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PSLE

PSLE Foundation Mathematics

<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.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvcGFzdGVkLzE3NjkzMzExMzcxMjAtb3VidHdhYTRkbGYucG5nIiwic2NvcGUiOiJkb3dubG9hZCIsImlhdCI6MTc5MjY5NTk1MywiZXhwIjoxNzkyNjk2MjUzfQ.lN_ZAXHXrzxLWuoVQ772lia6qSbiCwbSpfLmsbwRvsc" 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.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvcGFzdGVkLzE3NjkzMzEyMjM0NDYtbWFiMmd1a2NodTgucG5nIiwic2NvcGUiOiJkb3dubG9hZCIsImlhdCI6MTc5MjY5NTk1MywiZXhwIjoxNzkyNjk2MjUzfQ.KZWNzQN-VqvGT7shbhTWT-U5WdOW0dsOC4U2112jPWU" 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

Box-and-Whisker Plots

Effects of Changing Data on Statistical Measures

Cumulative Frequency Table and Curve

Mean and Standard Deviation for Grouped Data

Statistics

<p>A teacher recorded the individual time taken by $200$ students to complete a cross-country race. The results are presented in the form of a cumulative frequency curve.</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/1769330452944-u09rnsjaqz.png?token=eyJraWQiOiJiZTM3ZjNhZS05OWM4LTQ5ZGQtYjRiNS1iMTBhYmJhNjY5MWYiLCJhbGciOiJIUzI1NiJ9.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvcGFzdGVkLzE3NjkzMzA0NTI5NDQtdTA5cm5zamFxei5wbmciLCJzY29wZSI6ImRvd25sb2FkIiwiaWF0IjoxNzkyNjk1OTUzLCJleHAiOjE3OTI2OTYyNTN9.I69gieEgqMrYsYz_XVvqeztBwbsS6h9GvPPwoEC9rP4" style="max-width: min(400px, 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">Use the curve to estimate</span></div><ol class="i-list"><li><div class="list-item-content"><span class="list-item-text">the median time taken to run the race,</span><span class="inline-marks">[1]</span></div></li><li><div class="list-item-content"><span class="list-item-text">the interquartile range of the distribution,</span><span class="inline-marks">[2]</span></div></li><li><div class="list-item-content"><span class="list-item-text">the percentage of students who took longer than $66$ min to finish the race,</span><span class="inline-marks">[2]</span></div></li><li><div class="list-item-content"><span class="list-item-text">the probability of choosing a student who took $45$ min or less time to finish the race.</span><span class="inline-marks">[2]</span></div></li></ol></li><li><div class="list-item-content"><span class="list-item-text">The frequency table relates to the same cross-country race results.</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">Frequency</th><th style="height: 23px; min-height: 23px; text-align: center; --cell-justify: center">Time ($t$ min)</th></tr></thead><tbody><tr style="height: 23px;"><td style="height: 23px; min-height: 23px; text-align: center; --cell-justify: center">$13$</td><td style="height: 23px; min-height: 23px; text-align: center; --cell-justify: center">$30 &lt; t \le 40$</td></tr><tr style="height: 23px;"><td style="height: 23px; min-height: 23px; text-align: center; --cell-justify: center">$r$</td><td style="height: 23px; min-height: 23px; text-align: center; --cell-justify: center">$40 &lt; t \le 50$</td></tr><tr style="height: 23px;"><td style="height: 23px; min-height: 23px; text-align: center; --cell-justify: center">$90$</td><td style="height: 23px; min-height: 23px; text-align: center; --cell-justify: center">$50 &lt; t \le 60$</td></tr><tr style="height: 23px;"><td style="height: 23px; min-height: 23px; text-align: center; --cell-justify: center">$s$</td><td style="height: 23px; min-height: 23px; text-align: center; --cell-justify: center">$60 &lt; t \le 70$</td></tr><tr style="height: 23px;"><td style="height: 23px; min-height: 23px; text-align: center; --cell-justify: center">$9$</td><td style="height: 23px; min-height: 23px; text-align: center; --cell-justify: center">$70 &lt; t \le 80$</td></tr><tr style="height: 23px;"><td style="height: 23px; min-height: 23px; text-align: center; --cell-justify: center">$4$</td><td style="height: 23px; min-height: 23px; text-align: center; --cell-justify: center">$80 &lt; t \le 90$</td></tr></tbody></table></div></div>
<ol class="i-list"><li><div class="list-item-content"><span class="list-item-text">Find the value of $r$ and the value of $s$.</span><span class="inline-marks">[2]</span></div></li><li><div class="list-item-content"><span class="list-item-text">Showing your method clearly, estimate the mean time required to run the race.</span><span class="inline-marks">[3]</span></div></li><li><div class="list-item-content"><span class="list-item-text">Estimate the standard deviation of the distribution.</span><span class="inline-marks">[2]</span></div></li></ol>

