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>The box-and-whisker plot represents a set of data with \(80\) data points.</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/1769497950121-106nfxli3zxd.png?token=eyJraWQiOiJiZTM3ZjNhZS05OWM4LTQ5ZGQtYjRiNS1iMTBhYmJhNjY5MWYiLCJhbGciOiJIUzI1NiJ9.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvcGFzdGVkLzE3Njk0OTc5NTAxMjEtMTA2bmZ4bGkzenhkLnBuZyIsInNjb3BlIjoiZG93bmxvYWQiLCJpYXQiOjE3OTI2OTU3MzEsImV4cCI6MTc5MjY5NjAzMX0.a0bYlVK_BEhkJbn6V9Wfdi7aLsqg8lkyoHXkUfCBUZY" style="max-width: min(400px, 100%); height: auto; display: block;" alt="Box-and-whisker plot showing data values at 7, 48, 65, 78, and 85." class="aligncenter custom-width" /></figure></div>
<ol class="i-list"><li><div class="list-item-content"><span class="list-item-text">Find the greatest and the least possible number of data points with the value of \(78\).</span></div></li><li><div class="list-item-content"><span class="list-item-text">Find the greatest and the least possible number of data points with values at least \(78\).</span></div></li><li><div class="list-item-content"><span class="list-item-text">Find the greatest and the least possible number of data points with the value of \(85\).</span></div></li></ol>

The box-and-whisker plot represents a set of data with \(80\) data points.

Find the greatest and the least possible number of data points with the value of \(78\).

Find the greatest and the least possible number of data points with values at least \(78\).

Find the greatest and the least possible number of data points with the value of \(85\).

