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<h1 class="title">Topic 10: Introduction to Inference Lab</h1>
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<div class="sourceCode cell-code hidden" id="cb1" data-startfrom="44" data-source-offset="0"><pre class="sourceCode js code-with-copy"><code class="sourceCode javascript" style="counter-reset: source-line 43;"><span id="cb1-44"><a href="#cb1-44" aria-hidden="true" tabindex="-1"></a><span class="kw">function</span> <span class="fu">ok_checkbox</span>(response<span class="op">,</span> n) {</span>
<span id="cb1-45"><a href="#cb1-45" aria-hidden="true" tabindex="-1"></a> <span class="cf">if</span> (<span class="op">!</span>response <span class="op">||</span> response<span class="op">.</span><span class="at">length</span> <span class="op">===</span> <span class="dv">0</span>) </span>
<span id="cb1-46"><a href="#cb1-46" aria-hidden="true" tabindex="-1"></a> <span class="cf">return</span> <span class="fu">html</span><span class="vs">`<span style="color:purple">You haven't answered yet.</span>`</span><span class="op">;</span></span>
<span id="cb1-47"><a href="#cb1-47" aria-hidden="true" tabindex="-1"></a> <span class="cf">if</span> (response<span class="op">.</span><span class="fu">toString</span>() <span class="op">===</span> n) </span>
<span id="cb1-48"><a href="#cb1-48" aria-hidden="true" tabindex="-1"></a> <span class="cf">return</span> <span class="fu">html</span><span class="vs">`<span style="color:green">Correct ✓</span>`</span><span class="op">;</span></span>
<span id="cb1-49"><a href="#cb1-49" aria-hidden="true" tabindex="-1"></a> <span class="cf">return</span> <span class="fu">html</span><span class="vs">`<span style="color:red">Not Yet! ✗</span>`</span><span class="op">;</span></span>
<span id="cb1-50"><a href="#cb1-50" aria-hidden="true" tabindex="-1"></a>}</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
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<p>In this lab, we investigate the ways in which statistics from a random sample can serve as point estimates for population parameters. We dig deeper into the Central Limit Theorem, explore connections between sample size and uncertainty, and introduce the notion of the confidence interval.</p>
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<div class="sourceCode cell-code hidden" id="cb2" data-startfrom="131" data-source-offset="0"><pre class="sourceCode js code-with-copy"><code class="sourceCode javascript" style="counter-reset: source-line 130;"><span id="cb2-131"><a href="#cb2-131" aria-hidden="true" tabindex="-1"></a>{</span>
<span id="cb2-132"><a href="#cb2-132" aria-hidden="true" tabindex="-1"></a> <span class="kw">const</span> btn <span class="op">=</span> <span class="fu">html</span><span class="vs">`<button style="</span></span>
<span id="cb2-133"><a href="#cb2-133" aria-hidden="true" tabindex="-1"></a><span class="vs"> background: #436b95;</span></span>
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<span id="cb2-140"><a href="#cb2-140" aria-hidden="true" tabindex="-1"></a><span class="vs"> ">🔄 Reset My Responses</button>`</span><span class="op">;</span></span>
<span id="cb2-141"><a href="#cb2-141" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb2-142"><a href="#cb2-142" aria-hidden="true" tabindex="-1"></a> btn<span class="op">.</span><span class="at">onclick</span> <span class="op">=</span> () <span class="kw">=></span> {</span>
<span id="cb2-143"><a href="#cb2-143" aria-hidden="true" tabindex="-1"></a> <span class="cf">if</span> (<span class="fu">confirm</span>(<span class="st">'Reset all responses for this activity? This cannot be undone.'</span>)) {</span>
<span id="cb2-144"><a href="#cb2-144" aria-hidden="true" tabindex="-1"></a> <span class="bu">Object</span><span class="op">.</span><span class="fu">keys</span>(localStorage)</span>
<span id="cb2-145"><a href="#cb2-145" aria-hidden="true" tabindex="-1"></a> <span class="op">.</span><span class="fu">filter</span>(k <span class="kw">=></span> k<span class="op">.</span><span class="fu">endsWith</span>(<span class="st">'_selected_t10'</span>) <span class="op">||</span> k<span class="op">.</span><span class="fu">endsWith</span>(<span class="st">'_correct_t10'</span>) <span class="op">||</span> k<span class="op">.</span><span class="fu">endsWith</span>(<span class="st">'_result_t10'</span>))</span>
<span id="cb2-146"><a href="#cb2-146" aria-hidden="true" tabindex="-1"></a> <span class="op">.</span><span class="fu">forEach</span>(k <span class="kw">=></span> localStorage<span class="op">.</span><span class="fu">removeItem</span>(k))<span class="op">;</span></span>
<span id="cb2-147"><a href="#cb2-147" aria-hidden="true" tabindex="-1"></a> location<span class="op">.</span><span class="fu">reload</span>()<span class="op">;</span></span>
<span id="cb2-148"><a href="#cb2-148" aria-hidden="true" tabindex="-1"></a> }</span>
<span id="cb2-149"><a href="#cb2-149" aria-hidden="true" tabindex="-1"></a> }<span class="op">;</span></span>
<span id="cb2-150"><a href="#cb2-150" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb2-151"><a href="#cb2-151" aria-hidden="true" tabindex="-1"></a> <span class="cf">return</span> btn<span class="op">;</span></span>
<span id="cb2-152"><a href="#cb2-152" aria-hidden="true" tabindex="-1"></a>}</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
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<p><em>Note.</em> The button above resets multiple choice and checkbox questions. Currently, resetting code cells must be done manually via hitting the <em>Start Over</em> button on each individual interactive cell.</p>
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<p>This is a derivative of a product of OpenIntro that is released under a <a href="http://creativecommons.org/licenses/by-sa/3.0">Creative Commons Attribution-ShareAlike 3.0 Unported</a> license. This lab was adapted for OpenIntro by Andrew Bray and Mine Çetinkaya-Rundel from a lab written by Mark Hansen of UCLA Statistics.</p>
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<section id="intro-to-inference-lab" class="level2">
<h2 class="anchored" data-anchor-id="intro-to-inference-lab">Intro to Inference Lab</h2>