A teacher recorded the individual time taken by $200$ students to complete a cross-country race. The results are presented in the form of a cumulative frequency curve.

The frequency table relates to the same cross-country race results.

Find the value of $r$ and the value of $s$.

Showing your method clearly, estimate the mean time required to run the race.

Estimate the standard deviation of the distribution.

Probability of a Single Event

Probability

<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.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvcGFzdGVkLzE3Njc5NDc0MjAwMDQtOWdtY2JuMmp1bC5wbmciLCJzY29wZSI6ImRvd25sb2FkIiwiaWF0IjoxNzkyNjk1OTUzLCJleHAiOjE3OTI2OTYyNTN9.K3cbtgJ9YgtRfUwdWW8o7vrDzs5KAGXqFDhtJaUVtrs" 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.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvcGFzdGVkLzE3Njc5NDc2NzUxODQtNzJ4cGt2aDRlMHkucG5nIiwic2NvcGUiOiJkb3dubG9hZCIsImlhdCI6MTc5MjY5NTk1MywiZXhwIjoxNzkyNjk2MjUzfQ.rbUbgtS7l5Oj8D-AnouMzqPtS4rlnydfaeNpO3LGXzI" 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.

Comparing Distributions Using Centre and Spread

From Raw Test Scores to Box-and-Whisker Visualizations

<p>The cumulative frequency curve shows the marks obtained by $250$ pupils in school $X$ in a particular examination. The maximum mark is $80$.</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/1767937951531-5z3aqm29xgk.png?token=eyJraWQiOiJiZTM3ZjNhZS05OWM4LTQ5ZGQtYjRiNS1iMTBhYmJhNjY5MWYiLCJhbGciOiJIUzI1NiJ9.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvcGFzdGVkLzE3Njc5Mzc5NTE1MzEtNXozYXFtMjl4Z2sucG5nIiwic2NvcGUiOiJkb3dubG9hZCIsImlhdCI6MTc5MjY5NTk1MywiZXhwIjoxNzkyNjk2MjUzfQ.DEhAYhkmNs7GauF_4pMMefonAoALNMp6Ruh_Su0rtAE" style="max-width: min(500px, 100%); height: auto; display: block;" alt="Cumulative frequency curve of marks obtained by pupils" class="aligncenter custom-width" /></figure></div>
<ol class="abc-list"><li><div class="list-item-content"><span class="list-item-text">If $\frac{3}{5}$ of the pupils passed the examination, what is the passing mark?</span></div></li><li><div class="list-item-content"><span class="list-item-text">The cumulative frequency curve can be represented in the following frequency table.</span></div></li></ol>
<div class="content-block content-block--table"><div class="table-container"><table><thead><tr><th style="text-align: center; --cell-justify: center">Marks obtained by pupils, $x$</th><th style="text-align: center; --cell-justify: center">No. of pupils</th></tr></thead><tbody><tr><td style="text-align: center; --cell-justify: center">$0 \le x &lt; 20$</td><td style="text-align: center; --cell-justify: center">$30$</td></tr><tr><td style="text-align: center; --cell-justify: center">$20 \le x &lt; 40$</td><td style="text-align: center; --cell-justify: center">$p$</td></tr><tr><td style="text-align: center; --cell-justify: center">$40 \le x &lt; 60$</td><td style="text-align: center; --cell-justify: center">$q$</td></tr><tr><td style="text-align: center; --cell-justify: center">$60 \le x &lt; 80$</td><td style="text-align: center; --cell-justify: center">$20$</td></tr></tbody></table></div></div>
<p>Find the value of $p$ and of $q$.</p>