Finding Unknowns from Averages and Spread

Box-and-Whisker Plots

IP2U15 HOT Q4

Statistics

<p>The height of students at a school is shown as a cumulative frequency graph below.</p>
<div class="content-block"><figure class="question-figure aligncenter" style="text-align: center;"><img src="https://vocwkpgapvksartxhhor.supabase.co/storage/v1/object/sign/question-images/pasted/1769331137120-oubtwaa4dlf.png?token=eyJraWQiOiJiZTM3ZjNhZS05OWM4LTQ5ZGQtYjRiNS1iMTBhYmJhNjY5MWYiLCJhbGciOiJIUzI1NiJ9.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvcGFzdGVkLzE3NjkzMzExMzcxMjAtb3VidHdhYTRkbGYucG5nIiwic2NvcGUiOiJkb3dubG9hZCIsImlhdCI6MTc5MjY5NTczMSwiZXhwIjoxNzkyNjk2MDMxfQ.D0bDwr-jEBRF4V62f6wjJqu_SMr93WiLWkr9XR1_JKE" style="max-width: min(400px, 100%); height: auto; display: block;" alt="Cumulative frequency graph showing Number of students vs Height (cm)" class="aligncenter custom-width" /></figure></div>
<ol class="abc-list"><li><div class="list-item-content"><span class="list-item-text">Use the graph to estimate</span></div><ol class="i-list"><li><div class="list-item-content"><span class="list-item-text">the median,</span></div></li><li><div class="list-item-content"><span class="list-item-text">the inter-quartile range.</span></div></li></ol></li><li><div class="list-item-content"><span class="list-item-text">If&nbsp;\(20\)% of the students are taller than \(h\) cm, find the value of \(h\).</span></div></li><li><div class="list-item-content"><span class="list-item-text">Copy and complete the grouped frequency table of students' heights.</span></div></li></ol>
<div class="content-block content-block--table"><div class="table-container"><table><thead><tr style="height: 23px;"><th style="height: 23px; min-height: 23px; text-align: center; --cell-justify: center">Heights (cm)</th><th style="height: 23px; min-height: 23px; text-align: center; --cell-justify: center">No. of students</th></tr></thead><tbody><tr style="height: 23px;"><td style="height: 23px; min-height: 23px; text-align: center; --cell-justify: center">\(120 \le x &lt; 130\)</td><td style="height: 23px; min-height: 23px; text-align: left; --cell-justify: flex-start"></td></tr><tr style="height: 23px;"><td style="height: 23px; min-height: 23px; text-align: center; --cell-justify: center">\(130 \le x &lt; 140\)</td><td style="height: 23px; min-height: 23px; text-align: left; --cell-justify: flex-start"></td></tr><tr style="height: 23px;"><td style="height: 23px; min-height: 23px; text-align: center; --cell-justify: center">\(140 \le x &lt; 150\)</td><td style="height: 23px; min-height: 23px; text-align: left; --cell-justify: flex-start"></td></tr><tr style="height: 23px;"><td style="height: 23px; min-height: 23px; text-align: center; --cell-justify: center">\(150 \le x &lt; 160\)</td><td style="height: 23px; min-height: 23px; text-align: left; --cell-justify: flex-start"></td></tr><tr style="height: 23px;"><td style="height: 23px; min-height: 23px; text-align: center; --cell-justify: center">\(160 \le x &lt; 170\)</td><td style="height: 23px; min-height: 23px; text-align: left; --cell-justify: flex-start"></td></tr><tr style="height: 23px;"><td style="height: 23px; min-height: 23px; text-align: center; --cell-justify: center">\(170 \le x &lt; 180\)</td><td style="height: 23px; min-height: 23px; text-align: left; --cell-justify: flex-start"></td></tr></tbody></table></div></div>
<ol class="abc-list" start="4"><li><div class="list-item-paragraph">Using your grouped frequency table, calculate an estimate of the standard deviation.</div></li><li><div class="list-item-paragraph">The students at the school took measurements of their weights using a faulty weighing machine. The box and whisker graph below shows the students' weights (in kg) measured by the faulty weight machine.</div><div class="content-block list-item-image" style="text-align: center;"><img src="https://vocwkpgapvksartxhhor.supabase.co/storage/v1/object/sign/question-images/pasted/1769331223446-mab2gukchu8.png?token=eyJraWQiOiJiZTM3ZjNhZS05OWM4LTQ5ZGQtYjRiNS1iMTBhYmJhNjY5MWYiLCJhbGciOiJIUzI1NiJ9.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvcGFzdGVkLzE3NjkzMzEyMjM0NDYtbWFiMmd1a2NodTgucG5nIiwic2NvcGUiOiJkb3dubG9hZCIsImlhdCI6MTc5MjY5NTczMSwiZXhwIjoxNzkyNjk2MDMxfQ.RV0MC0zqI9Vsc9Iz1BzbGbtgMiklTzibz35qqDVDWBI" alt="List item image" class="aligncenter" style="max-width: 100%; height: auto;" /></div><ol class="i-list"><li><div class="list-item-paragraph">If every student's true weight was actually \(5\) kg lower, describe briefly how the box and whisker graph will differ from the given graph.</div></li><li><div class="list-item-paragraph">State the correct value of the median weight.</div></li></ol></li></ol>

