A Math

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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>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.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvcGFzdGVkLzE3NjU0MzE0NzU3NTktNjJqMTJjdnNjYmYucG5nIiwic2NvcGUiOiJkb3dubG9hZCIsImlhdCI6MTc5MjY5NTg2MSwiZXhwIjoxNzkyNjk2MTYxfQ.ETstY5gxq5XfuKrfrYjS3yp_sqIUlY2rgM229oGpM6Q" 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 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.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvcGFzdGVkLzE3NjU0MjIwMjIzNjQtZnZrbGpjc3RveHcucG5nIiwic2NvcGUiOiJkb3dubG9hZCIsImlhdCI6MTc5MjY5NTg2MSwiZXhwIjoxNzkyNjk2MTYxfQ.ILlxF37RmKB_Z0fd3hFjxXXpEdUjXdiorWUdDZdBcpA" 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.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvcGFzdGVkLzE3NjU0MjE3ODgxNDUtbG1ob3FwMWdoanAucG5nIiwic2NvcGUiOiJkb3dubG9hZCIsImlhdCI6MTc5MjY5NTg2MSwiZXhwIjoxNzkyNjk2MTYxfQ.8L-b6yM-gPqynu6aImuhyLEmEe_pYz_1R5-6NtBBz0Q" 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.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvcGFzdGVkLzE3NjU0MjE1MjI3MTUtenB0dWtwN3plMS5wbmciLCJzY29wZSI6ImRvd25sb2FkIiwiaWF0IjoxNzkyNjk1ODYxLCJleHAiOjE3OTI2OTYxNjF9.5yzUvE5zjBlPly4SwZ0OnQAxuCa6GTomgV8F6V2UOdY" 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.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvcGFzdGVkLzE3NjUzNjYxMDc5MDktaTVtdGxobXJrbS5wbmciLCJzY29wZSI6ImRvd25sb2FkIiwiaWF0IjoxNzkyNjk1ODYxLCJleHAiOjE3OTI2OTYxNjF9.I2qepw2VM7ZxR14C9m0dew7gUvJkmCwmV8I15z0VktM" style="max-width: min(280px, 100%); height: auto; display: block;" class="alignright custom-width" /></figure></div></div></div></div>

Daily Latecomer Count: 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 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.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvcGFzdGVkLzE3NjUzNjQ5MTEzODgtN3Q4anRqbWdvZDgucG5nIiwic2NvcGUiOiJkb3dubG9hZCIsImlhdCI6MTc5MjY5NTg2MSwiZXhwIjoxNzkyNjk2MTYxfQ.p4qg2V_S7ZkazgkfRTlV5pgdOj-JhVbp5y1z66ViIvY" style="max-width: min(250px, 100%); height: auto; display: block;" class="alignright custom-width" /></figure></div></div></div></div>

Books Read in a Month: Mode Calculation

<p>The dot diagram shows the number of children in several households. </p>
<p></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 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/1765363561068-2kqj7v8utaq.png?token=eyJraWQiOiJiZTM3ZjNhZS05OWM4LTQ5ZGQtYjRiNS1iMTBhYmJhNjY5MWYiLCJhbGciOiJIUzI1NiJ9.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvcGFzdGVkLzE3NjUzNjM1NjEwNjgtMmtxajd2OHV0YXEucG5nIiwic2NvcGUiOiJkb3dubG9hZCIsImlhdCI6MTc5MjY5NTg2MSwiZXhwIjoxNzkyNjk2MTYxfQ.AHfCVhYchaMBXsZRpL-HlDZtNGIxygF9nM0viUQscmA" 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. 

Median

Median Number of Children in Households

<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 median 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/1765363393332-x25fizro5vc.png?token=eyJraWQiOiJiZTM3ZjNhZS05OWM4LTQ5ZGQtYjRiNS1iMTBhYmJhNjY5MWYiLCJhbGciOiJIUzI1NiJ9.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvcGFzdGVkLzE3NjUzNjMzOTMzMzIteDI1Zml6cm81dmMucG5nIiwic2NvcGUiOiJkb3dubG9hZCIsImlhdCI6MTc5MjY5NTg2MSwiZXhwIjoxNzkyNjk2MTYxfQ.g-I5JmkC-2YMLa2VQTMJfyxbpDMghCo4oqXrNIS6xOI" style="max-width: min(250px, 100%); height: auto; display: block;" class="alignright custom-width" /></figure></div></div></div></div>