The cumulative frequency curve shows the marks obtained by $250$ pupils in school $X$ in a particular examination. The maximum mark is $80$.

If $\frac{3}{5}$ of the pupils passed the examination, what is the passing mark?

The cumulative frequency curve can be represented in the following frequency table.

Statistical Analysis of Examination Performance

<p>The table shows the average time taken to travel to school daily by a group of students.</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">Time taken ($t$ min)</th><th style="height: 43px; min-height: 43px; text-align: center; --cell-justify: center">Number of students</th></tr></thead><tbody><tr style="height: 43px;"><td style="height: 43px; min-height: 43px; text-align: center; --cell-justify: center">$10 &lt; t \le 20$</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">$20 &lt; t \le 30$</td><td style="height: 43px; min-height: 43px; text-align: center; --cell-justify: center">$16$</td></tr><tr style="height: 43px;"><td style="height: 43px; min-height: 43px; text-align: center; --cell-justify: center">$30 &lt; t \le 40$</td><td style="height: 43px; min-height: 43px; text-align: center; --cell-justify: center">$8$</td></tr><tr style="height: 43px;"><td style="height: 43px; min-height: 43px; text-align: center; --cell-justify: center">$40 &lt; t \le 50$</td><td style="height: 43px; min-height: 43px; text-align: center; --cell-justify: center">$X$</td></tr><tr style="height: 43px;"><td style="height: 43px; min-height: 43px; text-align: center; --cell-justify: center">$50 &lt; t \le 60$</td><td style="height: 43px; min-height: 43px; text-align: center; --cell-justify: center">$3$</td></tr><tr style="height: 43px;"><td style="height: 43px; min-height: 43px; text-align: center; --cell-justify: center">$60 &lt; t \le 70$</td><td style="height: 43px; min-height: 43px; text-align: center; --cell-justify: center">$2$</td></tr></tbody></table></div></div>
<p>Find</p>
<ol class="abc-list"><li><div class="list-item-content"><span class="list-item-text">the values of $X$, $Y$ and $Z$ if the cumulative frequency table is given as follow.</span></div></li></ol>
<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">Time ($t$ min)</th><th style="height: 43px; min-height: 43px; text-align: center; --cell-justify: center">Number of students</th></tr></thead><tbody><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">$22$</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">$Y$</td></tr><tr style="height: 43px;"><td style="height: 43px; min-height: 43px; text-align: center; --cell-justify: center">$\le 40$</td><td style="height: 43px; min-height: 43px; text-align: center; --cell-justify: center">$46$</td></tr><tr style="height: 43px;"><td style="height: 43px; min-height: 43px; text-align: center; --cell-justify: center">$\le 50$</td><td style="height: 43px; min-height: 43px; text-align: center; --cell-justify: center">$55$</td></tr><tr style="height: 43px;"><td style="height: 43px; min-height: 43px; text-align: center; --cell-justify: center">$\le 60$</td><td style="height: 43px; min-height: 43px; text-align: center; --cell-justify: center">$58$</td></tr><tr style="height: 43px;"><td style="height: 43px; min-height: 43px; text-align: center; --cell-justify: center">$\le 70$</td><td style="height: 43px; min-height: 43px; text-align: center; --cell-justify: center">$Z$</td></tr></tbody></table></div></div>
<ol class="abc-list" start="2"><li><div class="list-item-content"><span class="list-item-text">the number of students who took more than $40$ minutes to travel to school daily.</span></div></li></ol>

The table shows the average time taken to travel to school daily by a group of students.

the values of $X$, $Y$ and $Z$ if the cumulative frequency table is given as follow.

the number of students who took more than $40$ minutes to travel to school daily.

