</p></th><th style="text-align: center; --cell-justify: center"><p>$166$</p></th><th style="text-align: center; --cell-justify: center"><p>$183$</p></th><th style="text-align: center; --cell-justify: center"><p>$149$</p></th><th style="text-align: center; --cell-justify: center"><p>$166$</p></th><th style="text-align: center; --cell-justify: center"><p>$160$</p></th><th style="text-align: center; --cell-justify: center"><p>$180$</p></th><th style="text-align: center; --cell-justify: center"><p>$160$</p></th></tr></thead><tbody><tr><td style="text-align: center; --cell-justify: center"><p>$183$</p></td><td style="text-align: center; --cell-justify: center"><p>$149$</p></td><td style="text-align: center; --cell-justify: center"><p>$169$</p></td><td style="text-align: center; --cell-justify: center"><p>$160$</p></td><td style="text-align: center; --cell-justify: center"><p>$194$</p></td><td style="text-align: center; --cell-justify: center"><p>$174$</p></td><td style="text-align: center; --cell-justify: center"><p>$177$</p></td><td style="text-align: center; --cell-justify: center"><p>$157$</p></td><td style="text-align: center; --cell-justify: center"><p>$174$</p></td><td style="text-align: center; --cell-justify: center"><p>$169$</p></td></tr></tbody></table></div></div>
<ol class="abc-list"><li><div class="list-item-paragraph">Represent the data above in a stem-and-leaf diagram.</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/1765432423685-3w5tj6n819n.png?token=eyJraWQiOiJiZTM3ZjNhZS05OWM4LTQ5ZGQtYjRiNS1iMTBhYmJhNjY5MWYiLCJhbGciOiJIUzI1NiJ9.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvcGFzdGVkLzE3NjU0MzI0MjM2ODUtM3c1dGo2bjgxOW4ucG5nIiwic2NvcGUiOiJkb3dubG9hZCIsImlhdCI6MTc5MjY5NTczMCwiZXhwIjoxNzkyNjk2MDMwfQ.BWRP99C_BaPYPP7m1rcBccz4pGOPJ74YxK8yTNMVB0Q" alt="List item image" class="aligncenter custom-width" style="max-width: min(350px, 100%); height: auto;" /></div></li><li><div class="list-item-paragraph">For this distribution, find the</div><ol class="i-list"><li><div class="list-item-paragraph">median,</div></li><li><div class="list-item-paragraph">mode,</div></li><li><div class="list-item-paragraph">mean.</div></li></ol></li></ol>

Mean of Ungrouped Data

Height Distribution: Median, Mode, and Mean

<p>The masses of $12$ bags of apples are shown in the stem-and-leaf diagram below.</p>
<div class="content-block content-block--columns"><div class="question-columns question-columns--1-2" data-layout="1-2"><div class="question-column" style="flex: 1; align-self: flex-start;"><ol class="i-list"><li data-list-item-id="item-1779011851616-qo4p2b3x6"><div class="list-item-paragraph">Calculate the mean mass of the bags of apples.</div></li><li data-list-item-id="item-1779011852492-j3teys217"><div class="list-item-paragraph">Find the median mass of the bags of apples.</div></li></ol></div><div class="question-column" style="flex: 2; align-self: flex-start;"><div class="content-block"><figure class="question-figure alignright" style="text-align: right;"><img src="https://vocwkpgapvksartxhhor.supabase.co/storage/v1/object/sign/question-images/pasted/1765431843645-nlnblmyly1q.png?token=eyJraWQiOiJiZTM3ZjNhZS05OWM4LTQ5ZGQtYjRiNS1iMTBhYmJhNjY5MWYiLCJhbGciOiJIUzI1NiJ9.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvcGFzdGVkLzE3NjU0MzE4NDM2NDUtbmxuYmxteWx5MXEucG5nIiwic2NvcGUiOiJkb3dubG9hZCIsImlhdCI6MTc5MjY5NTczMCwiZXhwIjoxNzkyNjk2MDMwfQ.gGCWklZfyFBuz46j3jtHG47On7igt-gxt7ZAev_21o0" style="max-width: min(350px, 100%); height: auto; display: block;" class="alignright custom-width" /></figure></div></div></div></div>

The masses of $12$ bags of apples are shown in the stem-and-leaf diagram below.