<p>In this activity, we investigate the ways in which statistics from a random sample of data can serve as point estimates for population parameters. This activity builds off of the content from Topic 9, where we were exposed to the <em>sampling distribution</em> and the <em>Central Limit Theorem</em>. Here we will work to become more familiar with these two ideas and how we can use the sampling distribution to make claims about population-level data.</p>
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<section id="the-data" class="level2">
<h2 class="anchored" data-anchor-id="the-data">The Data</h2>
<p>We consider real estate data from the city of Ames, Iowa. The details of every real estate transaction in Ames is recorded by the City Assessor’s office. Our particular focus for this lab will be a dataset containing all residential home sales in Ames between 2006 and 2010. This collection represents our <em>population</em> of interest. While we typically don’t have access to population-level data, this will allow us to see the Central Limit Theorem in action and to measure how close our estimates come to the corresponding true population mean.</p>
<p>In this lab we investigate what we can learn about the full population of these home sales through random sampling. We’ll see how well our small samples can be used to estimate a population parameter. The data has been loaded for you and is stored in a variable called <code>ames</code>.</p>
<p>Use the code block below to answer some basic questions about the <code>ames</code> dataset.</p>
<div class="cell" data-exercise="explore-ames" data-caption="Ungraded, Exploratory Only">
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<div class="hint webr-ojs-exercise exercise-hint d-none" data-exercise="explore-ames">
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<p>You can call a data frame by name to print it out. You can also use functions like <code>head()</code>, <code>dim()</code>, and <code>glimpse()</code> to gain information as well.</p>
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Check Your Understanding: The <code>ames</code> Dataset I
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<p>What does each observation in the <code>ames</code> dataset represent?</p>
<div class="cell">
<div class="sourceCode cell-code hidden" id="cb3" data-startfrom="204" data-source-offset="-1"><pre class="sourceCode js code-with-copy"><code class="sourceCode javascript" style="counter-reset: source-line 203;"><span id="cb3-204"><a href="#cb3-204" aria-hidden="true" tabindex="-1"></a>mutable ok_response <span class="op">=</span> (response<span class="op">,</span> n) <span class="kw">=></span> { <span class="cf">return</span> <span class="fu">html</span><span class="vs">`Loading...`</span> }<span class="op">;</span></span>
<span id="cb3-205"><a href="#cb3-205" aria-hidden="true" tabindex="-1"></a>viewof q1 <span class="op">=</span> Inputs<span class="op">.</span><span class="fu">radio</span>(</span>
<span id="cb3-206"><a href="#cb3-206" aria-hidden="true" tabindex="-1"></a> <span class="kw">new</span> <span class="bu">Map</span>([</span>
<span id="cb3-207"><a href="#cb3-207" aria-hidden="true" tabindex="-1"></a> [<span class="st">"The sale of a home in Ames, Iowa during the time period 2006 to 2010."</span><span class="op">,</span> <span class="dv">1</span>]<span class="op">,</span></span>
<span id="cb3-208"><a href="#cb3-208" aria-hidden="true" tabindex="-1"></a> [<span class="st">"A house in Ames, Iowa."</span><span class="op">,</span> <span class="dv">2</span>]<span class="op">,</span></span>
<span id="cb3-209"><a href="#cb3-209" aria-hidden="true" tabindex="-1"></a> [<span class="st">"A person."</span><span class="op">,</span> <span class="dv">3</span>]<span class="op">,</span></span>
<span id="cb3-210"><a href="#cb3-210" aria-hidden="true" tabindex="-1"></a> [<span class="st">"A house listed for sale in Ames, Iowa."</span><span class="op">,</span> <span class="dv">4</span>]</span>
<span id="cb3-211"><a href="#cb3-211" aria-hidden="true" tabindex="-1"></a> ])<span class="op">,</span></span>
<span id="cb3-212"><a href="#cb3-212" aria-hidden="true" tabindex="-1"></a> {<span class="dt">value</span><span class="op">:</span> <span class="bu">JSON</span><span class="op">.</span><span class="fu">parse</span>(localStorage<span class="op">.</span><span class="fu">getItem</span>(<span class="st">"q1_selected_t10"</span>) <span class="op">??</span> <span class="st">"null"</span>)}</span>
<span id="cb3-213"><a href="#cb3-213" aria-hidden="true" tabindex="-1"></a>)<span class="op">;</span></span>
<span id="cb3-214"><a href="#cb3-214" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb3-215"><a href="#cb3-215" aria-hidden="true" tabindex="-1"></a>{</span>
<span id="cb3-216"><a href="#cb3-216" aria-hidden="true" tabindex="-1"></a> localStorage<span class="op">.</span><span class="fu">setItem</span>(<span class="st">"q1_selected_t10"</span><span class="op">,</span> <span class="bu">JSON</span><span class="op">.</span><span class="fu">stringify</span>(q1))<span class="op">;</span></span>
<span id="cb3-217"><a href="#cb3-217" aria-hidden="true" tabindex="-1"></a> localStorage<span class="op">.</span><span class="fu">setItem</span>(<span class="st">"q1_correct_t10"</span><span class="op">,</span> <span class="st">"1"</span>)<span class="op">;</span></span>
<span id="cb3-218"><a href="#cb3-218" aria-hidden="true" tabindex="-1"></a> localStorage<span class="op">.</span><span class="fu">setItem</span>(<span class="st">"q1_result_t10"</span><span class="op">,</span> q1 <span class="op">===</span> <span class="kw">null</span> <span class="op">?</span> <span class="st">"unattempted"</span> <span class="op">:</span> (q1 <span class="op">==</span> <span class="dv">1</span> <span class="op">?</span> <span class="st">"correct"</span> <span class="op">:</span> <span class="st">"incorrect"</span>))<span class="op">;</span></span>
<span id="cb3-219"><a href="#cb3-219" aria-hidden="true" tabindex="-1"></a>}</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