Median Number of Goals Scored

<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 median number 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/1765363082047-m75cow5nxx.png?token=eyJraWQiOiJiZTM3ZjNhZS05OWM4LTQ5ZGQtYjRiNS1iMTBhYmJhNjY5MWYiLCJhbGciOiJIUzI1NiJ9.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvcGFzdGVkLzE3NjUzNjMwODIwNDctbTc1Y293NW54eC5wbmciLCJzY29wZSI6ImRvd25sb2FkIiwiaWF0IjoxNzkyNjk1ODYxLCJleHAiOjE3OTI2OTYxNjF9.8FsCaqB3sB7uVfUc7hLY-wm8Z233lGRg6UswEFbxgD0" style="max-width: min(230px, 100%); height: auto; display: block;" class="alignright custom-width" /></figure></div></div></div></div>

Finding the Median from Magazine Count Data

<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 median number of the distribution. <br></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/1765362947523-mkohwus8id.png?token=eyJraWQiOiJiZTM3ZjNhZS05OWM4LTQ5ZGQtYjRiNS1iMTBhYmJhNjY5MWYiLCJhbGciOiJIUzI1NiJ9.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvcGFzdGVkLzE3NjUzNjI5NDc1MjMtbWtvaHd1czhpZC5wbmciLCJzY29wZSI6ImRvd25sb2FkIiwiaWF0IjoxNzkyNjk1ODYxLCJleHAiOjE3OTI2OTYxNjF9.x33aXsJEBfqHUIsPLMpfwvz8Cvs-SaowIYOH7WBC0Ew" style="max-width: min(270px, 100%); height: auto; display: block;" class="alignright custom-width" /></figure></div></div></div></div>

Finding the Median from a Dot Plot of Latecomers

<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 median 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/1765361505695-meoqbko0gin.png?token=eyJraWQiOiJiZTM3ZjNhZS05OWM4LTQ5ZGQtYjRiNS1iMTBhYmJhNjY5MWYiLCJhbGciOiJIUzI1NiJ9.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvcGFzdGVkLzE3NjUzNjE1MDU2OTUtbWVvcWJrbzBnaW4ucG5nIiwic2NvcGUiOiJkb3dubG9hZCIsImlhdCI6MTc5MjY5NTg2MSwiZXhwIjoxNzkyNjk2MTYxfQ.TQu1_T1yZaCyI7v9SmdVfdnZWUqNKaT9jf-sW4wOgFc" style="max-width: min(230px, 100%); height: auto; display: block;" class="alignright custom-width" /></figure></div></div></div></div>

Number of Books Read: Dot Plot and Median

<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.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvcGFzdGVkLzE3NjUzNTY2MDU2NjQtcjFodnNlYXkwM2QucG5nIiwic2NvcGUiOiJkb3dubG9hZCIsImlhdCI6MTc5MjY5NTg2MSwiZXhwIjoxNzkyNjk2MTYxfQ.vd_IIYTMg5eUrzx9Fq-PcuuF3E1INuoR6EXK71uD0K8" 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 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.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvcGFzdGVkLzE3NjUzNTMzNjU1NzMtODI3bTF3Ym94em8ucG5nIiwic2NvcGUiOiJkb3dubG9hZCIsImlhdCI6MTc5MjY5NTg2MSwiZXhwIjoxNzkyNjk2MTYxfQ.PMAvPyDp7DKlxOyE5Ex1h9_bCjDmdtmhCVq7u_dWYNw" 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>Each student in a class was asked how long (in the nearest minute) it took them to solve a problem.</p>
<p>The results are 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: 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>$2$</p></th><th style="text-align: center; --cell-justify: center"><p>$7$</p></th><th style="text-align: center; --cell-justify: center"><p>$4$</p></th><th style="text-align: center; --cell-justify: center"><p>$2$</p></th><th style="text-align: center; --cell-justify: center"><p>$1$</p></th><th style="text-align: center; --cell-justify: center"><p>$3$</p></th><th style="text-align: center; --cell-justify: center"><p>$8$</p></th><th style="text-align: center; --cell-justify: center"><p>$7$</p></th></tr></thead><tbody><tr><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>$2$</p></td><td style="text-align: center; --cell-justify: center"><p>$5$</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>$8$</p></td></tr><tr><td style="text-align: center; --cell-justify: center"><p>$8$</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>$11$</p></td><td style="text-align: center; --cell-justify: center"><p>$4$</p></td><td style="text-align: center; --cell-justify: center"><p>$6$</p></td><td style="text-align: center; --cell-justify: center"><p>$2$</p></td><td style="text-align: center; --cell-justify: center"><p>$6$</p></td></tr></tbody></table></div></div>
<ol class="abc-list"><li><div class="list-item-paragraph">Represent the data on a dot diagram.</div></li><li><div class="list-item-paragraph">Briefly describe the distribution of the data.</div></li><li><div class="list-item-paragraph">A student is selected at random. The probability that the student uses at most $x$ minutes to solve the problem is $\frac{2}{3}$ . Find the values of $x$. </div></li></ol>

