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.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvcGFzdGVkLzE3Njc5NTM3NzE4MTctajZ5ajNsZmJhOS5wbmciLCJzY29wZSI6ImRvd25sb2FkIiwiaWF0IjoxNzkyNjk1Nzc1LCJleHAiOjE3OTI2OTYwNzV9.G2Z6chshU2vidkKjNCaxL2HgW9mqHbRcJvCv1dt0Egg" 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.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvcGFzdGVkLzE3Njc5NDY5OTAxNzktaG5yY3ZwbHh2emcucG5nIiwic2NvcGUiOiJkb3dubG9hZCIsImlhdCI6MTc5MjY5NTc3NSwiZXhwIjoxNzkyNjk2MDc1fQ.bjHLIE5BXGkj-uyLlDbhuMOlN4x5Kxw5tjLgVJmt9Q8" 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.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvcGFzdGVkLzE3Njc5NDcwMDU0MzItb3cwemJsdG54bGEucG5nIiwic2NvcGUiOiJkb3dubG9hZCIsImlhdCI6MTc5MjY5NTc3NSwiZXhwIjoxNzkyNjk2MDc1fQ.bhQOtb8t79F5bfZMru7AIyEJO_R0c6512KWy8oPY4AE" 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>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.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvcGFzdGVkLzE3NjU0MzI3NjY0MzktMnl1c2FtNWUxdHYucG5nIiwic2NvcGUiOiJkb3dubG9hZCIsImlhdCI6MTc5MjY5NTc3NSwiZXhwIjoxNzkyNjk2MDc1fQ.J28os6KCr8QEw6rVaozBxEJh_l2ryFlM4a1sS1pSefw" 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.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvcGFzdGVkLzE3NjU0MzI0MjM2ODUtM3c1dGo2bjgxOW4ucG5nIiwic2NvcGUiOiJkb3dubG9hZCIsImlhdCI6MTc5MjY5NTc3NSwiZXhwIjoxNzkyNjk2MDc1fQ.bynqTLdYewS78DXdCMlmE-4uWASG2tl1wF01oweT6ko" 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 following data shows the number of hours $24$ students of a class spent studying per day.</p>
<div class="content-block content-block--table"><div class="table-container"><table style="table-layout: fixed; width: 400px;"><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;"></colgroup><thead><tr><th style="text-align: center; --cell-justify: center"><p>$4$</p></th><th style="text-align: center; --cell-justify: center"><p>$3$</p></th><th style="text-align: center; --cell-justify: center"><p>$4$</p></th><th style="text-align: center; --cell-justify: center"><p>$6$</p></th><th style="text-align: center; --cell-justify: center"><p>$1$</p></th><th style="text-align: center; --cell-justify: center"><p>$4$</p></th><th style="text-align: center; --cell-justify: center"><p>$0$</p></th><th style="text-align: center; --cell-justify: center"><p>$5$</p></th></tr></thead><tbody><tr><td style="text-align: center; --cell-justify: center"><p>$3$</p></td><td style="text-align: center; --cell-justify: center"><p>$1$</p></td><td style="text-align: center; --cell-justify: center"><p>$4$</p></td><td style="text-align: center; --cell-justify: center"><p>$4$</p></td><td style="text-align: center; --cell-justify: center"><p>$1$</p></td><td style="text-align: center; --cell-justify: center"><p>$4$</p></td><td style="text-align: center; --cell-justify: center"><p>$5$</p></td><td style="text-align: center; --cell-justify: center"><p>$6$</p></td></tr><tr><td style="text-align: center; --cell-justify: center"><p>$0$</p></td><td style="text-align: center; --cell-justify: center"><p>$3$</p></td><td style="text-align: center; --cell-justify: center"><p>$4$</p></td><td style="text-align: center; --cell-justify: center"><p>$0$</p></td><td style="text-align: center; --cell-justify: center"><p>$4$</p></td><td style="text-align: center; --cell-justify: center"><p>$0$</p></td><td style="text-align: center; --cell-justify: center"><p>$3$</p></td><td style="text-align: center; --cell-justify: center"><p>$3$</p></td></tr></tbody></table></div></div>
<ol class="abc-list"><li><div class="list-item-paragraph">Using the grid below, draw a dot 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/1765431475759-62j12cvscbf.png?token=eyJraWQiOiJiZTM3ZjNhZS05OWM4LTQ5ZGQtYjRiNS1iMTBhYmJhNjY5MWYiLCJhbGciOiJIUzI1NiJ9.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvcGFzdGVkLzE3NjU0MzE0NzU3NTktNjJqMTJjdnNjYmYucG5nIiwic2NvcGUiOiJkb3dubG9hZCIsImlhdCI6MTc5MjY5NTc3NSwiZXhwIjoxNzkyNjk2MDc1fQ.fERXQFMA1cJw7-ksrcLMkYNnTFvYeBGN_NpPz4TlCjI" alt="List item image" class="aligncenter custom-width" style="max-width: min(350px, 100%); height: auto;" /></div></li><li><div class="list-item-paragraph">What is the modal number of hours the students spent studying?</div></li><li><div class="list-item-paragraph">Calculate the mean number of hours the students spent studying.</div></li><li><div class="list-item-paragraph">If the above data was presented on a pie chart, what is the size of the angle that represents the number of students who study at least $3$ hours a day?</div></li><li><div class="list-item-paragraph">What is the probability of a student studying $4$ hours a day?	</div></li></ol>