Apple Bag Masses: Mean and Median Calculation

<p>During a health check-up, the weights of $20$ students of the same height were recorded. </p>
<p>The stem-and-leaf diagram below illustrates their results.</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/1765430994441-kl6y6j4p12.png?token=eyJraWQiOiJiZTM3ZjNhZS05OWM4LTQ5ZGQtYjRiNS1iMTBhYmJhNjY5MWYiLCJhbGciOiJIUzI1NiJ9.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvcGFzdGVkLzE3NjU0MzA5OTQ0NDEta2w2eTZqNHAxMi5wbmciLCJzY29wZSI6ImRvd25sb2FkIiwiaWF0IjoxNzkyNjk1NzMwLCJleHAiOjE3OTI2OTYwMzB9.GDOHn8ufGS3FBWNMJ70wp5x1b2bxwOfu1uLIVn-aeds" style="max-width: min(350px, 100%); height: auto; display: block;" class="aligncenter custom-width" /></figure></div>
<ol class="i-list"><li><div class="list-item-paragraph">If the median weight of the students is $56$ kg, write down the value of $w$.</div></li><li><div class="list-item-paragraph">A student is considered underweight when weighs less than $45$ kg. Find the percentage of students who are underweight.</div></li></ol>

During a health check-up, the weights of $20$ students of the same height were recorded. 

The stem-and-leaf diagram below illustrates their results.

Finding Unknowns from Averages and Spread

Student Weight Distribution: Median and Underweight Percentage

<p>The height of $12$ students in a class was measured. The information is displayed in the stem and leaf diagram below.</p>
<div class="content-block content-block--columns"><div class="question-columns question-columns--2" data-layout="2"><div class="question-column" style="flex: 1; align-self: flex-start;"><p>Find</p><ol class="abc-list"><li><div class="list-item-paragraph">the mode,</div></li><li><div class="list-item-paragraph">the median,</div></li><li><div class="list-item-paragraph">the mean of the heights.</div></li></ol></div><div class="question-column" style="flex: 1; align-self: flex-start;"><div class="content-block"><figure class="question-figure alignright" style="text-align: right;"><img src="https://vocwkpgapvksartxhhor.supabase.co/storage/v1/object/sign/question-images/pasted/1765426064806-tpl1w0a9ua.png?token=eyJraWQiOiJiZTM3ZjNhZS05OWM4LTQ5ZGQtYjRiNS1iMTBhYmJhNjY5MWYiLCJhbGciOiJIUzI1NiJ9.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvcGFzdGVkLzE3NjU0MjYwNjQ4MDYtdHBsMXcwYTl1YS5wbmciLCJzY29wZSI6ImRvd25sb2FkIiwiaWF0IjoxNzkyNjk1NzMwLCJleHAiOjE3OTI2OTYwMzB9.FUxuypHw-2n5Sni6s7w7ErP1ptXWWHzd8hTvRKMRDgk" style="max-width: min(230px, 100%); height: auto; display: block;" class="alignright custom-width" /></figure></div></div></div></div>

The height of $12$ students in a class was measured. The information is displayed in the stem and leaf diagram below.