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

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

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

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

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

Percentiles and Quartiles from Cumulative Frequency Curves

Effects of Changing Data on Statistical Measures

Cumulative Frequency Table and Curve

Mean and Standard Deviation for Grouped Data

<p>The weights of \(200\) secondary two pupils at Ace Secondary School are represented by the cumulative frequency curve shown below.</p>
<div class="content-block"><figure class="question-figure aligncenter" style="text-align: center;"><img src="https://vocwkpgapvksartxhhor.supabase.co/storage/v1/object/sign/question-images/pasted/1769330982039-i6xy3zqu22q.png?token=eyJraWQiOiJiZTM3ZjNhZS05OWM4LTQ5ZGQtYjRiNS1iMTBhYmJhNjY5MWYiLCJhbGciOiJIUzI1NiJ9.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvcGFzdGVkLzE3NjkzMzA5ODIwMzktaTZ4eTN6cXUyMnEucG5nIiwic2NvcGUiOiJkb3dubG9hZCIsImlhdCI6MTc5MjY5NTczMSwiZXhwIjoxNzkyNjk2MDMxfQ.HQfxWFSbHOjkL09Xt9wg0NeoMrGsAZYZUXU21-oCPyc" style="max-width: min(400px, 100%); height: auto; display: block;" alt="Cumulative Frequency Curve for Weights of Pupils" class="aligncenter custom-width" /></figure></div>
<ol class="abc-list"><li><div class="list-item-content"><span class="list-item-text">Use the graph to find</span></div><ol class="i-list"><li><div class="list-item-paragraph">the median weight of the pupils,</div></li><li><div class="list-item-paragraph">the interquartile range,</div></li><li><div class="list-item-paragraph">the probability that at least one of two pupils chosen at random weighs at least \(55\) kg.</div></li></ol></li><li><div class="list-item-paragraph">The weights of the pupils are represented in the box-and-whiskers plot shown below. Write down the values of \(a\), \(b\), \(c\), \(d\) and \(e\).</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/1769331007631-b9z4edd5xs5.png?token=eyJraWQiOiJiZTM3ZjNhZS05OWM4LTQ5ZGQtYjRiNS1iMTBhYmJhNjY5MWYiLCJhbGciOiJIUzI1NiJ9.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvcGFzdGVkLzE3NjkzMzEwMDc2MzEtYjl6NGVkZDV4czUucG5nIiwic2NvcGUiOiJkb3dubG9hZCIsImlhdCI6MTc5MjY5NTczMSwiZXhwIjoxNzkyNjk2MDMxfQ.rgW8ppmvnuNPGlzAYRdeAPhp8IWB46ziQqEThkjS9dU" alt="List item image" class="aligncenter" style="max-width: 100%; height: auto;" /></div></li><li><div class="list-item-paragraph">The weights of another \(200\) secondary two pupils at Best Secondary School are represented in another box-and-whiskers plot shown below. Compare briefly the weights of the secondary two pupils from the two schools.</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/1769331018689-izkd9lsqqf.png?token=eyJraWQiOiJiZTM3ZjNhZS05OWM4LTQ5ZGQtYjRiNS1iMTBhYmJhNjY5MWYiLCJhbGciOiJIUzI1NiJ9.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvcGFzdGVkLzE3NjkzMzEwMTg2ODktaXprZDlsc3FxZi5wbmciLCJzY29wZSI6ImRvd25sb2FkIiwiaWF0IjoxNzkyNjk1NzMxLCJleHAiOjE3OTI2OTYwMzF9.Q1Ix7qEkVfchl05Q4OIN9DBnMEBeR-KvEsLo-QbeoS4" alt="List item image" class="aligncenter" style="max-width: 100%; height: auto;" /></div></li></ol>

The weights of \(200\) secondary two pupils at Ace Secondary School are represented by the cumulative frequency curve shown below.

The weights of the pupils are represented in the box-and-whiskers plot shown below. Write down the values of \(a\), \(b\), \(c\), \(d\) and \(e\).

Probabilities of Successive Events

Comparing Distributions Using Centre and Spread

Probability

<p>The mass \(x\) grams of each of \(90\) oranges of variety \(A\) were recorded. The data obtained was illustrated as shown in the table.</p>
<div class="content-block content-block--table"><div class="table-container"><table><thead><tr style="height: 23px;"><th style="height: 23px; min-height: 23px; text-align: center; --cell-justify: center">Mass \(x\) grams</th><th style="height: 23px; min-height: 23px; text-align: center; --cell-justify: center">No. of oranges</th></tr></thead><tbody><tr style="height: 23px;"><td style="height: 23px; min-height: 23px; text-align: center; --cell-justify: center">\(60 &lt; x \le 70\)</td><td style="height: 23px; min-height: 23px; text-align: center; --cell-justify: center">\(1\)</td></tr><tr style="height: 23px;"><td style="height: 23px; min-height: 23px; text-align: center; --cell-justify: center">\(70 &lt; x \le 80\)</td><td style="height: 23px; min-height: 23px; text-align: center; --cell-justify: center">\(3\)</td></tr><tr style="height: 23px;"><td style="height: 23px; min-height: 23px; text-align: center; --cell-justify: center">\(80 &lt; x \le 90\)</td><td style="height: 23px; min-height: 23px; text-align: center; --cell-justify: center">\(9\)</td></tr><tr style="height: 23px;"><td style="height: 23px; min-height: 23px; text-align: center; --cell-justify: center">\(90 &lt; x \le 100\)</td><td style="height: 23px; min-height: 23px; text-align: center; --cell-justify: center">\(28\)</td></tr><tr style="height: 23px;"><td style="height: 23px; min-height: 23px; text-align: center; --cell-justify: center">\(100 &lt; x \le 110\)</td><td style="height: 23px; min-height: 23px; text-align: center; --cell-justify: center">\(37\)</td></tr><tr style="height: 23px;"><td style="height: 23px; min-height: 23px; text-align: center; --cell-justify: center">\(110 &lt; x \le 120\)</td><td style="height: 23px; min-height: 23px; text-align: center; --cell-justify: center">\(8\)</td></tr><tr style="height: 23px;"><td style="height: 23px; min-height: 23px; text-align: center; --cell-justify: center">\(120 &lt; x \le 130\)</td><td style="height: 23px; min-height: 23px; text-align: center; --cell-justify: center">\(4\)</td></tr></tbody></table></div></div>
<ol class="abc-list"><li><div class="list-item-content"><span class="list-item-text">Find the mean and standard deviation for the above data.</span></div></li><li><div class="list-item-content"><span class="list-item-text">In an another variety, variety \(B\), of the \(90\) oranges, the lightest orange has the mass \(55\) grams and the heaviest orange has the mass \(138\) grams. The median, lower quartile and upper quartile are \(102\) grams, \(93\) grams and \(109\) grams respectively. Draw the box-whisker diagram for this data.</span></div></li><li><div class="list-item-content"><span class="list-item-text">If you were to buy some oranges, which variety would you buy? Explain your answer.</span></div></li></ol>