The following data shows the number of hours $24$ students of a class spent studying per day.

Mean of a Frequency Distribution

Constructing and Interpreting Frequency Tables

Pie Charts

Probability of a Single Event

Dot Diagrams

Number of Hours Spent Studying: Mode, Mean, and Probability

Probability

<p>The table below shows the number of cars per household.</p>
<div class="content-block content-block--table"><div class="table-container"><table style="table-layout: fixed; width: 360px;"><colgroup><col style="width: 110px;"><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><strong>Number of cars</strong></p></th><th style="text-align: center; --cell-justify: center"><p>$0$</p></th><th style="text-align: center; --cell-justify: center"><p>$1$</p></th><th style="text-align: center; --cell-justify: center"><p>$2$</p></th><th style="text-align: center; --cell-justify: center"><p>$3$</p></th><th style="text-align: center; --cell-justify: center"><p>$4$</p></th></tr></thead><tbody><tr><td style="text-align: center; --cell-justify: center"><p><strong>Number of households</strong></p></td><td style="text-align: center; --cell-justify: center"><p>$6$</p></td><td style="text-align: center; --cell-justify: center"><p>$5$</p></td><td style="text-align: center; --cell-justify: center"><p>$3$</p></td><td style="text-align: center; --cell-justify: center"><p>$x$</p></td><td style="text-align: center; --cell-justify: center"><p>$1$</p></td></tr></tbody></table></div></div>
<ol class="abc-list"><li><div class="list-item-paragraph">If the median number of cars is $1$, find the possible values of $x$.</div></li><li><div class="list-item-paragraph">If&nbsp;$x=5$,</div><ol class="i-list"><li><div class="list-item-paragraph">state the modal number of cars,</div></li><li><div class="list-item-paragraph">find the probability of choosing a household with at least $2$ cars.</div></li></ol></li></ol>

The table below shows the number of cars per household.