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<div class="sourceCode cell-code hidden" id="cb4" data-startfrom="220" data-source-offset="-601"><pre class="sourceCode js code-with-copy"><code class="sourceCode javascript" style="counter-reset: source-line 219;"><span id="cb4-220"><a href="#cb4-220" aria-hidden="true" tabindex="-1"></a><span class="fu">ok_response</span>(q1<span class="op">,</span> <span class="st">"1"</span>)<span class="op">;</span></span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
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Check Your Understanding: The <code>ames</code> Dataset II
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<p>How many observations are there in the <code>ames</code> dataset?</p>
<div class="cell">
<div class="sourceCode cell-code hidden" id="cb5" data-startfrom="233" data-source-offset="-1"><pre class="sourceCode js code-with-copy"><code class="sourceCode javascript" style="counter-reset: source-line 232;"><span id="cb5-233"><a href="#cb5-233" aria-hidden="true" tabindex="-1"></a>viewof q2 <span class="op">=</span> Inputs<span class="op">.</span><span class="fu">radio</span>(</span>
<span id="cb5-234"><a href="#cb5-234" aria-hidden="true" tabindex="-1"></a> <span class="kw">new</span> <span class="bu">Map</span>([</span>
<span id="cb5-235"><a href="#cb5-235" aria-hidden="true" tabindex="-1"></a> [<span class="st">"1"</span><span class="op">,</span> <span class="dv">1</span>]<span class="op">,</span></span>
<span id="cb5-236"><a href="#cb5-236" aria-hidden="true" tabindex="-1"></a> [<span class="st">"82"</span><span class="op">,</span> <span class="dv">2</span>]<span class="op">,</span></span>
<span id="cb5-237"><a href="#cb5-237" aria-hidden="true" tabindex="-1"></a> [<span class="st">"2,006"</span><span class="op">,</span> <span class="dv">3</span>]<span class="op">,</span></span>
<span id="cb5-238"><a href="#cb5-238" aria-hidden="true" tabindex="-1"></a> [<span class="st">"2,930"</span><span class="op">,</span> <span class="dv">4</span>]<span class="op">,</span></span>
<span id="cb5-239"><a href="#cb5-239" aria-hidden="true" tabindex="-1"></a> [<span class="st">"It is impossible to tell."</span><span class="op">,</span> <span class="dv">5</span>]</span>
<span id="cb5-240"><a href="#cb5-240" aria-hidden="true" tabindex="-1"></a> ])<span class="op">,</span></span>
<span id="cb5-241"><a href="#cb5-241" aria-hidden="true" tabindex="-1"></a> {<span class="dt">value</span><span class="op">:</span> <span class="bu">JSON</span><span class="op">.</span><span class="fu">parse</span>(localStorage<span class="op">.</span><span class="fu">getItem</span>(<span class="st">"q2_selected_t10"</span>) <span class="op">??</span> <span class="st">"null"</span>)}</span>
<span id="cb5-242"><a href="#cb5-242" aria-hidden="true" tabindex="-1"></a>)<span class="op">;</span></span>
<span id="cb5-243"><a href="#cb5-243" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb5-244"><a href="#cb5-244" aria-hidden="true" tabindex="-1"></a>{</span>
<span id="cb5-245"><a href="#cb5-245" aria-hidden="true" tabindex="-1"></a> localStorage<span class="op">.</span><span class="fu">setItem</span>(<span class="st">"q2_selected_t10"</span><span class="op">,</span> <span class="bu">JSON</span><span class="op">.</span><span class="fu">stringify</span>(q2))<span class="op">;</span></span>
<span id="cb5-246"><a href="#cb5-246" aria-hidden="true" tabindex="-1"></a> localStorage<span class="op">.</span><span class="fu">setItem</span>(<span class="st">"q2_correct_t10"</span><span class="op">,</span> <span class="st">"4"</span>)<span class="op">;</span></span>
<span id="cb5-247"><a href="#cb5-247" aria-hidden="true" tabindex="-1"></a> localStorage<span class="op">.</span><span class="fu">setItem</span>(<span class="st">"q2_result_t10"</span><span class="op">,</span> q2 <span class="op">===</span> <span class="kw">null</span> <span class="op">?</span> <span class="st">"unattempted"</span> <span class="op">:</span> (q2 <span class="op">==</span> <span class="dv">4</span> <span class="op">?</span> <span class="st">"correct"</span> <span class="op">:</span> <span class="st">"incorrect"</span>))<span class="op">;</span></span>
<span id="cb5-248"><a href="#cb5-248" aria-hidden="true" tabindex="-1"></a>}</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
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<div class="sourceCode cell-code hidden" id="cb6" data-startfrom="249" data-source-offset="-446"><pre class="sourceCode js code-with-copy"><code class="sourceCode javascript" style="counter-reset: source-line 248;"><span id="cb6-249"><a href="#cb6-249" aria-hidden="true" tabindex="-1"></a><span class="fu">ok_response</span>(q2<span class="op">,</span> <span class="st">"4"</span>)<span class="op">;</span></span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
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Check Your Understanding: The <code>ames</code> Dataset III
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<p>How many variables are there in the <code>ames</code> dataset?</p>
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<div class="sourceCode cell-code hidden" id="cb7" data-startfrom="262" data-source-offset="-1"><pre class="sourceCode js code-with-copy"><code class="sourceCode javascript" style="counter-reset: source-line 261;"><span id="cb7-262"><a href="#cb7-262" aria-hidden="true" tabindex="-1"></a>viewof q3 <span class="op">=</span> Inputs<span class="op">.</span><span class="fu">radio</span>(</span>
<span id="cb7-263"><a href="#cb7-263" aria-hidden="true" tabindex="-1"></a> <span class="kw">new</span> <span class="bu">Map</span>([</span>
<span id="cb7-264"><a href="#cb7-264" aria-hidden="true" tabindex="-1"></a> [<span class="st">"1"</span><span class="op">,</span> <span class="dv">1</span>]<span class="op">,</span></span>
<span id="cb7-265"><a href="#cb7-265" aria-hidden="true" tabindex="-1"></a> [<span class="st">"82"</span><span class="op">,</span> <span class="dv">2</span>]<span class="op">,</span></span>
<span id="cb7-266"><a href="#cb7-266" aria-hidden="true" tabindex="-1"></a> [<span class="st">"2,006"</span><span class="op">,</span> <span class="dv">3</span>]<span class="op">,</span></span>
<span id="cb7-267"><a href="#cb7-267" aria-hidden="true" tabindex="-1"></a> [<span class="st">"2,930"</span><span class="op">,</span> <span class="dv">4</span>]<span class="op">,</span></span>