Analyzing Student Heights: Mode, Median, and Mean

<p>Ten boys and ten girls took a Mathematics test.  The marks are shown in the stem-and-leaf diagram.</p>
<div class="content-block content-block--columns"><div class="question-columns question-columns--1-2" data-layout="1-2"><div class="question-column" style="flex: 1; align-self: flex-start;"><p>Find the modal mark for</p><ol class="i-list"><li data-list-item-id="item-1779008983925-vmcx07zhn"><div class="list-item-paragraph">the boys’ Mathematics test,</div></li><li data-list-item-id="item-1779008984504-89w45d1bf"><div class="list-item-paragraph">the girls’ Mathematics test.</div></li></ol></div><div class="question-column" style="flex: 2; align-self: flex-start;"><div class="content-block"><figure class="question-figure alignright" style="text-align: right;"><img src="https://vocwkpgapvksartxhhor.supabase.co/storage/v1/object/sign/question-images/pasted/1765423910641-jedom7eabc9.png?token=eyJraWQiOiJiZTM3ZjNhZS05OWM4LTQ5ZGQtYjRiNS1iMTBhYmJhNjY5MWYiLCJhbGciOiJIUzI1NiJ9.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvcGFzdGVkLzE3NjU0MjM5MTA2NDEtamVkb203ZWFiYzkucG5nIiwic2NvcGUiOiJkb3dubG9hZCIsImlhdCI6MTc5MjY5NTczMCwiZXhwIjoxNzkyNjk2MDMwfQ.4RyelkATY4x1cv_-moQqHQht8UkXjuUmYa91ytEHHHY" style="max-width: min(500px, 100%); height: auto; display: block;" class="alignright custom-width" /></figure></div></div></div></div>

Ten boys and ten girls took a Mathematics test.  The marks are shown in the stem-and-leaf diagram.

Math Performance Data: Mode Calculation

<p>The stem-and-leaf diagram represents the distance travelled to work by a group of workers.</p>
<div class="content-block content-block--columns"><div class="question-columns question-columns--1-2" data-layout="1-2"><div class="question-column" style="flex: 1; align-self: flex-start;"><p>Find the modal distance travelled by the workers.</p></div><div class="question-column" style="flex: 2; align-self: flex-start;"><div class="content-block"><figure class="question-figure alignright" style="text-align: right;"><img src="https://vocwkpgapvksartxhhor.supabase.co/storage/v1/object/sign/question-images/pasted/1765423685811-ho608udeys5.png?token=eyJraWQiOiJiZTM3ZjNhZS05OWM4LTQ5ZGQtYjRiNS1iMTBhYmJhNjY5MWYiLCJhbGciOiJIUzI1NiJ9.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvcGFzdGVkLzE3NjU0MjM2ODU4MTEtaG82MDh1ZGV5czUucG5nIiwic2NvcGUiOiJkb3dubG9hZCIsImlhdCI6MTc5MjY5NTczMCwiZXhwIjoxNzkyNjk2MDMwfQ.mINGY1OD7O03WnnxqkjvbhCLSfxYuf7Ctqr8Oun9hyM" style="max-width: min(400px, 100%); height: auto; display: block;" class="alignright custom-width" /></figure></div></div></div></div>

The stem-and-leaf diagram represents the distance travelled to work by a group of workers.

Commute Distance Distribution: Mode Calculation

<p>In a test, the marks obtained by $20$ students are represented on a stem and leaf diagram as follows:</p>
<div class="content-block content-block--columns"><div class="question-columns question-columns--1-2" data-layout="1-2"><div class="question-column" style="flex: 1; align-self: flex-start;"><p>Find the modal mark of the students.</p></div><div class="question-column" style="flex: 2; align-self: flex-start;"><div class="content-block"><figure class="question-figure alignright" style="text-align: right;"><img src="https://vocwkpgapvksartxhhor.supabase.co/storage/v1/object/sign/question-images/pasted/1765365081098-22v0tjetrte.png?token=eyJraWQiOiJiZTM3ZjNhZS05OWM4LTQ5ZGQtYjRiNS1iMTBhYmJhNjY5MWYiLCJhbGciOiJIUzI1NiJ9.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvcGFzdGVkLzE3NjUzNjUwODEwOTgtMjJ2MHRqZXRydGUucG5nIiwic2NvcGUiOiJkb3dubG9hZCIsImlhdCI6MTc5MjY5NTczMCwiZXhwIjoxNzkyNjk2MDMwfQ.-d2qm76insEDa54Tb9GtygoPqikMqJCRKOumcu9lIf4" style="max-width: min(400px, 100%); height: auto; display: block;" class="alignright custom-width" /></figure></div></div></div></div>

In a test, the marks obtained by $20$ students are represented on a stem and leaf diagram as follows:

Test Score Distribution: Identifying the Mode

<p>Ten boys and ten girls took a Mathematics test.  The marks are shown in the stem-and-leaf diagram.</p>
<div class="content-block content-block--columns"><div class="question-columns question-columns--2" data-layout="2"><div class="question-column" style="flex: 1; align-self: flex-start;"><p>Find the median mark for</p><ol class="i-list"><li><div class="list-item-paragraph">the boys’ Mathematics test,</div></li><li><div class="list-item-paragraph">the girls’ Mathematics test.</div></li></ol></div><div class="question-column" style="flex: 1; align-self: flex-start;"><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/1765363887460-7np7x6ivdxh.png?token=eyJraWQiOiJiZTM3ZjNhZS05OWM4LTQ5ZGQtYjRiNS1iMTBhYmJhNjY5MWYiLCJhbGciOiJIUzI1NiJ9.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvcGFzdGVkLzE3NjUzNjM4ODc0NjAtN25wN3g2aXZkeGgucG5nIiwic2NvcGUiOiJkb3dubG9hZCIsImlhdCI6MTc5MjY5NTczMCwiZXhwIjoxNzkyNjk2MDMwfQ.H0BRMzp4vfBQ8tQBqvS_628qmKGXnE_E3fCg4Pt50CI" style="max-width: min(400px, 100%); height: auto; display: block;" class="aligncenter custom-width" /></figure></div></div></div></div>

Boys’ and Girls’ Math Scores: Median Calculation

<p>The stem-and-leaf diagram represents the distance travelled to work by a group of workers.<br>Find the median distance travelled by the workers.</p>
<div class="content-block"><figure class="question-figure alignright" style="text-align: right;"><img src="https://vocwkpgapvksartxhhor.supabase.co/storage/v1/object/sign/question-images/pasted/1765363708778-8qim8pc6rjc.png?token=eyJraWQiOiJiZTM3ZjNhZS05OWM4LTQ5ZGQtYjRiNS1iMTBhYmJhNjY5MWYiLCJhbGciOiJIUzI1NiJ9.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvcGFzdGVkLzE3NjUzNjM3MDg3NzgtOHFpbThwYzZyamMucG5nIiwic2NvcGUiOiJkb3dubG9hZCIsImlhdCI6MTc5MjY5NTczMCwiZXhwIjoxNzkyNjk2MDMwfQ.Jn0rlhp7APZASZ8NpUPH0Gf2Lmhf4gDAhGK8FP1KbGE" style="max-width: min(350px, 100%); height: auto; display: block;" class="alignright custom-width" /></figure></div>

The stem-and-leaf diagram represents the distance travelled to work by a group of workers.
Find the median distance travelled by the workers.

Median Distance Travelled by Workers

<p>In a test, the marks obtained by 20 students are represented on a stem and leaf diagram as follows:<br>Find the median mark of the students. </p>
<div class="content-block"><figure class="question-figure alignright" style="text-align: right;"><img src="https://vocwkpgapvksartxhhor.supabase.co/storage/v1/object/sign/question-images/pasted/1765365081098-22v0tjetrte.png?token=eyJraWQiOiJiZTM3ZjNhZS05OWM4LTQ5ZGQtYjRiNS1iMTBhYmJhNjY5MWYiLCJhbGciOiJIUzI1NiJ9.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvcGFzdGVkLzE3NjUzNjUwODEwOTgtMjJ2MHRqZXRydGUucG5nIiwic2NvcGUiOiJkb3dubG9hZCIsImlhdCI6MTc5MjY5NTczMCwiZXhwIjoxNzkyNjk2MDMwfQ.-d2qm76insEDa54Tb9GtygoPqikMqJCRKOumcu9lIf4" style="max-width: min(350px, 100%); height: auto; display: block;" class="alignright custom-width" /></figure></div>

In a test, the marks obtained by 20 students are represented on a stem and leaf diagram as follows:
Find the median mark of the students. 