Finding Unknowns from Averages and Spread

Household Car Ownership: Median, Mode, and Probability

<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.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvcGFzdGVkLzE3NjU0MjYwNjQ4MDYtdHBsMXcwYTl1YS5wbmciLCJzY29wZSI6ImRvd25sb2FkIiwiaWF0IjoxNzkyNjk1Nzc1LCJleHAiOjE3OTI2OTYwNzV9.DoNxC7oSxT2wE6ZhP22O9BniJqBWRYr53XskkvtmfnY" 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>The following numbers are the number of words in each line from a page of an article.</p>
<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>$8$</p></th><th style="text-align: center; --cell-justify: center"><p>$8$</p></th><th style="text-align: center; --cell-justify: center"><p>$12$</p></th><th style="text-align: center; --cell-justify: center"><p>$11$</p></th><th style="text-align: center; --cell-justify: center"><p>$14$</p></th><th style="text-align: center; --cell-justify: center"><p>$9$</p></th><th style="text-align: center; --cell-justify: center"><p>$11$</p></th><th style="text-align: center; --cell-justify: center"><p>$7$</p></th><th style="text-align: center; --cell-justify: center"><p>$8$</p></th><th style="text-align: center; --cell-justify: center"><p>$13$</p></th></tr></thead><tbody><tr><td style="text-align: center; --cell-justify: center"><p>$6$</p></td><td style="text-align: center; --cell-justify: center"><p>$12$</p></td><td style="text-align: center; --cell-justify: center"><p>$11$</p></td><td style="text-align: center; --cell-justify: center"><p>$5$</p></td><td style="text-align: center; --cell-justify: center"><p>$14$</p></td><td style="text-align: center; --cell-justify: center"><p>$10$</p></td><td style="text-align: center; --cell-justify: center"><p>$13$</p></td><td style="text-align: center; --cell-justify: center"><p>$5$</p></td><td style="text-align: center; --cell-justify: center"><p>$8$</p></td><td style="text-align: center; --cell-justify: center"><p>$9$</p></td></tr><tr><td style="text-align: center; --cell-justify: center"><p>$4$</p></td><td style="text-align: center; --cell-justify: center"><p>$8$</p></td><td style="text-align: center; --cell-justify: center"><p>$14$</p></td><td style="text-align: center; --cell-justify: center"><p>$13$</p></td><td style="text-align: center; --cell-justify: center"><p>$10$</p></td><td style="text-align: center; --cell-justify: center"><p>$11$</p></td><td style="text-align: center; --cell-justify: center"><p>$13$</p></td><td style="text-align: center; --cell-justify: center"><p>$12$</p></td><td style="text-align: center; --cell-justify: center"><p>$13$</p></td><td style="text-align: center; --cell-justify: center"><p>$10$</p></td></tr></tbody></table></div></div>
<ol class="abc-list"><li><div class="list-item-paragraph">Fill in the given frequency table.</div><div class="table-container"><table style="table-layout: fixed; width: 280px;"><colgroup><col style="width: 80px;"><col style="width: 100px;"><col style="width: 100px;"></colgroup><thead><tr><th style="text-align: center; --cell-justify: center"><p><strong>$x$</strong></p></th><th style="text-align: center; --cell-justify: center"><p><strong>$f$</strong></p></th><th style="text-align: center; --cell-justify: center"><p><strong>$fx$</strong></p></th></tr></thead><tbody><tr><td style="text-align: center; --cell-justify: center"><p>$4$</p></td><td style="text-align: left; --cell-justify: flex-start"></td><td style="text-align: left; --cell-justify: flex-start"></td></tr><tr><td style="text-align: center; --cell-justify: center"><p>$5$</p></td><td style="text-align: left; --cell-justify: flex-start"></td><td style="text-align: left; --cell-justify: flex-start"></td></tr><tr><td style="text-align: center; --cell-justify: center"><p>$6$</p></td><td style="text-align: left; --cell-justify: flex-start"></td><td style="text-align: left; --cell-justify: flex-start"></td></tr><tr><td style="text-align: center; --cell-justify: center"><p>$7$</p></td><td style="text-align: left; --cell-justify: flex-start"></td><td style="text-align: left; --cell-justify: flex-start"></td></tr><tr><td style="text-align: center; --cell-justify: center"><p>$8$</p></td><td style="text-align: left; --cell-justify: flex-start"></td><td style="text-align: left; --cell-justify: flex-start"></td></tr><tr><td style="text-align: center; --cell-justify: center"><p>$9$</p></td><td style="text-align: left; --cell-justify: flex-start"></td><td style="text-align: left; --cell-justify: flex-start"></td></tr><tr><td style="text-align: center; --cell-justify: center"><p>$10$</p></td><td style="text-align: left; --cell-justify: flex-start"></td><td style="text-align: left; --cell-justify: flex-start"></td></tr><tr><td style="text-align: center; --cell-justify: center"><p>$11$</p></td><td style="text-align: left; --cell-justify: flex-start"></td><td style="text-align: left; --cell-justify: flex-start"></td></tr><tr><td style="text-align: center; --cell-justify: center"><p>$12$</p></td><td style="text-align: left; --cell-justify: flex-start"></td><td style="text-align: left; --cell-justify: flex-start"></td></tr><tr><td style="text-align: center; --cell-justify: center"><p>$13$</p></td><td style="text-align: left; --cell-justify: flex-start"></td><td style="text-align: left; --cell-justify: flex-start"></td></tr><tr><td style="text-align: center; --cell-justify: center"><p>$14$</p></td><td style="text-align: left; --cell-justify: flex-start"></td><td style="text-align: left; --cell-justify: flex-start"></td></tr><tr><td style="text-align: center; --cell-justify: center"><p><strong>Total</strong></p></td><td style="text-align: left; --cell-justify: flex-start"></td><td style="text-align: left; --cell-justify: flex-start"></td></tr></tbody></table></div></li><li><div class="list-item-paragraph" style="margin-left: 0.5rem">Calculate the</div><ol class="i-list"><li><div class="list-item-paragraph">mean,</div></li><li><div class="list-item-paragraph">median,</div></li><li><div class="list-item-paragraph">mode.</div></li></ol></li></ol>