<span id="cb7-268"><a href="#cb7-268" aria-hidden="true" tabindex="-1"></a> [<span class="st">"It is impossible to tell."</span><span class="op">,</span> <span class="dv">5</span>]</span>
<span id="cb7-269"><a href="#cb7-269" aria-hidden="true" tabindex="-1"></a> ])<span class="op">,</span></span>
<span id="cb7-270"><a href="#cb7-270" aria-hidden="true" tabindex="-1"></a> {<span class="dt">value</span><span class="op">:</span> <span class="bu">JSON</span><span class="op">.</span><span class="fu">parse</span>(localStorage<span class="op">.</span><span class="fu">getItem</span>(<span class="st">"q3_selected_t10"</span>) <span class="op">??</span> <span class="st">"null"</span>)}</span>
<span id="cb7-271"><a href="#cb7-271" aria-hidden="true" tabindex="-1"></a>)<span class="op">;</span></span>
<span id="cb7-272"><a href="#cb7-272" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb7-273"><a href="#cb7-273" aria-hidden="true" tabindex="-1"></a>{</span>
<span id="cb7-274"><a href="#cb7-274" aria-hidden="true" tabindex="-1"></a> localStorage<span class="op">.</span><span class="fu">setItem</span>(<span class="st">"q3_selected_t10"</span><span class="op">,</span> <span class="bu">JSON</span><span class="op">.</span><span class="fu">stringify</span>(q3))<span class="op">;</span></span>
<span id="cb7-275"><a href="#cb7-275" aria-hidden="true" tabindex="-1"></a> localStorage<span class="op">.</span><span class="fu">setItem</span>(<span class="st">"q3_correct_t10"</span><span class="op">,</span> <span class="st">"2"</span>)<span class="op">;</span></span>
<span id="cb7-276"><a href="#cb7-276" aria-hidden="true" tabindex="-1"></a> localStorage<span class="op">.</span><span class="fu">setItem</span>(<span class="st">"q3_result_t10"</span><span class="op">,</span> q3 <span class="op">===</span> <span class="kw">null</span> <span class="op">?</span> <span class="st">"unattempted"</span> <span class="op">:</span> (q3 <span class="op">==</span> <span class="dv">2</span> <span class="op">?</span> <span class="st">"correct"</span> <span class="op">:</span> <span class="st">"incorrect"</span>))<span class="op">;</span></span>
<span id="cb7-277"><a href="#cb7-277" aria-hidden="true" tabindex="-1"></a>}</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
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<div class="sourceCode cell-code hidden" id="cb8" data-startfrom="278" data-source-offset="-446"><pre class="sourceCode js code-with-copy"><code class="sourceCode javascript" style="counter-reset: source-line 277;"><span id="cb8-278"><a href="#cb8-278" aria-hidden="true" tabindex="-1"></a><span class="fu">ok_response</span>(q3<span class="op">,</span> <span class="st">"2"</span>)<span class="op">;</span></span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
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<p>We see that there are quite a few variables in the data set — enough to do a very in-depth analysis. For this lab, we’ll restrict our attention to just two of the variables: the above ground living <code>area</code> of the house in square feet and the sale <code>price</code>. To save some effort throughout the lab, we’ll create two variables with short names that represent these two variables. The code block below is pre-set to define the <code>area</code> vector — add a second line which creates the <code>price</code> vector.</p>
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<div id="callout-7" class="callout-7-contents callout-collapse collapse show">
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<p>Start by copying the existing code and making changes to it. What needs to change?</p>
<div class="cell">
<div class="sourceCode cell-code" id="cb9"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb9-1"><a href="#cb9-1" aria-hidden="true" tabindex="-1"></a>area <span class="ot"><-</span> ames <span class="sc">|></span></span>
<span id="cb9-2"><a href="#cb9-2" aria-hidden="true" tabindex="-1"></a> <span class="fu">pull</span>(area)</span>
<span id="cb9-3"><a href="#cb9-3" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb9-4"><a href="#cb9-4" aria-hidden="true" tabindex="-1"></a>area <span class="ot"><-</span> ames <span class="sc">|></span></span>
<span id="cb9-5"><a href="#cb9-5" aria-hidden="true" tabindex="-1"></a> <span class="fu">pull</span>(area)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
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Hint 2
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<p>We want to use a different variable name because (i) we don’t want to overwrite the existing <code>area</code> variable, and (ii) we want the name to be meaningful.</p>
<p>We also don’t want to extract the <code>area</code> column again.</p>
<div class="cell">
<div class="sourceCode cell-code" id="cb10"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb10-1"><a href="#cb10-1" aria-hidden="true" tabindex="-1"></a>area <span class="ot"><-</span> ames <span class="sc">|></span></span>
<span id="cb10-2"><a href="#cb10-2" aria-hidden="true" tabindex="-1"></a> <span class="fu">pull</span>(area)</span>
<span id="cb10-3"><a href="#cb10-3" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb10-4"><a href="#cb10-4" aria-hidden="true" tabindex="-1"></a>___ <span class="ot"><-</span> ames <span class="sc">|></span></span>
<span id="cb10-5"><a href="#cb10-5" aria-hidden="true" tabindex="-1"></a> <span class="fu">pull</span>(___)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
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Hint 3
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<div class="callout-btn-toggle d-inline-block border-0 py-1 ps-1 pe-0 float-end"><i class="callout-toggle"></i></div>
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<p>Store the results into a new variable called <code>price</code>, as requested in the prompt. What column from the <code>ames</code> data frame do you want to extract?</p>
<div class="cell">
<div class="sourceCode cell-code" id="cb11"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb11-1"><a href="#cb11-1" aria-hidden="true" tabindex="-1"></a>area <span class="ot"><-</span> ames <span class="sc">|></span></span>
<span id="cb11-2"><a href="#cb11-2" aria-hidden="true" tabindex="-1"></a> <span class="fu">pull</span>(area)</span>
