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<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.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvcGFzdGVkLzE3NjU0MzE0NzU3NTktNjJqMTJjdnNjYmYucG5nIiwic2NvcGUiOiJkb3dubG9hZCIsImlhdCI6MTc5MjY5NTg2MiwiZXhwIjoxNzkyNjk2MTYyfQ.m-ht4OFsh8J755j1Uo87x28S5XJOUPKYdhFbi586q1Q" 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

Mode

Dot Diagrams

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

Statistics

Probability

<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.

Median

Frequency Table of Words per Line

<p>The following data shows the number of customers across $12$ restaurants at a given moment.</p>
<div class="content-block content-block--table"><div class="table-container"><table style="table-layout: fixed; width: 400px;"><colgroup><col style="width: 100px;"><col style="width: 100px;"><col style="width: 100px;"><col style="width: 100px;"></colgroup><thead><tr><th style="text-align: center; --cell-justify: center"><p>$15$</p></th><th style="text-align: center; --cell-justify: center"><p>$15$</p></th><th style="text-align: center; --cell-justify: center"><p>$18$</p></th><th style="text-align: center; --cell-justify: center"><p>$16$</p></th></tr></thead><tbody><tr><td style="text-align: center; --cell-justify: center"><p>$12$</p></td><td style="text-align: center; --cell-justify: center"><p>$16$</p></td><td style="text-align: center; --cell-justify: center"><p>$16$</p></td><td style="text-align: center; --cell-justify: center"><p>$15$</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>$14$</p></td><td style="text-align: center; --cell-justify: center"><p>$16$</p></td><td style="text-align: center; --cell-justify: center"><p>$12$</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></li><li><div class="list-item-paragraph">Calculate the mean number of customers across the restaurants.</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 restaurants that have at most $14$ customers?</div></li><li><div class="list-item-paragraph">What is the probability of a restaurant having $15$ customers at a given moment?</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/1765356605664-r1hvseay03d.png?token=eyJraWQiOiJiZTM3ZjNhZS05OWM4LTQ5ZGQtYjRiNS1iMTBhYmJhNjY5MWYiLCJhbGciOiJIUzI1NiJ9.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvcGFzdGVkLzE3NjUzNTY2MDU2NjQtcjFodnNlYXkwM2QucG5nIiwic2NvcGUiOiJkb3dubG9hZCIsImlhdCI6MTc5MjY5NTg2MiwiZXhwIjoxNzkyNjk2MTYyfQ.vPzU2vK3me16QJ93H4lfiA3laSCXj551Uoe7HK1Qcws" alt="List item image" class="aligncenter custom-width" style="max-width: min(400px, 100%); height: auto;" /></div></li></ol>

The following data shows the number of customers across $12$ restaurants at a given moment.

Number of Customers Across Restaurants

<p>The number of days the employees in an organisation were absent from work in a year was recorded. </p>
<div class="table-container"><table><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;"><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"><p><strong>Number of days absent</strong></p></th><th style="text-align: center"><p>$0$</p></th><th style="text-align: center"><p>$1$</p></th><th style="text-align: center"><p>$2$</p></th><th style="text-align: center"><p>$3$</p></th><th style="text-align: center"><p>$4$</p></th><th style="text-align: center"><p>$5$</p></th><th style="text-align: center"><p>$6$</p></th><th style="text-align: center"><p>$7$</p></th><th style="text-align: center"><p>$8$</p></th><th style="text-align: center"><p>$9$</p></th></tr></thead><tbody><tr><td style="text-align: center"><p><strong>Number of employees</strong></p></td><td style="text-align: center"><p>$31$</p></td><td style="text-align: center"><p>$4$</p></td><td style="text-align: center"><p>$9$</p></td><td style="text-align: center"><p>$7$</p></td><td style="text-align: center"><p>$5$</p></td><td style="text-align: center"><p>$4$</p></td><td style="text-align: center"><p>$12$</p></td><td style="text-align: center"><p>$3$</p></td><td style="text-align: center"><p>$3$</p></td><td style="text-align: center"><p>$2$</p></td></tr></tbody></table></div>
<p>Find the mean number of days of absence. </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 mean number of days of absence. 

Number of Days Absent: Frequency and Mean 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: 44.4444%;"><col style="width: 11.1111%;"><col style="width: 11.1111%;"><col style="width: 11.1111%;"><col style="width: 11.1111%;"><col style="width: 11.1111%;"></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>Calculate</p>
<ol class="abc-list"><li data-list-item-id="item-1765355755230-uwkpbq7o5" data-list-item-path="item-1765355755230-uwkpbq7o5"><div class="list-item-paragraph">the total number of portfolios,</div></li><li data-list-item-id="item-1765355755792-0q658effg" data-list-item-path="item-1765355755792-0q658effg"><div class="list-item-paragraph">the sum of the numerical percentage returns across the portfolios,</div></li><li data-list-item-id="item-1765355756460-shivgcbkp" data-list-item-path="item-1765355756460-shivgcbkp"><div class="list-item-paragraph">the mean return, in percentage, of financial investments by the portfolios.</div></li></ol>

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

Investment Returns: Frequency Table and Mean Return

<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: 560px;"><colgroup><col style="width: 70px;"><col style="width: 70px;"><col style="width: 70px;"><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>$3$</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>$2$</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>$0$</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>$4$</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>$2$</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>$0$</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></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><div class="content-block list-item-image" style="text-align: center;"><img src="https://vocwkpgapvksartxhhor.supabase.co/storage/v1/object/sign/question-images/pasted/1765353365573-827m1wboxzo.png?token=eyJraWQiOiJiZTM3ZjNhZS05OWM4LTQ5ZGQtYjRiNS1iMTBhYmJhNjY5MWYiLCJhbGciOiJIUzI1NiJ9.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvcGFzdGVkLzE3NjUzNTMzNjU1NzMtODI3bTF3Ym94em8ucG5nIiwic2NvcGUiOiJkb3dubG9hZCIsImlhdCI6MTc5MjY5NTg2MiwiZXhwIjoxNzkyNjk2MTYyfQ.454GIKaMk3weAJhR0SHdKr14G4db8V7NGBE70WznLmM" alt="List item image" class="aligncenter custom-width" style="max-width: min(400px, 100%); height: auto;" /></div></li></ol>

Finding The Mean From A Dot Diagram

<p>The number of hours per week spent in doing homework by some students is shown in the table below.</p>
<div class="content-block content-block--table"><div class="table-container"><table style="table-layout: fixed; width: 400px;"><colgroup><col style="width: 200px;"><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 hours per week</strong></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></tr></thead><tbody><tr><td style="text-align: center; --cell-justify: center"><p><strong>Number of students</strong></p></td><td style="text-align: center; --cell-justify: center"><p>$10$</p></td><td style="text-align: center; --cell-justify: center"><p>$16$</p></td><td style="text-align: center; --cell-justify: center"><p>$13$</p></td><td style="text-align: center; --cell-justify: center"><p>$6$</p></td></tr></tbody></table></div></div>
<p>Calculate</p>
<ol class="abc-list"><li><div class="list-item-paragraph">the total number of students,</div></li><li><div class="list-item-paragraph">the total number of hours spent by all the students,</div></li><li><div class="list-item-paragraph">the mean number of hours per week spent by the students.</div></li></ol>

The number of hours per week spent in doing homework by some students is shown in the table below.

<p><strong>Number of hours per week</strong></p>

Math Question Bank