Median Mark from Stem-and-Leaf Data

<p>The following set of data shows the average number of hours spent on social media by a group of $20$ students in a week during the holidays.</p>
<div class="content-block content-block--table"><div class="table-container"><table style="table-layout: fixed; width: 350px;"><colgroup><col style="width: 70px;"><col style="width: 70px;"><col style="width: 70px;"><col style="width: 70px;"><col style="width: 70px;"></colgroup><thead><tr><th style="text-align: center; --cell-justify: center"><p>$8$</p></th><th style="text-align: center; --cell-justify: center"><p>$3$</p></th><th style="text-align: center; --cell-justify: center"><p>$9$</p></th><th style="text-align: center; --cell-justify: center"><p>$24$</p></th><th style="text-align: center; --cell-justify: center"><p>$12$</p></th></tr></thead><tbody><tr><td style="text-align: center; --cell-justify: center"><p>$16$</p></td><td style="text-align: center; --cell-justify: center"><p>$12$</p></td><td style="text-align: center; --cell-justify: center"><p>$30$</p></td><td style="text-align: center; --cell-justify: center"><p>$13$</p></td><td style="text-align: center; --cell-justify: center"><p>$8$</p></td></tr><tr><td style="text-align: center; --cell-justify: center"><p>$5$</p></td><td style="text-align: center; --cell-justify: center"><p>$6$</p></td><td style="text-align: center; --cell-justify: center"><p>$15$</p></td><td style="text-align: center; --cell-justify: center"><p>21</p></td><td style="text-align: center; --cell-justify: center"><p>$25$</p></td></tr><tr><td style="text-align: center; --cell-justify: center"><p>$13$</p></td><td style="text-align: center; --cell-justify: center"><p>$19$</p></td><td style="text-align: center; --cell-justify: center"><p>$12$</p></td><td style="text-align: center; --cell-justify: center"><p>$5$</p></td><td style="text-align: center; --cell-justify: center"><p>$18$</p></td></tr></tbody></table></div></div>
<ol class="abc-list"><li><div class="list-item-paragraph">Complete the following stem-and-leaf diagram to represent the above data.</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/1769853279608-odi2s0x1m.png?token=eyJraWQiOiJiZTM3ZjNhZS05OWM4LTQ5ZGQtYjRiNS1iMTBhYmJhNjY5MWYiLCJhbGciOiJIUzI1NiJ9.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvcGFzdGVkLzE3Njk4NTMyNzk2MDgtb2RpMnMweDFtLnBuZyIsInNjb3BlIjoiZG93bmxvYWQiLCJpYXQiOjE3OTI2OTU3MzAsImV4cCI6MTc5MjY5NjAzMH0.HZpFCfFZnH5Hq_ztC4HI4AU17h15NU8Qd-Y8XOIWqmo" alt="List item image" class="aligncenter custom-width" style="max-width: min(350px, 100%); height: auto;" /></div></li><li><div class="list-item-paragraph">Find the mean number of hours spent on social media.</div></li></ol>

The following set of data shows the average number of hours spent on social media by a group of $20$ students in a week during the holidays.

Hours Spent on Social Media by Students

<p>The height of $14$ students in a class was measured. The information is displayed in the stem and leaf diagram below.</p>
<div class="content-block content-block--columns"><div class="question-columns question-columns--2" data-layout="2"><div class="question-column" style="flex: 1; align-self: flex-start;"><p>Find mean of the heights of the students.</p></div><div class="question-column" style="flex: 1; align-self: flex-start;"><div class="content-block"><figure class="question-figure alignright" style="text-align: right;"><img src="https://vocwkpgapvksartxhhor.supabase.co/storage/v1/object/sign/question-images/pasted/1765356921454-7j9jztqcfjw.png?token=eyJraWQiOiJiZTM3ZjNhZS05OWM4LTQ5ZGQtYjRiNS1iMTBhYmJhNjY5MWYiLCJhbGciOiJIUzI1NiJ9.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvcGFzdGVkLzE3NjUzNTY5MjE0NTQtN2o5anp0cWNmancucG5nIiwic2NvcGUiOiJkb3dubG9hZCIsImlhdCI6MTc5MjY5NTczMCwiZXhwIjoxNzkyNjk2MDMwfQ.5X-EYRNditoCQKbEBaDm0i7wRow2wFXHqJis_abgCp8" style="max-width: min(230px, 100%); height: auto; display: block;" class="alignright custom-width" /></figure></div></div></div></div>

The height of $14$ students in a class was measured. The information is displayed in the stem and leaf diagram below.