The following numbers are the number of words in each line from a page of an article.

Frequency Table of Words per Line

<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.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvcGFzdGVkLzE3NjU0MjM5MTA2NDEtamVkb203ZWFiYzkucG5nIiwic2NvcGUiOiJkb3dubG9hZCIsImlhdCI6MTc5MjY5NTc3NSwiZXhwIjoxNzkyNjk2MDc1fQ.iDcbqujOs3WB4jmJgKzcYQuhAvjKLiSneKGpiIXhOKk" 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.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvcGFzdGVkLzE3NjU0MjM2ODU4MTEtaG82MDh1ZGV5czUucG5nIiwic2NvcGUiOiJkb3dubG9hZCIsImlhdCI6MTc5MjY5NTc3NSwiZXhwIjoxNzkyNjk2MDc1fQ.9I2pQcTZvdU7SswyCaDfKnCAHpLq7ThsFbGXyoPJrVg" 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>The dot diagram shows the number of children in several households.</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 modal number of children of the households.</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/1765422022364-fvkljcstoxw.png?token=eyJraWQiOiJiZTM3ZjNhZS05OWM4LTQ5ZGQtYjRiNS1iMTBhYmJhNjY5MWYiLCJhbGciOiJIUzI1NiJ9.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvcGFzdGVkLzE3NjU0MjIwMjIzNjQtZnZrbGpjc3RveHcucG5nIiwic2NvcGUiOiJkb3dubG9hZCIsImlhdCI6MTc5MjY5NTc3NSwiZXhwIjoxNzkyNjk2MDc1fQ.fcJL8E6raz-SPXM0ljWzmGzsuzEAQuJE8oPyhKCuxe0" style="max-width: min(250px, 100%); height: auto; display: block;" class="alignright custom-width" /></figure></div></div></div></div>

The dot diagram shows the number of children in several households.

Family Size Distribution: Mode Calculation

<p>The dot diagram shows the number of goals a football team score in some of the matches they played in a season. </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 modal number of goals.</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/1765421788145-lmhoqp1ghjp.png?token=eyJraWQiOiJiZTM3ZjNhZS05OWM4LTQ5ZGQtYjRiNS1iMTBhYmJhNjY5MWYiLCJhbGciOiJIUzI1NiJ9.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvcGFzdGVkLzE3NjU0MjE3ODgxNDUtbG1ob3FwMWdoanAucG5nIiwic2NvcGUiOiJkb3dubG9hZCIsImlhdCI6MTc5MjY5NTc3NSwiZXhwIjoxNzkyNjk2MDc1fQ.0ONAL7fJjcs6pRjGDxcgQDLKtbz1iC5VL75CAn2vKWA" style="max-width: min(300px, 100%); height: auto; display: block;" class="alignright custom-width" /></figure></div></div></div></div>

The dot diagram shows the number of goals a football team score in some of the matches they played in a season. 