<span id="cb11-3"><a href="#cb11-3" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb11-4"><a href="#cb11-4" aria-hidden="true" tabindex="-1"></a>price <span class="ot"><-</span> ames <span class="sc">|></span></span>
<span id="cb11-5"><a href="#cb11-5" aria-hidden="true" tabindex="-1"></a> <span class="fu">pull</span>(___)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
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<p>Store the results into a new variable called <code>price</code>, as requested in the prompt. You want to extract the <code>price</code> column.</p>
<div class="cell">
<div class="sourceCode cell-code" id="cb12"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb12-1"><a href="#cb12-1" aria-hidden="true" tabindex="-1"></a>area <span class="ot"><-</span> ames <span class="sc">|></span></span>
<span id="cb12-2"><a href="#cb12-2" aria-hidden="true" tabindex="-1"></a> <span class="fu">pull</span>(area)</span>
<span id="cb12-3"><a href="#cb12-3" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb12-4"><a href="#cb12-4" aria-hidden="true" tabindex="-1"></a>price <span class="ot"><-</span> ames <span class="sc">|></span></span>
<span id="cb12-5"><a href="#cb12-5" aria-hidden="true" tabindex="-1"></a> <span class="fu">pull</span>(price)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
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<div class="webr-ojs-exercise exercise-solution d-none" data-exercise="assign">
<code id="interpolate-7" class="solution-code d-none">
area <- ames |>
pull(area)
price <- ames |>
pull(price)</code>
<div class="sourceCode cell-code" id="interpolate-8"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="interpolate-8-1"><a href="#interpolate-8-1" aria-hidden="true" tabindex="-1"></a></span>
<span id="interpolate-8-2"><a href="#interpolate-8-2" aria-hidden="true" tabindex="-1"></a>area <span class="ot"><-</span> ames <span class="sc">|></span></span>
<span id="interpolate-8-3"><a href="#interpolate-8-3" aria-hidden="true" tabindex="-1"></a> <span class="fu">pull</span>(area)</span>
<span id="interpolate-8-4"><a href="#interpolate-8-4" aria-hidden="true" tabindex="-1"></a></span>
<span id="interpolate-8-5"><a href="#interpolate-8-5" aria-hidden="true" tabindex="-1"></a>price <span class="ot"><-</span> ames <span class="sc">|></span></span>
<span id="interpolate-8-6"><a href="#interpolate-8-6" aria-hidden="true" tabindex="-1"></a> <span class="fu">pull</span>(price)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
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<section id="initial-exploration" class="level2">
<h2 class="anchored" data-anchor-id="initial-exploration">Initial Exploration</h2>
<p>Let’s look at the distributions of <code>price</code> and <code>area</code> in our population of home sales by calculating a few summary statistics. Use the code block below to find the mean and median for both <code>price</code> and <code>area</code>. Use your results to answer the questions that follow.</p>
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<p>The <code>area</code> and <code>price</code> objects are vectors of values. Pass them, one at a time, to the <code>mean()</code> and <code>median()</code> functions.</p>
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<p>Fill in the blanks:</p>
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<div class="sourceCode cell-code" id="cb13"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb13-1"><a href="#cb13-1" aria-hidden="true" tabindex="-1"></a><span class="fu">mean</span>(___)</span>
<span id="cb13-2"><a href="#cb13-2" aria-hidden="true" tabindex="-1"></a><span class="fu">median</span>(___)</span>
<span id="cb13-3"><a href="#cb13-3" aria-hidden="true" tabindex="-1"></a><span class="fu">mean</span>(___)</span>
<span id="cb13-4"><a href="#cb13-4" aria-hidden="true" tabindex="-1"></a><span class="fu">median</span>(___)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
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Check Your Understanding: Summary Statistics I
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<div class="callout-body-container callout-body">
<p>Which of the following is the mean of the <code>price</code> variable?</p>
<div class="cell">
<div class="sourceCode cell-code hidden" id="cb14" data-startfrom="446" data-source-offset="-1"><pre class="sourceCode js code-with-copy"><code class="sourceCode javascript" style="counter-reset: source-line 445;"><span id="cb14-446"><a href="#cb14-446" aria-hidden="true" tabindex="-1"></a>viewof q4 <span class="op">=</span> Inputs<span class="op">.</span><span class="fu">radio</span>(</span>
<span id="cb14-447"><a href="#cb14-447" aria-hidden="true" tabindex="-1"></a> <span class="kw">new</span> <span class="bu">Map</span>([</span>
<span id="cb14-448"><a href="#cb14-448" aria-hidden="true" tabindex="-1"></a> [<span class="st">"$160,000"</span><span class="op">,</span> <span class="dv">1</span>]<span class="op">,</span></span>
<span id="cb14-449"><a href="#cb14-449" aria-hidden="true" tabindex="-1"></a> [<span class="st">"$167,842.47"</span><span class="op">,</span> <span class="dv">2</span>]<span class="op">,</span></span>
<span id="cb14-450"><a href="#cb14-450" aria-hidden="true" tabindex="-1"></a> [<span class="st">"$180,796.10"</span><span class="op">,</span> <span class="dv">3</span>]<span class="op">,</span></span>
<span id="cb14-451"><a href="#cb14-451" aria-hidden="true" tabindex="-1"></a> [<span class="st">"$200,000"</span><span class="op">,</span> <span class="dv">4</span>]</span>
<span id="cb14-452"><a href="#cb14-452" aria-hidden="true" tabindex="-1"></a> ])<span class="op">,</span></span>
<span id="cb14-453"><a href="#cb14-453" aria-hidden="true" tabindex="-1"></a> {<span class="dt">value</span><span class="op">:</span> <span class="bu">JSON</span><span class="op">.</span><span class="fu">parse</span>(localStorage<span class="op">.</span><span class="fu">getItem</span>(<span class="st">"q4_selected_t10"</span>) <span class="op">??</span> <span class="st">"null"</span>)}</span>
<span id="cb14-454"><a href="#cb14-454" aria-hidden="true" tabindex="-1"></a>)<span class="op">;</span></span>