The mass \(x\) grams of each of \(90\) oranges of variety \(A\) were recorded. The data obtained was illustrated as shown in the table.

Find the mean and standard deviation for the above data.

In an another variety, variety \(B\), of the \(90\) oranges, the lightest orange has the mass \(55\) grams and the heaviest orange has the mass \(138\) grams. The median, lower quartile and upper quartile are \(102\) grams, \(93\) grams and \(109\) grams respectively. Draw the box-whisker diagram for this data.

If you were to buy some oranges, which variety would you buy? Explain your answer.

<p>The cumulative frequency curve below illustrates the marks obtained by \(120\) students in a Science test for Class \(A\).</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/1769330518184-k7awj2ogt0h.png?token=eyJraWQiOiJiZTM3ZjNhZS05OWM4LTQ5ZGQtYjRiNS1iMTBhYmJhNjY5MWYiLCJhbGciOiJIUzI1NiJ9.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvcGFzdGVkLzE3NjkzMzA1MTgxODQtazdhd2oyb2d0MGgucG5nIiwic2NvcGUiOiJkb3dubG9hZCIsImlhdCI6MTc5MjY5NTczMSwiZXhwIjoxNzkyNjk2MDMxfQ.ylXo8XAQVPo5Y2MEz_6H7QqL8T9NDc44M0rTuyxnd3c" style="max-width: min(400px, 100%); height: auto; display: block;" alt="Cumulative frequency curve for Science test marks" class="aligncenter custom-width" /></figure></div>
<ol class="abc-list"><li><div class="list-item-content"><span class="list-item-text">Use the graph to find,</span></div><ol class="i-list"><li><div class="list-item-paragraph">the \(80^{th}\) percentile.</div></li><li><div class="list-item-paragraph">the interquartile range.</div><div class="list-item-paragraph">In this test, only \(15\)% of the students scored a distinction.</div></li><li><div class="list-item-paragraph">Find the least marks for a student to be considered for distinction.</div><div class="list-item-paragraph">Two student are chosen at random.</div></li><li><div class="list-item-paragraph">Find the probability that both the students scored above \(80\) marks.</div></li></ol></li><li><div class="list-item-paragraph">The cumulative frequency curve can be represented using the following box-and-whisker 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/1769330604036-b08esn5p68u.png?token=eyJraWQiOiJiZTM3ZjNhZS05OWM4LTQ5ZGQtYjRiNS1iMTBhYmJhNjY5MWYiLCJhbGciOiJIUzI1NiJ9.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvcGFzdGVkLzE3NjkzMzA2MDQwMzYtYjA4ZXNuNXA2OHUucG5nIiwic2NvcGUiOiJkb3dubG9hZCIsImlhdCI6MTc5MjY5NTczMSwiZXhwIjoxNzkyNjk2MDMxfQ.vezGtQiL2GpBOLbXLDPtVFqwyXszsEqFJ1fgR8AzOQk" alt="List item image" class="aligncenter" style="max-width: 100%; height: auto;" /></div><ol class="i-list"><li><div class="list-item-paragraph">State the value of \(x_{3}\).</div></li><li><div class="list-item-paragraph">State the value of \(x_{5}-x_{1}\). What does \(x_{5}-x_{1}\) represent?</div></li></ol></li><li><div class="list-item-paragraph">The box-and-whisker diagram below illustrates the marks obtained by \(120\) students in a Science test for Class \(B\).</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/1769499239663-n5u3oytoth.png?token=eyJraWQiOiJiZTM3ZjNhZS05OWM4LTQ5ZGQtYjRiNS1iMTBhYmJhNjY5MWYiLCJhbGciOiJIUzI1NiJ9.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvcGFzdGVkLzE3Njk0OTkyMzk2NjMtbjV1M295dG90aC5wbmciLCJzY29wZSI6ImRvd25sb2FkIiwiaWF0IjoxNzkyNjk1NzMxLCJleHAiOjE3OTI2OTYwMzF9.5ui9jLXpvx9DWV8rKWRd_fItlRnxJDz53v6v-etPZAk" alt="List item image" class="aligncenter custom-width" style="max-width: min(400px, 100%); height: auto;" /></div><div class="list-item-paragraph">Compare the test results for the two classes in two different ways.</div></li><li><div class="list-item-paragraph">The results of the science test of Class \(C\) of \(120\) students have the same median but a smaller standard deviation. Describe how the cumulative frequency curve will differ from the given curve.</div></li></ol>