Calculating the Mean Height from a Stem-and-Leaf Diagram

<p>The heights, in cm, of students from a class are shown below. </p>
<div class="content-block content-block--table"><div class="table-container"><table style="table-layout: fixed; width: 450px;"><colgroup><col style="width: 100px;"><col style="width: 50px;"><col style="width: 50px;"><col style="width: 50px;"><col style="width: 50px;"><col style="width: 50px;"><col style="width: 50px;"><col style="width: 50px;"></colgroup><tbody><tr><td rowspan="2" style="text-align: center; --cell-justify: center"><p><strong>Boys</strong></p></td><td style="text-align: center; --cell-justify: center"><p>$165$</p></td><td style="text-align: center; --cell-justify: center"><p>$175$</p></td><td style="text-align: center; --cell-justify: center"><p>$169$</p></td><td style="text-align: center; --cell-justify: center"><p>$174$</p></td><td style="text-align: center; --cell-justify: center"><p>$166$</p></td><td style="text-align: center; --cell-justify: center"><p>$171$</p></td><td style="text-align: center; --cell-justify: center"><p>$180$</p></td></tr><tr><td style="text-align: center; --cell-justify: center"><p>$175$</p></td><td style="text-align: center; --cell-justify: center"><p>$168$</p></td><td style="text-align: center; --cell-justify: center"><p>$182$</p></td><td style="text-align: center; --cell-justify: center"><p>$170$</p></td><td style="text-align: center; --cell-justify: center"><p>$177$</p></td><td style="text-align: center; --cell-justify: center"><p>$178$</p></td><td style="text-align: center; --cell-justify: center"><p>$169$</p></td></tr><tr><td rowspan="2" style="text-align: center; --cell-justify: center"><p><strong>Girls</strong></p></td><td style="text-align: center; --cell-justify: center"><p>$149$</p></td><td style="text-align: center; --cell-justify: center"><p>$159$</p></td><td style="text-align: center; --cell-justify: center"><p>$166$</p></td><td style="text-align: center; --cell-justify: center"><p>$161$</p></td><td style="text-align: center; --cell-justify: center"><p>$152$</p></td><td style="text-align: center; --cell-justify: center"><p>$175$</p></td><td style="text-align: center; --cell-justify: center"><p>$160$</p></td></tr><tr><td style="text-align: center; --cell-justify: center"><p>$157$</p></td><td style="text-align: center; --cell-justify: center"><p>$158$</p></td><td style="text-align: center; --cell-justify: center"><p>$180$</p></td><td style="text-align: center; --cell-justify: center"><p>$158$</p></td><td style="text-align: center; --cell-justify: center"><p>$168$</p></td><td style="text-align: center; --cell-justify: center"><p>$154$</p></td><td style="text-align: center; --cell-justify: center"><p>$160$</p></td></tr></tbody></table></div></div>
<ol class="i-list"><li><div class="list-item-paragraph">Represent these two sets of data by a back-to-back stem-and-leaf diagram. </div></li><li><div class="list-item-paragraph">Find the probability that a student is taller than $170$ cm. </div></li></ol>

The heights, in cm, of students from a class are shown below. 