<span id="cb14-455"><a href="#cb14-455" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb14-456"><a href="#cb14-456" aria-hidden="true" tabindex="-1"></a>{</span>
<span id="cb14-457"><a href="#cb14-457" aria-hidden="true" tabindex="-1"></a> localStorage<span class="op">.</span><span class="fu">setItem</span>(<span class="st">"q4_selected_t10"</span><span class="op">,</span> <span class="bu">JSON</span><span class="op">.</span><span class="fu">stringify</span>(q4))<span class="op">;</span></span>
<span id="cb14-458"><a href="#cb14-458" aria-hidden="true" tabindex="-1"></a> localStorage<span class="op">.</span><span class="fu">setItem</span>(<span class="st">"q4_correct_t10"</span><span class="op">,</span> <span class="st">"3"</span>)<span class="op">;</span></span>
<span id="cb14-459"><a href="#cb14-459" aria-hidden="true" tabindex="-1"></a> localStorage<span class="op">.</span><span class="fu">setItem</span>(<span class="st">"q4_result_t10"</span><span class="op">,</span> q4 <span class="op">===</span> <span class="kw">null</span> <span class="op">?</span> <span class="st">"unattempted"</span> <span class="op">:</span> (q4 <span class="op">==</span> <span class="dv">3</span> <span class="op">?</span> <span class="st">"correct"</span> <span class="op">:</span> <span class="st">"incorrect"</span>))<span class="op">;</span></span>
<span id="cb14-460"><a href="#cb14-460" aria-hidden="true" tabindex="-1"></a>}</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
<div class="cell-output cell-output-display">
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<div id="ojs-cell-6-1" data-nodetype="declaration">
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<div class="sourceCode cell-code hidden" id="cb15" data-startfrom="461" data-source-offset="-433"><pre class="sourceCode js code-with-copy"><code class="sourceCode javascript" style="counter-reset: source-line 460;"><span id="cb15-461"><a href="#cb15-461" aria-hidden="true" tabindex="-1"></a><span class="fu">ok_response</span>(q4<span class="op">,</span> <span class="st">"3"</span>)<span class="op">;</span></span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
<div class="cell-output cell-output-display">
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<div id="ojs-cell-6-3" data-nodetype="expression">
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<div class="callout callout-style-default callout-caution callout-titled">
<div class="callout-header d-flex align-content-center">
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<i class="callout-icon"></i>
</div>
<div class="callout-title-container flex-fill">
Check Your Understanding: Summary Statistics II
</div>
</div>
<div class="callout-body-container callout-body">
<p>Which of the following is the median of the <code>price</code> variable?</p>
<div class="cell">
<div class="sourceCode cell-code hidden" id="cb16" data-startfrom="474" data-source-offset="-1"><pre class="sourceCode js code-with-copy"><code class="sourceCode javascript" style="counter-reset: source-line 473;"><span id="cb16-474"><a href="#cb16-474" aria-hidden="true" tabindex="-1"></a>viewof q5 <span class="op">=</span> Inputs<span class="op">.</span><span class="fu">radio</span>(</span>
<span id="cb16-475"><a href="#cb16-475" aria-hidden="true" tabindex="-1"></a> <span class="kw">new</span> <span class="bu">Map</span>([</span>
<span id="cb16-476"><a href="#cb16-476" aria-hidden="true" tabindex="-1"></a> [<span class="st">"$160,000"</span><span class="op">,</span> <span class="dv">1</span>]<span class="op">,</span></span>
<span id="cb16-477"><a href="#cb16-477" aria-hidden="true" tabindex="-1"></a> [<span class="st">"$167,842.47"</span><span class="op">,</span> <span class="dv">2</span>]<span class="op">,</span></span>
<span id="cb16-478"><a href="#cb16-478" aria-hidden="true" tabindex="-1"></a> [<span class="st">"$180,796.10"</span><span class="op">,</span> <span class="dv">3</span>]<span class="op">,</span></span>
<span id="cb16-479"><a href="#cb16-479" aria-hidden="true" tabindex="-1"></a> [<span class="st">"$200,000"</span><span class="op">,</span> <span class="dv">4</span>]</span>
<span id="cb16-480"><a href="#cb16-480" aria-hidden="true" tabindex="-1"></a> ])<span class="op">,</span></span>
<span id="cb16-481"><a href="#cb16-481" aria-hidden="true" tabindex="-1"></a> {<span class="dt">value</span><span class="op">:</span> <span class="bu">JSON</span><span class="op">.</span><span class="fu">parse</span>(localStorage<span class="op">.</span><span class="fu">getItem</span>(<span class="st">"q5_selected_t10"</span>) <span class="op">??</span> <span class="st">"null"</span>)}</span>
<span id="cb16-482"><a href="#cb16-482" aria-hidden="true" tabindex="-1"></a>)<span class="op">;</span></span>
<span id="cb16-483"><a href="#cb16-483" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb16-484"><a href="#cb16-484" aria-hidden="true" tabindex="-1"></a>{</span>
<span id="cb16-485"><a href="#cb16-485" aria-hidden="true" tabindex="-1"></a> localStorage<span class="op">.</span><span class="fu">setItem</span>(<span class="st">"q5_selected_t10"</span><span class="op">,</span> <span class="bu">JSON</span><span class="op">.</span><span class="fu">stringify</span>(q5))<span class="op">;</span></span>
<span id="cb16-486"><a href="#cb16-486" aria-hidden="true" tabindex="-1"></a> localStorage<span class="op">.</span><span class="fu">setItem</span>(<span class="st">"q5_correct_t10"</span><span class="op">,</span> <span class="st">"1"</span>)<span class="op">;</span></span>
<span id="cb16-487"><a href="#cb16-487" aria-hidden="true" tabindex="-1"></a> localStorage<span class="op">.</span><span class="fu">setItem</span>(<span class="st">"q5_result_t10"</span><span class="op">,</span> q5 <span class="op">===</span> <span class="kw">null</span> <span class="op">?</span> <span class="st">"unattempted"</span> <span class="op">:</span> (q5 <span class="op">==</span> <span class="dv">1</span> <span class="op">?</span> <span class="st">"correct"</span> <span class="op">:</span> <span class="st">"incorrect"</span>))<span class="op">;</span></span>
<span id="cb16-488"><a href="#cb16-488" aria-hidden="true" tabindex="-1"></a>}</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
<div class="cell-output cell-output-display">