The cumulative frequency curve below illustrates the marks obtained by \(120\) students in a Science test for Class \(A\).

<p>The cumulative frequency curve below shows the amount of weight loss, measured to the nearest kg, of 200 men in Glow Fitness Centre.</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/1767947420004-9gmcbn2jul.png?token=eyJraWQiOiJiZTM3ZjNhZS05OWM4LTQ5ZGQtYjRiNS1iMTBhYmJhNjY5MWYiLCJhbGciOiJIUzI1NiJ9.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvcGFzdGVkLzE3Njc5NDc0MjAwMDQtOWdtY2JuMmp1bC5wbmciLCJzY29wZSI6ImRvd25sb2FkIiwiaWF0IjoxNzkyNjk1NzMxLCJleHAiOjE3OTI2OTYwMzF9.oLCzQh_HOA7MLUQpigsZx8GsksQkddzmQfNIRozKX9s" style="max-width: min(500px, 100%); height: auto; display: block;" class="aligncenter custom-width" /></figure></div>
<p>The corresponding cumulative frequency table for this distribution is as shown below.</p>
<div class="content-block content-block--table"><div class="table-container"><table><colgroup><col style="width: 150px;"><col style="width: 150px;"></colgroup><thead><tr style="height: 43px;"><th style="height: 43px; min-height: 43px; text-align: center; --cell-justify: center">Weight loss (\(x\) kg)</th><th style="height: 43px; min-height: 43px; text-align: center; --cell-justify: center">Cumulative Frequency</th></tr></thead><tbody><tr style="height: 43px;"><td style="height: 43px; min-height: 43px; text-align: center; --cell-justify: center">\(\le 10\)</td><td style="height: 43px; min-height: 43px; text-align: center; --cell-justify: center">22</td></tr><tr style="height: 43px;"><td style="height: 43px; min-height: 43px; text-align: center; --cell-justify: center">\(\le 15\)</td><td style="height: 43px; min-height: 43px; text-align: center; --cell-justify: center">\(a\)</td></tr><tr style="height: 43px;"><td style="height: 43px; min-height: 43px; text-align: center; --cell-justify: center">\(\le 20\)</td><td style="height: 43px; min-height: 43px; text-align: center; --cell-justify: center">100</td></tr><tr style="height: 43px;"><td style="height: 43px; min-height: 43px; text-align: center; --cell-justify: center">\(\le 25\)</td><td style="height: 43px; min-height: 43px; text-align: center; --cell-justify: center">168</td></tr><tr style="height: 43px;"><td style="height: 43px; min-height: 43px; text-align: center; --cell-justify: center">\(\le 30\)</td><td style="height: 43px; min-height: 43px; text-align: center; --cell-justify: center">190</td></tr><tr style="height: 43px;"><td style="height: 43px; min-height: 43px; text-align: center; --cell-justify: center">\(\le 35\)</td><td style="height: 43px; min-height: 43px; text-align: center; --cell-justify: center">200</td></tr></tbody></table></div></div>
<ol class="abc-list"><li><div class="list-item-content"><span class="list-item-text">Determine the value of \(a\).</span></div></li><li><div class="list-item-content"><span class="list-item-text">Use your graph to find the</span></div><ol class="i-list"><li><div class="list-item-content"><span class="list-item-text">median weight loss,</span></div></li><li><div class="list-item-content"><span class="list-item-text">interquartile range,</span></div></li><li><div class="list-item-content"><span class="list-item-text">\(44^{\mathrm{th}}\) percentile weight loss.</span></div></li></ol></li><li><div class="list-item-paragraph">A second fitness centre, Saturn Fitness Centre also measured the amount of weight loss by \(200\) of their men. The box-and-whisker diagram below illustrates their weight loss achieved.</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/1767947675184-72xpkvh4e0y.png?token=eyJraWQiOiJiZTM3ZjNhZS05OWM4LTQ5ZGQtYjRiNS1iMTBhYmJhNjY5MWYiLCJhbGciOiJIUzI1NiJ9.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvcGFzdGVkLzE3Njc5NDc2NzUxODQtNzJ4cGt2aDRlMHkucG5nIiwic2NvcGUiOiJkb3dubG9hZCIsImlhdCI6MTc5MjY5NTczMSwiZXhwIjoxNzkyNjk2MDMxfQ.ALpL1LGaEMDKZHG0029Ie7I1R2aNzNTHwPHCziH260I" alt="List item image" class="aligncenter custom-width" style="max-width: min(400px, 100%); height: auto;" /></div><ol class="i-list"><li><div class="list-item-paragraph">Find the interquartile range.</div></li><li><div class="list-item-paragraph">A physical instructor claimed that the weight loss program at Glow Fitness Centre is more effective than Saturn Fitness Centre. Explain if his statement is true.</div></li></ol></li></ol>