Back-to-Back Stem-and-Leaf Diagram and Height Analysis

<p>The results scored by students from two classes in a test are shown below. </p>
<div class="content-block content-block--table"><div class="table-container"><table style="table-layout: fixed; width: 600px;"><colgroup><col style="width: 100px;"><col style="width: 50px;"><col style="width: 50px;"><col style="width: 50px;"><col style="width: 50px;"><col style="width: 50px;"><col style="width: 50px;"><col style="width: 50px;"><col style="width: 50px;"><col style="width: 50px;"><col style="width: 50px;"></colgroup><tbody><tr><td rowspan="2" style="text-align: center; --cell-justify: center"><p><strong>Class P</strong></p></td><td style="text-align: center; --cell-justify: center"><p>$58$</p></td><td style="text-align: center; --cell-justify: center"><p>$63$</p></td><td style="text-align: center; --cell-justify: center"><p>$75$</p></td><td style="text-align: center; --cell-justify: center"><p>$67$</p></td><td style="text-align: center; --cell-justify: center"><p>$54$</p></td><td style="text-align: center; --cell-justify: center"><p>$66$</p></td><td style="text-align: center; --cell-justify: center"><p>$69$</p></td><td style="text-align: center; --cell-justify: center"><p>$64$</p></td><td style="text-align: center; --cell-justify: center"><p>$81$</p></td><td style="text-align: center; --cell-justify: center"><p>$83$</p></td></tr><tr><td style="text-align: center; --cell-justify: center"><p>$68$</p></td><td style="text-align: center; --cell-justify: center"><p>$77$</p></td><td style="text-align: center; --cell-justify: center"><p>$78$</p></td><td style="text-align: center; --cell-justify: center"><p>$61$</p></td><td style="text-align: center; --cell-justify: center"><p>$75$</p></td><td style="text-align: center; --cell-justify: center"><p>$68$</p></td><td style="text-align: center; --cell-justify: center"><p>$73$</p></td><td style="text-align: center; --cell-justify: center"><p>$82$</p></td><td style="text-align: center; --cell-justify: center"><p>$53$</p></td><td style="text-align: center; --cell-justify: center"><p>$85$</p></td></tr><tr><td rowspan="2" style="text-align: center; --cell-justify: center"><p><strong>Class Q</strong></p></td><td style="text-align: center; --cell-justify: center"><p>$50$</p></td><td style="text-align: center; --cell-justify: center"><p>$51$</p></td><td style="text-align: center; --cell-justify: center"><p>$62$</p></td><td style="text-align: center; --cell-justify: center"><p>$59$</p></td><td style="text-align: center; --cell-justify: center"><p>$65$</p></td><td style="text-align: center; --cell-justify: center"><p>$54$</p></td><td style="text-align: center; --cell-justify: center"><p>$52$</p></td><td style="text-align: center; --cell-justify: center"><p>$60$</p></td><td style="text-align: center; --cell-justify: center"><p>$70$</p></td><td style="text-align: center; --cell-justify: center"><p>$75$</p></td></tr><tr><td style="text-align: center; --cell-justify: center"><p>$80$</p></td><td style="text-align: center; --cell-justify: center"><p>$75$</p></td><td style="text-align: center; --cell-justify: center"><p>$57$</p></td><td style="text-align: center; --cell-justify: center"><p>$61$</p></td><td style="text-align: center; --cell-justify: center"><p>$69$</p></td><td style="text-align: center; --cell-justify: center"><p>$57$</p></td><td style="text-align: center; --cell-justify: center"><p>$61$</p></td><td style="text-align: center; --cell-justify: center"><p>$87$</p></td><td style="text-align: center; --cell-justify: center"><p>$76$</p></td><td style="text-align: center; --cell-justify: center"><p>$73$</p></td></tr></tbody></table></div></div>
<ol class="i-list"><li><div class="list-item-paragraph">Represent these two sets of data by a back-to-back stem-and-leaf diagram. </div></li><li><div class="list-item-paragraph">Which class has the highest score?</div></li><li><div class="list-item-paragraph">Which class has the lowest score? </div></li><li><div class="list-item-paragraph">Which class performed better in the test? Explain your answer. </div></li></ol>

The results scored by students from two classes in a test are shown below. 