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<div id="ojs-cell-7-1" data-nodetype="declaration">
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<div class="sourceCode cell-code hidden" id="cb17" data-startfrom="489" data-source-offset="-433"><pre class="sourceCode js code-with-copy"><code class="sourceCode javascript" style="counter-reset: source-line 488;"><span id="cb17-489"><a href="#cb17-489" aria-hidden="true" tabindex="-1"></a><span class="fu">ok_response</span>(q5<span class="op">,</span> <span class="st">"1"</span>)<span class="op">;</span></span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
<div class="cell-output cell-output-display">
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<div id="ojs-cell-7-3" data-nodetype="expression">
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<div class="callout callout-style-default callout-caution callout-titled">
<div class="callout-header d-flex align-content-center">
<div class="callout-icon-container">
<i class="callout-icon"></i>
</div>
<div class="callout-title-container flex-fill">
Check Your Understanding: Summary Statistics III
</div>
</div>
<div class="callout-body-container callout-body">
<p>What does the relationship between the mean and median tell you about the distribution of <code>price</code>?</p>
<div class="cell">
<div class="sourceCode cell-code hidden" id="cb18" data-startfrom="502" data-source-offset="-1"><pre class="sourceCode js code-with-copy"><code class="sourceCode javascript" style="counter-reset: source-line 501;"><span id="cb18-502"><a href="#cb18-502" aria-hidden="true" tabindex="-1"></a>viewof q6 <span class="op">=</span> Inputs<span class="op">.</span><span class="fu">radio</span>(</span>
<span id="cb18-503"><a href="#cb18-503" aria-hidden="true" tabindex="-1"></a> <span class="kw">new</span> <span class="bu">Map</span>([</span>
<span id="cb18-504"><a href="#cb18-504" aria-hidden="true" tabindex="-1"></a> [<span class="st">"The `price` variable is skewed right."</span><span class="op">,</span> <span class="dv">1</span>]<span class="op">,</span></span>
<span id="cb18-505"><a href="#cb18-505" aria-hidden="true" tabindex="-1"></a> [<span class="st">"The `price` variable is skewed left."</span><span class="op">,</span> <span class="dv">2</span>]<span class="op">,</span></span>
<span id="cb18-506"><a href="#cb18-506" aria-hidden="true" tabindex="-1"></a> [<span class="st">"The `price` variable is bimodal."</span><span class="op">,</span> <span class="dv">3</span>]<span class="op">,</span></span>
<span id="cb18-507"><a href="#cb18-507" aria-hidden="true" tabindex="-1"></a> [<span class="st">"The `price` variable is symmetric."</span><span class="op">,</span> <span class="dv">4</span>]</span>
<span id="cb18-508"><a href="#cb18-508" aria-hidden="true" tabindex="-1"></a> ])<span class="op">,</span></span>
<span id="cb18-509"><a href="#cb18-509" aria-hidden="true" tabindex="-1"></a> {<span class="dt">value</span><span class="op">:</span> <span class="bu">JSON</span><span class="op">.</span><span class="fu">parse</span>(localStorage<span class="op">.</span><span class="fu">getItem</span>(<span class="st">"q6_selected_t10"</span>) <span class="op">??</span> <span class="st">"null"</span>)}</span>
<span id="cb18-510"><a href="#cb18-510" aria-hidden="true" tabindex="-1"></a>)<span class="op">;</span></span>
<span id="cb18-511"><a href="#cb18-511" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb18-512"><a href="#cb18-512" aria-hidden="true" tabindex="-1"></a>{</span>
<span id="cb18-513"><a href="#cb18-513" aria-hidden="true" tabindex="-1"></a> localStorage<span class="op">.</span><span class="fu">setItem</span>(<span class="st">"q6_selected_t10"</span><span class="op">,</span> <span class="bu">JSON</span><span class="op">.</span><span class="fu">stringify</span>(q6))<span class="op">;</span></span>
<span id="cb18-514"><a href="#cb18-514" aria-hidden="true" tabindex="-1"></a> localStorage<span class="op">.</span><span class="fu">setItem</span>(<span class="st">"q6_correct_t10"</span><span class="op">,</span> <span class="st">"1"</span>)<span class="op">;</span></span>
<span id="cb18-515"><a href="#cb18-515" aria-hidden="true" tabindex="-1"></a> localStorage<span class="op">.</span><span class="fu">setItem</span>(<span class="st">"q6_result_t10"</span><span class="op">,</span> q6 <span class="op">===</span> <span class="kw">null</span> <span class="op">?</span> <span class="st">"unattempted"</span> <span class="op">:</span> (q6 <span class="op">==</span> <span class="dv">1</span> <span class="op">?</span> <span class="st">"correct"</span> <span class="op">:</span> <span class="st">"incorrect"</span>))<span class="op">;</span></span>
<span id="cb18-516"><a href="#cb18-516" aria-hidden="true" tabindex="-1"></a>}</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
<div class="cell-output cell-output-display">
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<div id="ojs-cell-8-1" data-nodetype="declaration">
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<div class="sourceCode cell-code hidden" id="cb19" data-startfrom="517" data-source-offset="-534"><pre class="sourceCode js code-with-copy"><code class="sourceCode javascript" style="counter-reset: source-line 516;"><span id="cb19-517"><a href="#cb19-517" aria-hidden="true" tabindex="-1"></a><span class="fu">ok_response</span>(q6<span class="op">,</span> <span class="st">"1"</span>)<span class="op">;</span></span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
<div class="cell-output cell-output-display">
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<div id="ojs-cell-8-3" data-nodetype="expression">
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<div class="callout callout-style-default callout-caution callout-titled">
<div class="callout-header d-flex align-content-center">
<div class="callout-icon-container">
<i class="callout-icon"></i>
</div>
<div class="callout-title-container flex-fill">
Check Your Understanding: Summary Statistics IV
</div>
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<div class="callout-body-container callout-body">
<p>Which of the following is the mean of the <code>area</code> variable?</p>
<div class="cell">