Statistical Data Analysis: School Commute Times

<p>The cumulative frequency graph represents the heights of a sample of $200$ children from a primary school.</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/1767937213219-vj5tvedoy2.png?token=eyJraWQiOiJiZTM3ZjNhZS05OWM4LTQ5ZGQtYjRiNS1iMTBhYmJhNjY5MWYiLCJhbGciOiJIUzI1NiJ9.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvcGFzdGVkLzE3Njc5MzcyMTMyMTktdmo1dHZlZG95Mi5wbmciLCJzY29wZSI6ImRvd25sb2FkIiwiaWF0IjoxNzkyNjk1OTUzLCJleHAiOjE3OTI2OTYyNTN9.LiocNQh7-EipaPBIqLZebZkcUHZ7oQIQ5o-UdnOAbjc" style="max-width: min(500px, 100%); height: auto; display: block;" class="aligncenter custom-width" /></figure></div>
<p>Copy and complete the grouped frequency table below of the height of the students.</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">Height ($x$) cm</th><th style="height: 43px; min-height: 43px; text-align: center; --cell-justify: center">Number of students</th></tr></thead><tbody><tr style="height: 43px;"><td style="height: 43px; min-height: 43px; text-align: center; --cell-justify: center">$0 &lt; x \le 100$</td><td style="height: 43px; min-height: 43px; text-align: center; --cell-justify: center">$0$</td></tr><tr style="height: 43px;"><td style="height: 43px; min-height: 43px; text-align: center; --cell-justify: center">$100 &lt; x \le 110$</td><td style="height: 43px; min-height: 43px; text-align: center; --cell-justify: center"> </td></tr><tr style="height: 43px;"><td style="height: 43px; min-height: 43px; text-align: center; --cell-justify: center">$110 &lt; x \le 120$</td><td style="height: 43px; min-height: 43px; text-align: center; --cell-justify: center"> </td></tr><tr style="height: 43px;"><td style="height: 43px; min-height: 43px; text-align: center; --cell-justify: center">$120 &lt; x \le 130$</td><td style="height: 43px; min-height: 43px; text-align: center; --cell-justify: center"> </td></tr><tr style="height: 43px;"><td style="height: 43px; min-height: 43px; text-align: center; --cell-justify: center">$130 &lt; x \le 140$</td><td style="height: 43px; min-height: 43px; text-align: center; --cell-justify: center"> </td></tr><tr style="height: 43px;"><td style="height: 43px; min-height: 43px; text-align: center; --cell-justify: center">$140 &lt; x \le 150$</td><td style="height: 43px; min-height: 43px; text-align: center; --cell-justify: center"> </td></tr></tbody></table></div></div>

The cumulative frequency graph represents the heights of a sample of $200$ children from a primary school.

Copy and complete the grouped frequency table below of the height of the students.