Each student in a class was asked how long (in the nearest minute) it took them to solve a problem.

The results are shown in the table below.

Dot Plot Representation and Probability

<p>The table shows the number of books read by $20$ students in a class in a particular month. </p>
<div class="content-block content-block--table"><div class="table-container"><table style="table-layout: fixed; width: 400px;"><colgroup><col style="width: 80px;"><col style="width: 80px;"><col style="width: 80px;"><col style="width: 80px;"><col style="width: 80px;"></colgroup><thead><tr><th style="text-align: center; --cell-justify: center"><p>$0$</p></th><th style="text-align: center; --cell-justify: center"><p>$3$</p></th><th style="text-align: center; --cell-justify: center"><p>$1$</p></th><th style="text-align: center; --cell-justify: center"><p>$3$</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>$2$</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>$4$</p></td><td style="text-align: center; --cell-justify: center"><p>$4$</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>$1$</p></td><td style="text-align: center; --cell-justify: center"><p>$2$</p></td><td style="text-align: center; --cell-justify: center"><p>$2$</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>$1$</p></td><td style="text-align: center; --cell-justify: center"><p>$0$</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>$0$</p></td></tr></tbody></table></div></div>
<ol class="abc-list"><li><div class="list-item-paragraph">Represent the data on a dot diagram.</div></li><li><div class="list-item-paragraph">Briefly describe the distribution of the data.</div></li><li><div class="list-item-paragraph">A student is selected at random. The probability that the student reads at least $x$ books is $\frac{1}{5}$ . Find the values of $x$.</div></li></ol>

The table shows the number of books read by $20$ students in a class in a particular month. 

Dot Plot and Probability Problem

<p>The table below shows the marks obtained by $20$ students in a mathematics test. </p>
<div class="content-block content-block--table"><div class="table-container"><table style="table-layout: fixed; width: 400px;"><colgroup><col style="width: 80px;"><col style="width: 80px;"><col style="width: 80px;"><col style="width: 80px;"><col style="width: 80px;"></colgroup><thead><tr><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>$8$</p></th><th style="text-align: center; --cell-justify: center"><p>$13$</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>$7$</p></td><td style="text-align: center; --cell-justify: center"><p>$13$</p></td><td style="text-align: center; --cell-justify: center"><p>$11$</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></tr><tr><td style="text-align: center; --cell-justify: center"><p>$8$</p></td><td style="text-align: center; --cell-justify: center"><p>$12$</p></td><td style="text-align: center; --cell-justify: center"><p>$9$</p></td><td style="text-align: center; --cell-justify: center"><p>$9$</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>$1$</p></td><td style="text-align: center; --cell-justify: center"><p>$14$</p></td><td style="text-align: center; --cell-justify: center"><p>$7$</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></tbody></table></div></div>
<ol class="abc-list"><li><div class="list-item-paragraph">Represent the data on a dot diagram.</div></li><li><div class="list-item-paragraph">Briefly describe the distribution of the data.</div></li><li><div class="list-item-paragraph">A student is selected at random. The probability that the student obtains at most $x$ 	marks is $\frac{3}{5}$. Find the values of $x$. </div></li></ol>

The table below shows the marks obtained by $20$ students in a mathematics test. 

Math Question Bank