The cumulative frequency curve below shows the amount of weight loss, measured to the nearest kg, of 200 men in Glow Fitness Centre.

The corresponding cumulative frequency table for this distribution is as shown below.

From Raw Test Scores to Box-and-Whisker Visualizations

<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.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvcGFzdGVkLzE3Njc5NDY5OTAxNzktaG5yY3ZwbHh2emcucG5nIiwic2NvcGUiOiJkb3dubG9hZCIsImlhdCI6MTc5MjY5NTczMSwiZXhwIjoxNzkyNjk2MDMxfQ.XiRFDEVaJfzn8-1qCXA_JLmiEQ6uyMmkXuDbntwYuCc" 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.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvcGFzdGVkLzE3Njc5NDcwMDU0MzItb3cwemJsdG54bGEucG5nIiwic2NvcGUiOiJkb3dubG9hZCIsImlhdCI6MTc5MjY5NTczMSwiZXhwIjoxNzkyNjk2MDMxfQ.v1EPqzx0rPmcbkBhEVKHoDkTIpV_To2GXK33Ziz0-Ng" 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 \(b\).

Expressing One Quantity as a Percentage of Another

Mode

Stem-and-Leaf Diagrams

Descriptive Statistics: Box Plot Construction and Interpretation

Percentages

<p>A set of pollutant standards index (PSI) has been taken on different parts of Singapore as follows.</p>
<div class="content-block content-block--table"><div class="table-container"><table style="width: 100%;"><thead><tr><th style="text-align: center; --cell-justify: center">28</th><th style="text-align: center; --cell-justify: center">29</th><th style="text-align: center; --cell-justify: center">30</th><th style="text-align: center; --cell-justify: center">24</th><th style="text-align: center; --cell-justify: center">25</th></tr></thead><tbody><tr><td style="text-align: center; --cell-justify: center">29</td><td style="text-align: center; --cell-justify: center">25</td><td style="text-align: center; --cell-justify: center">28</td><td style="text-align: center; --cell-justify: center">22</td><td style="text-align: center; --cell-justify: center">28</td></tr></tbody></table></div></div>
<ol class="abc-list"><li data-list-item-id="item-a" data-list-item-path="item-a"><div class="list-item-content"><span class="list-item-text">Find the</span></div><ol class="i-list"><li data-list-item-id="item-a-i" data-list-item-path="item-a/item-a-i"><div class="list-item-content"><span class="list-item-text">median,</span></div></li><li data-list-item-id="item-a-ii" data-list-item-path="item-a/item-a-ii"><div class="list-item-content"><span class="list-item-text">interquartile range.</span></div></li></ol></li><li data-list-item-id="item-b" data-list-item-path="item-b"><div class="list-item-content"><span class="list-item-text">Represent the data by a box-and-whisker plot.</span></div></li></ol>

A set of pollutant standards index (PSI) has been taken on different parts of Singapore as follows.