Football Season Goal Data: Identifying the Mode

<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>The dot diagram shows the number of magazines owned by a group of students.<br>Find the mode of the distribution.</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/1765421522715-zptukp7ze1.png?token=eyJraWQiOiJiZTM3ZjNhZS05OWM4LTQ5ZGQtYjRiNS1iMTBhYmJhNjY5MWYiLCJhbGciOiJIUzI1NiJ9.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvcGFzdGVkLzE3NjU0MjE1MjI3MTUtenB0dWtwN3plMS5wbmciLCJzY29wZSI6ImRvd25sb2FkIiwiaWF0IjoxNzkyNjk1Nzc1LCJleHAiOjE3OTI2OTYwNzV9.0efN2rYlrK30UMqiPo-dk2d18DTKmuaQ-8nR96wTGZ0" style="max-width: min(250px, 100%); height: auto; display: block;" class="alignright custom-width" /></figure></div></div></div></div>

Number of Magazines Owned: Mode Calculation

<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>The dot diagram represents the number of latecomers of a school in $30$ days.<br>Find the mode of the distribution.</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/1765366107909-i5mtlhmrkm.png?token=eyJraWQiOiJiZTM3ZjNhZS05OWM4LTQ5ZGQtYjRiNS1iMTBhYmJhNjY5MWYiLCJhbGciOiJIUzI1NiJ9.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvcGFzdGVkLzE3NjUzNjYxMDc5MDktaTVtdGxobXJrbS5wbmciLCJzY29wZSI6ImRvd25sb2FkIiwiaWF0IjoxNzkyNjk1Nzc1LCJleHAiOjE3OTI2OTYwNzV9.DQ4Sm_J9alxcK9ceuPK4ptUg9wMocMIbZKfZmaQHG8Q" style="max-width: min(280px, 100%); height: auto; display: block;" class="alignright custom-width" /></figure></div></div></div></div>

Daily Latecomer Count: Mode Calculation

<p>The number of days the employees in an organisation were absent from work in a year was recorded. </p>
<div class="content-block content-block--table"><div class="table-container"><table style="table-layout: fixed; width: 520px;"><colgroup><col style="width: 120px;"><col style="width: 40px;"><col style="width: 40px;"><col style="width: 40px;"><col style="width: 40px;"><col style="width: 40px;"><col style="width: 40px;"><col style="width: 40px;"><col style="width: 40px;"><col style="width: 40px;"><col style="width: 40px;"></colgroup><thead><tr><th style="text-align: center; --cell-justify: center"><p><strong>Number of days absent</strong></p></th><th style="text-align: center; --cell-justify: center"><p>$0$</p></th><th style="text-align: center; --cell-justify: center"><p>$1$</p></th><th style="text-align: center; --cell-justify: center"><p>$2$</p></th><th style="text-align: center; --cell-justify: center"><p>$3$</p></th><th style="text-align: center; --cell-justify: center"><p>$4$</p></th><th style="text-align: center; --cell-justify: center"><p>$5$</p></th><th style="text-align: center; --cell-justify: center"><p>$6$</p></th><th style="text-align: center; --cell-justify: center"><p>$7$</p></th><th style="text-align: center; --cell-justify: center"><p>$8$</p></th><th style="text-align: center; --cell-justify: center"><p>$9$</p></th></tr></thead><tbody><tr><td style="text-align: center; --cell-justify: center"><p><strong>Number of employees</strong></p></td><td style="text-align: center; --cell-justify: center"><p>$31$</p></td><td style="text-align: center; --cell-justify: center"><p>$4$</p></td><td style="text-align: center; --cell-justify: center"><p>$9$</p></td><td style="text-align: center; --cell-justify: center"><p>$7$</p></td><td style="text-align: center; --cell-justify: center"><p>$5$</p></td><td style="text-align: center; --cell-justify: center"><p>$4$</p></td><td style="text-align: center; --cell-justify: center"><p>$12$</p></td><td style="text-align: center; --cell-justify: center"><p>$3$</p></td><td style="text-align: center; --cell-justify: center"><p>$3$</p></td><td style="text-align: center; --cell-justify: center"><p>$2$</p></td></tr></tbody></table></div></div>
<p></p>
<p>Find the modal of the number of days the employees were absent from work. </p>

The number of days the employees in an organisation were absent from work in a year was recorded. 