Statistical Data Analysis: Heights of Primary Students

<p>The table below shows a grouped data of donations collected by $35$ students.</p>
<div class="content-block content-block--table"><div class="table-container"><table style="table-layout: fixed; width: 595px;"><colgroup><col style="width: 85px;"><col style="width: 85px;"><col style="width: 85px;"><col style="width: 85px;"><col style="width: 85px;"><col style="width: 85px;"><col style="width: 85px;"></colgroup><thead><tr style="height: 43px;"><th style="height: 43px; min-height: 43px; text-align: center; --cell-justify: center"><p>Donations </p><p>($\$x$)</p></th><th style="height: 43px; min-height: 43px; text-align: center; --cell-justify: center">$0 &lt; x \le 5$</th><th style="height: 43px; min-height: 43px; text-align: center; --cell-justify: center">$5 &lt; x \le 10$</th><th style="height: 43px; min-height: 43px; text-align: center; --cell-justify: center">$10 &lt; x \le 15$</th><th style="height: 43px; min-height: 43px; text-align: center; --cell-justify: center">$15 &lt; x \le 20$</th><th style="height: 43px; min-height: 43px; text-align: center; --cell-justify: center">$20 &lt; x \le 25$</th><th style="height: 43px; min-height: 43px; text-align: center; --cell-justify: center">$25 &lt; x \le 30$</th></tr></thead><tbody><tr style="height: 43px;"><td style="height: 43px; min-height: 43px; text-align: center; --cell-justify: center">Frequency</td><td style="height: 43px; min-height: 43px; text-align: center; --cell-justify: center">$2$</td><td style="height: 43px; min-height: 43px; text-align: center; --cell-justify: center">$2$</td><td style="height: 43px; min-height: 43px; text-align: center; --cell-justify: center">$6$</td><td style="height: 43px; min-height: 43px; text-align: center; --cell-justify: center">$6$</td><td style="height: 43px; min-height: 43px; text-align: center; --cell-justify: center">$15$</td><td style="height: 43px; min-height: 43px; text-align: center; --cell-justify: center">$a$</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 value of $a$.</span></div></li><li data-list-item-id="item-b" data-list-item-path="item-b"><div class="list-item-content"><span class="list-item-text">Using the information given above, copy and complete the following cumulative frequency table.</span></div></li></ol>
<div class="content-block content-block--table"><div class="table-container"><table style="table-layout: fixed; width: 595px;"><colgroup><col style="width: 85px;"><col style="width: 85px;"><col style="width: 85px;"><col style="width: 85px;"><col style="width: 85px;"><col style="width: 85px;"><col style="width: 85px;"></colgroup><thead><tr style="height: 43px;"><th style="height: 43px; min-height: 43px; text-align: center; --cell-justify: center"><p>Donations </p><p>($\$x$ or less)</p></th><th style="height: 43px; min-height: 43px; text-align: center; --cell-justify: center">$x \le 5$</th><th style="height: 43px; min-height: 43px; text-align: center; --cell-justify: center">$x \le 10$</th><th style="height: 43px; min-height: 43px; text-align: center; --cell-justify: center">$x \le 15$</th><th style="height: 43px; min-height: 43px; text-align: center; --cell-justify: center">$x \le 20$</th><th style="height: 43px; min-height: 43px; text-align: center; --cell-justify: center">$x \le 25$</th><th style="height: 43px; min-height: 43px; text-align: center; --cell-justify: center">$x \le 30$</th></tr></thead><tbody><tr style="height: 43px;"><td style="height: 43px; min-height: 43px; text-align: center; --cell-justify: center">Frequency</td><td style="height: 43px; min-height: 43px; text-align: center; --cell-justify: center"> </td><td style="height: 43px; min-height: 43px; text-align: center; --cell-justify: center"> </td><td style="height: 43px; min-height: 43px; text-align: center; --cell-justify: center"> </td><td style="height: 43px; min-height: 43px; text-align: center; --cell-justify: center"> </td><td style="height: 43px; min-height: 43px; text-align: center; --cell-justify: center"> </td><td style="height: 43px; min-height: 43px; text-align: center; --cell-justify: center"> </td></tr></tbody></table></div></div>
<ol class="abc-list" start="3"><li data-list-item-id="item-c" data-list-item-path="item-c"><div class="list-item-content"><span class="list-item-text">Calculate the number of students who collected $\$15$ or less.</span></div></li><li data-list-item-id="item-d" data-list-item-path="item-d"><div class="list-item-content"><span class="list-item-text">Calculate the number of students who collected more than $\$20$.</span></div></li></ol>

The table below shows a grouped data of donations collected by $35$ students.

Using the information given above, copy and complete the following cumulative frequency table.

<p>Donations </p><p>($\$x$ or less)</p>

Calculate the number of students who collected $\$15$ or less.

Calculate the number of students who collected more than $\$20$.

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