Represent the data by a box-and-whisker plot.

Median, Quartiles, Range and Interquartile Range

PSI: Median, Interquartile Range and Box Plot

<p>Eighty students took a Mathematics examination which consisted of two papers.</p>
<p>Each paper was marked out of 100. The diagram below shows the cumulative frequency curve for Paper 1.</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/1767945445447-1v9j87hueu8i.png?token=eyJraWQiOiJiZTM3ZjNhZS05OWM4LTQ5ZGQtYjRiNS1iMTBhYmJhNjY5MWYiLCJhbGciOiJIUzI1NiJ9.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvcGFzdGVkLzE3Njc5NDU0NDU0NDctMXY5ajg3aHVldThpLnBuZyIsInNjb3BlIjoiZG93bmxvYWQiLCJpYXQiOjE3OTI2OTU3MzEsImV4cCI6MTc5MjY5NjAzMX0.c6ccRfrlaQYzkE8Qrn_GKKdWhbzk4xvPeeu4vSBkMKY" style="max-width: min(500px, 100%); height: auto; display: block;" alt="Cumulative frequency curve for Paper 1" class="aligncenter custom-width" /></figure></div>
<ol class="abc-list"><li><div class="list-item-content"><span class="list-item-text">Estimate</span></div><ol class="i-list"><li><div class="list-item-content"><span class="list-item-text">the median mark,</span></div></li><li><div class="list-item-content"><span class="list-item-text">the interquartile range,</span></div></li><li><div class="list-item-content"><span class="list-item-text">the \(80^{\text{th}}\) percentile.</span></div></li></ol></li><li><div class="list-item-paragraph">The box-and-whisker diagram below represents the result for Paper 2.</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/1767945567740-72oa6ecltow.png?token=eyJraWQiOiJiZTM3ZjNhZS05OWM4LTQ5ZGQtYjRiNS1iMTBhYmJhNjY5MWYiLCJhbGciOiJIUzI1NiJ9.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvcGFzdGVkLzE3Njc5NDU1Njc3NDAtNzJvYTZlY2x0b3cucG5nIiwic2NvcGUiOiJkb3dubG9hZCIsImlhdCI6MTc5MjY5NTczMSwiZXhwIjoxNzkyNjk2MDMxfQ.nsDujokMs4N7kMKsu-0A6Se1AGPFTyR7mzwpsixdQpQ" alt="List item image" class="aligncenter custom-width" style="max-width: min(350px, 100%); height: auto;" /></div><div class="list-item-paragraph">State, with a reason, which you think was the more difficult paper.</div></li></ol>

Eighty students took a Mathematics examination which consisted of two papers.

Each paper was marked out of 100. The diagram below shows the cumulative frequency curve for Paper 1.

Visualizing Data Spread and Central Tendency

<p>The Mathematics Test results obtained by \(11\) students are as follows:</p>
<p style="text-align: center">\(52, 36, 67, 66, 37, 46, 70, 55, 50, 60, 61\)</p>
<p>A box-and-whisker plot is drawn to represent the data.</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/1767945085451-x0x93gdsbbd.png?token=eyJraWQiOiJiZTM3ZjNhZS05OWM4LTQ5ZGQtYjRiNS1iMTBhYmJhNjY5MWYiLCJhbGciOiJIUzI1NiJ9.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvcGFzdGVkLzE3Njc5NDUwODU0NTEteDB4OTNnZHNiYmQucG5nIiwic2NvcGUiOiJkb3dubG9hZCIsImlhdCI6MTc5MjY5NTczMSwiZXhwIjoxNzkyNjk2MDMxfQ.orsRzdLMmW-FJg11hNUTt6G8FknrG5ZnbS2v6wgXgJ0" style="max-width: min(400px, 100%); height: auto; display: block;" alt="Box-and-whisker plot of Mathematics Test results" class="aligncenter custom-width" /></figure></div>
<p>State the values of \(x\), \(y\) and \(z\).</p>

The Mathematics Test results obtained by \(11\) students are as follows:

\(52, 36, 67, 66, 37, 46, 70, 55, 50, 60, 61\)

A box-and-whisker plot is drawn to represent the data.

State the values of \(x\), \(y\) and \(z\).

Math Question Bank