<p><strong>Number of days absent</strong></p>

Find the modal of the number of days the employees were absent from work. 

Employee Absence Data: Mode Calculation

<p>The returns, in percentage, of some financial investments in a year by some financial portfolios are shown 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: 200px;"><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><strong>Returns (%)</strong></p></th><th style="text-align: center; --cell-justify: center"><p>$-10$</p></th><th style="text-align: center; --cell-justify: center"><p>$-5$</p></th><th style="text-align: center; --cell-justify: center"><p>$0$</p></th><th style="text-align: center; --cell-justify: center"><p>$5$</p></th><th style="text-align: center; --cell-justify: center"><p>$10$</p></th></tr></thead><tbody><tr><td style="text-align: center; --cell-justify: center"><p><strong>Number of portfolios</strong></p></td><td style="text-align: center; --cell-justify: center"><p>$5$</p></td><td style="text-align: center; --cell-justify: center"><p>$2$</p></td><td style="text-align: center; --cell-justify: center"><p>$3$</p></td><td style="text-align: center; --cell-justify: center"><p>$4$</p></td><td style="text-align: center; --cell-justify: center"><p>$3$</p></td></tr></tbody></table></div></div>
<p>Find the modal returns of the financial investments.</p>

The returns, in percentage, of some financial investments in a year by some financial portfolios are shown in the table below.  

Find the modal returns of the financial investments.

Investment Returns: Mode Calculation

<p>The scores of $10$ students in a History test are $54$, $89$, $71$, $64$, $64$, $83$, $72$ , $83$, $70$ and $64$.<br>Find the modal score of the students.</p>

The scores of $10$ students in a History test are $54$, $89$, $71$, $64$, $64$, $83$, $72$ , $83$, $70$ and $64$.
Find the modal score of the students.

History Test Scores: Mode Calculation

<p>The heights of $8$ students are $1.73$ m, $1.63$ m, $1.79$ m, $1.59$ m, $1.63$m, $1.73$ m, $1.73$ m and $1.82$ m.<br>Find the modal height of the students. </p>

The heights of $8$ students are $1.73$ m, $1.63$ m, $1.79$ m, $1.59$ m, $1.63$m, $1.73$ m, $1.73$ m and $1.82$ m.
Find the modal height of the students. 

Heights of Students: 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.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvcGFzdGVkLzE3NjUzNjUwODEwOTgtMjJ2MHRqZXRydGUucG5nIiwic2NvcGUiOiJkb3dubG9hZCIsImlhdCI6MTc5MjY5NTc3NSwiZXhwIjoxNzkyNjk2MDc1fQ.taOJVfMM9lXZUdBiI79jCFBbhhqfvfVSpXi_NzWr3dQ" 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

<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>The dot diagram below represents the number of books read by $18$ students in a month.<br>Find the modal number of books read by 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/1765364911388-7t8jtjmgod8.png?token=eyJraWQiOiJiZTM3ZjNhZS05OWM4LTQ5ZGQtYjRiNS1iMTBhYmJhNjY5MWYiLCJhbGciOiJIUzI1NiJ9.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvcGFzdGVkLzE3NjUzNjQ5MTEzODgtN3Q4anRqbWdvZDgucG5nIiwic2NvcGUiOiJkb3dubG9hZCIsImlhdCI6MTc5MjY5NTc3NSwiZXhwIjoxNzkyNjk2MDc1fQ.FCe3YFl3xopUKz-E2_TzphBrTeHr0aw2Rg-T3gAP8Dw" style="max-width: min(250px, 100%); height: auto; display: block;" class="alignright custom-width" /></figure></div></div></div></div>

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