<p>The stem-and-leaf diagram shows the distribution of the ages of the contestants in a cycling race, The median and range of the distribution are 33 years and 20 years respectively.</p>
<ol class="abc-list"><li><div class="list-item-paragraph">Find the value of x and of y,  given that x \(\geq\) 0 and y \(\geq\) 0.</div></li><li><div class="list-item-paragraph">Write down the modal age of the distribution.</div></li><li><div class="list-item-paragraph">Find the interquartile range of this distribution.</div></li></ol>
<div class="content-block content-block--table"><div class="table-container"><table><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;"></colgroup><thead><tr style="height: 43px;"><th style="height: 43px; min-height: 43px; text-align: center; --cell-justify: center"><p>2</p></th><th style="height: 43px; min-height: 43px; text-align: center; --cell-justify: center"><p>1</p></th><th style="height: 43px; min-height: 43px; text-align: center; --cell-justify: center"><p>3</p></th><th style="height: 43px; min-height: 43px; text-align: left; --cell-justify: flex-start"></th><th style="height: 43px; min-height: 43px; text-align: left; --cell-justify: flex-start"></th><th style="height: 43px; min-height: 43px; text-align: left; --cell-justify: flex-start"></th><th style="height: 43px; min-height: 43px; text-align: left; --cell-justify: flex-start"></th></tr></thead><tbody><tr style="height: 43px;"><td style="height: 43px; min-height: 43px; text-align: center; --cell-justify: center"><p>2</p></td><td style="height: 43px; min-height: 43px; text-align: center; --cell-justify: center"><p>5</p></td><td style="height: 43px; min-height: 43px; text-align: center; --cell-justify: center"><p>5</p></td><td style="height: 43px; min-height: 43px; text-align: center; --cell-justify: center"><p>7</p></td><td style="height: 43px; min-height: 43px; text-align: center; --cell-justify: center"><p>8</p></td><td style="height: 43px; min-height: 43px; text-align: left; --cell-justify: flex-start"></td><td style="height: 43px; min-height: 43px; text-align: left; --cell-justify: flex-start"></td></tr><tr style="height: 43px;"><td style="height: 43px; min-height: 43px; text-align: center; --cell-justify: center"><p>3</p></td><td style="height: 43px; min-height: 43px; text-align: center; --cell-justify: center"><p>0</p></td><td style="height: 43px; min-height: 43px; text-align: center; --cell-justify: center"><p>\(x\)</p></td><td style="height: 43px; min-height: 43px; text-align: center; --cell-justify: center"><p>4</p></td><td style="height: 43px; min-height: 43px; text-align: center; --cell-justify: center"><p>4</p></td><td style="height: 43px; min-height: 43px; text-align: left; --cell-justify: flex-start"></td><td style="height: 43px; min-height: 43px; text-align: left; --cell-justify: flex-start"></td></tr><tr style="height: 43px;"><td style="height: 43px; min-height: 43px; text-align: center; --cell-justify: center"><p>3</p></td><td style="height: 43px; min-height: 43px; text-align: center; --cell-justify: center"><p>5</p></td><td style="height: 43px; min-height: 43px; text-align: center; --cell-justify: center"><p>5</p></td><td style="height: 43px; min-height: 43px; text-align: center; --cell-justify: center"><p>9</p></td><td style="height: 43px; min-height: 43px; text-align: center; --cell-justify: center"><p>9</p></td><td style="height: 43px; min-height: 43px; text-align: center; --cell-justify: center"><p>9</p></td><td style="height: 43px; min-height: 43px; text-align: left; --cell-justify: flex-start"></td></tr><tr style="height: 43px;"><td style="height: 43px; min-height: 43px; text-align: center; --cell-justify: center"><p>4</p></td><td style="height: 43px; min-height: 43px; text-align: center; --cell-justify: center"><p>\(y\)</p></td><td style="height: 43px; min-height: 43px; text-align: left; --cell-justify: flex-start"></td><td style="height: 43px; min-height: 43px; text-align: left; --cell-justify: flex-start"></td><td style="height: 43px; min-height: 43px; text-align: left; --cell-justify: flex-start"></td><td style="height: 43px; min-height: 43px; text-align: left; --cell-justify: flex-start"></td><td style="height: 43px; min-height: 43px; text-align: left; --cell-justify: flex-start"></td></tr></tbody></table></div></div>

The stem-and-leaf diagram shows the distribution of the ages of the contestants in a cycling race, The median and range of the distribution are 33 years and 20 years respectively.

Find the value of x and of y,  given that x \(\geq\) 0 and y \(\geq\) 0.

Write down the modal age of the distribution.

Find the interquartile range of this distribution.

Statistics - Median, Quartiles, Range and Interquartile Range

Question 62c582da