Back-to-Back Stem-and-Leaf Diagram and Test Score Analysis

<p>The timing, in seconds, to complete a $100$ m freestyle laps of swimmers from two swimming schools are recorded in the table below. </p>
<div class="content-block content-block--table"><div class="table-container"><table style="table-layout: fixed; width: 450px;"><colgroup><col style="width: 100px;"><col style="width: 50px;"><col style="width: 50px;"><col style="width: 50px;"><col style="width: 50px;"><col style="width: 50px;"><col style="width: 50px;"><col style="width: 50px;"></colgroup><tbody><tr><td rowspan="2" style="text-align: center; --cell-justify: center"><p><strong>School A</strong></p></td><td style="text-align: center; --cell-justify: center"><p>$57.5$</p></td><td style="text-align: center; --cell-justify: center"><p>$58.6$</p></td><td style="text-align: center; --cell-justify: center"><p>$59.3$</p></td><td style="text-align: center; --cell-justify: center"><p>$58.0$</p></td><td style="text-align: center; --cell-justify: center"><p>$60.3$</p></td><td style="text-align: center; --cell-justify: center"><p>$57.8$</p></td><td style="text-align: center; --cell-justify: center"><p>$58.4$</p></td></tr><tr><td style="text-align: center; --cell-justify: center"><p>$59.3$</p></td><td style="text-align: center; --cell-justify: center"><p>$58.3$</p></td><td style="text-align: center; --cell-justify: center"><p>$59.8$</p></td><td style="text-align: center; --cell-justify: center"><p>$60.5$</p></td><td style="text-align: center; --cell-justify: center"><p>$56.9$</p></td><td style="text-align: center; --cell-justify: center"><p>$60.9$</p></td><td style="text-align: center; --cell-justify: center"><p>$58.8$</p></td></tr><tr><td rowspan="2" style="text-align: center; --cell-justify: center"><p><strong>School B</strong></p></td><td style="text-align: center; --cell-justify: center"><p>$57.1$</p></td><td style="text-align: center; --cell-justify: center"><p>$56.3$</p></td><td style="text-align: center; --cell-justify: center"><p>$57.8$</p></td><td style="text-align: center; --cell-justify: center"><p>$57.4$</p></td><td style="text-align: center; --cell-justify: center"><p>$59.7$</p></td><td style="text-align: center; --cell-justify: center"><p>$58.3$</p></td><td style="text-align: center; --cell-justify: center"><p>$60.1$</p></td></tr><tr><td style="text-align: center; --cell-justify: center"><p>$58.7$</p></td><td style="text-align: center; --cell-justify: center"><p>$56.0$</p></td><td style="text-align: center; --cell-justify: center"><p>$56.0$</p></td><td style="text-align: center; --cell-justify: center"><p>$59.4$</p></td><td style="text-align: center; --cell-justify: center"><p>$57.0$</p></td><td style="text-align: center; --cell-justify: center"><p>$56.7$</p></td><td style="text-align: center; --cell-justify: center"><p>$59.7$</p></td></tr></tbody></table></div></div>
<ol class="i-list"><li><div class="list-item-paragraph">Represent these two sets of data by a back-to-back stem-and-leaf diagram. </div></li><li><div class="list-item-paragraph">Which school produces better swimmers? Explain your answer.</div></li></ol>

The timing, in seconds, to complete a $100$ m freestyle laps of swimmers from two swimming schools are recorded in the table below. 

Back-to-Back Stem-and-Leaf Diagram and Performance Analysis

<p>The stem-and-leaf diagram represents the masses, in kg, of some delivery boxes.  </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/1765342970913-zfrpmrx0ku.png?token=eyJraWQiOiJiZTM3ZjNhZS05OWM4LTQ5ZGQtYjRiNS1iMTBhYmJhNjY5MWYiLCJhbGciOiJIUzI1NiJ9.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvcGFzdGVkLzE3NjUzNDI5NzA5MTMtemZycG1yeDBrdS5wbmciLCJzY29wZSI6ImRvd25sb2FkIiwiaWF0IjoxNzkyNjk1NzMwLCJleHAiOjE3OTI2OTYwMzB9.DieHy6KDdB4B1scdGvTns8RK0JDKfjzgEBb7n5gxiuE" style="max-width: min(400px, 100%); height: auto; display: block;" class="aligncenter custom-width" /></figure></div>
<ol class="i-list"><li><div class="list-item-paragraph">Construct a stem-and-leaf diagram with split stems. </div></li><li><div class="list-item-paragraph">Find the percentages of boxes with a mass of more than $25$ kg but less than $45$ kg.</div></li></ol>

The stem-and-leaf diagram represents the masses, in kg, of some delivery boxes.  

Math Question Bank