<div class="sourceCode cell-code hidden" id="cb20" data-startfrom="530" data-source-offset="-1"><pre class="sourceCode js code-with-copy"><code class="sourceCode javascript" style="counter-reset: source-line 529;"><span id="cb20-530"><a href="#cb20-530" aria-hidden="true" tabindex="-1"></a>viewof q7 <span class="op">=</span> Inputs<span class="op">.</span><span class="fu">radio</span>(</span>
<span id="cb20-531"><a href="#cb20-531" aria-hidden="true" tabindex="-1"></a> <span class="kw">new</span> <span class="bu">Map</span>([</span>
<span id="cb20-532"><a href="#cb20-532" aria-hidden="true" tabindex="-1"></a> [<span class="st">"1,442 sqft"</span><span class="op">,</span> <span class="dv">1</span>]<span class="op">,</span></span>
<span id="cb20-533"><a href="#cb20-533" aria-hidden="true" tabindex="-1"></a> [<span class="st">"1,458.42 sqft"</span><span class="op">,</span> <span class="dv">2</span>]<span class="op">,</span></span>
<span id="cb20-534"><a href="#cb20-534" aria-hidden="true" tabindex="-1"></a> [<span class="st">"1,462.5 sqft"</span><span class="op">,</span> <span class="dv">3</span>]<span class="op">,</span></span>
<span id="cb20-535"><a href="#cb20-535" aria-hidden="true" tabindex="-1"></a> [<span class="st">"1,499.69 sqft"</span><span class="op">,</span> <span class="dv">4</span>]</span>
<span id="cb20-536"><a href="#cb20-536" aria-hidden="true" tabindex="-1"></a> ])<span class="op">,</span></span>
<span id="cb20-537"><a href="#cb20-537" aria-hidden="true" tabindex="-1"></a> {<span class="dt">value</span><span class="op">:</span> <span class="bu">JSON</span><span class="op">.</span><span class="fu">parse</span>(localStorage<span class="op">.</span><span class="fu">getItem</span>(<span class="st">"q7_selected_t10"</span>) <span class="op">??</span> <span class="st">"null"</span>)}</span>
<span id="cb20-538"><a href="#cb20-538" aria-hidden="true" tabindex="-1"></a>)<span class="op">;</span></span>
<span id="cb20-539"><a href="#cb20-539" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb20-540"><a href="#cb20-540" aria-hidden="true" tabindex="-1"></a>{</span>
<span id="cb20-541"><a href="#cb20-541" aria-hidden="true" tabindex="-1"></a> localStorage<span class="op">.</span><span class="fu">setItem</span>(<span class="st">"q7_selected_t10"</span><span class="op">,</span> <span class="bu">JSON</span><span class="op">.</span><span class="fu">stringify</span>(q7))<span class="op">;</span></span>
<span id="cb20-542"><a href="#cb20-542" aria-hidden="true" tabindex="-1"></a> localStorage<span class="op">.</span><span class="fu">setItem</span>(<span class="st">"q7_correct_t10"</span><span class="op">,</span> <span class="st">"4"</span>)<span class="op">;</span></span>
<span id="cb20-543"><a href="#cb20-543" aria-hidden="true" tabindex="-1"></a> localStorage<span class="op">.</span><span class="fu">setItem</span>(<span class="st">"q7_result_t10"</span><span class="op">,</span> q7 <span class="op">===</span> <span class="kw">null</span> <span class="op">?</span> <span class="st">"unattempted"</span> <span class="op">:</span> (q7 <span class="op">==</span> <span class="dv">4</span> <span class="op">?</span> <span class="st">"correct"</span> <span class="op">:</span> <span class="st">"incorrect"</span>))<span class="op">;</span></span>
<span id="cb20-544"><a href="#cb20-544" aria-hidden="true" tabindex="-1"></a>}</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
<div class="cell-output cell-output-display">
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<div id="ojs-cell-9-1" data-nodetype="declaration">
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<div class="sourceCode cell-code hidden" id="cb21" data-startfrom="545" data-source-offset="-443"><pre class="sourceCode js code-with-copy"><code class="sourceCode javascript" style="counter-reset: source-line 544;"><span id="cb21-545"><a href="#cb21-545" aria-hidden="true" tabindex="-1"></a><span class="fu">ok_response</span>(q7<span class="op">,</span> <span class="st">"4"</span>)<span class="op">;</span></span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
<div class="cell-output cell-output-display">
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<div id="ojs-cell-9-3" data-nodetype="expression">
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<div class="callout callout-style-default callout-caution callout-titled">
<div class="callout-header d-flex align-content-center">
<div class="callout-icon-container">
<i class="callout-icon"></i>
</div>
<div class="callout-title-container flex-fill">
Check Your Understanding: Summary Statistics V
</div>
</div>
<div class="callout-body-container callout-body">
<p>Which of the following is the median of the <code>area</code> variable?</p>
<div class="cell">
<div class="sourceCode cell-code hidden" id="cb22" data-startfrom="558" data-source-offset="-1"><pre class="sourceCode js code-with-copy"><code class="sourceCode javascript" style="counter-reset: source-line 557;"><span id="cb22-558"><a href="#cb22-558" aria-hidden="true" tabindex="-1"></a>viewof q8 <span class="op">=</span> Inputs<span class="op">.</span><span class="fu">radio</span>(</span>
<span id="cb22-559"><a href="#cb22-559" aria-hidden="true" tabindex="-1"></a> <span class="kw">new</span> <span class="bu">Map</span>([</span>
<span id="cb22-560"><a href="#cb22-560" aria-hidden="true" tabindex="-1"></a> [<span class="st">"1,442 sqft"</span><span class="op">,</span> <span class="dv">1</span>]<span class="op">,</span></span>
<span id="cb22-561"><a href="#cb22-561" aria-hidden="true" tabindex="-1"></a> [<span class="st">"1,458.42 sqft"</span><span class="op">,</span> <span class="dv">2</span>]<span class="op">,</span></span>
<span id="cb22-562"><a href="#cb22-562" aria-hidden="true" tabindex="-1"></a> [<span class="st">"1,462.5 sqft"</span><span class="op">,</span> <span class="dv">3</span>]<span class="op">,</span></span>
<span id="cb22-563"><a href="#cb22-563" aria-hidden="true" tabindex="-1"></a> [<span class="st">"1,499.69 sqft"</span><span class="op">,</span> <span class="dv">4</span>]</span>
<span id="cb22-564"><a href="#cb22-564" aria-hidden="true" tabindex="-1"></a> ])<span class="op">,</span></span>
<span id="cb22-565"><a href="#cb22-565" aria-hidden="true" tabindex="-1"></a> {<span class="dt">value</span><span class="op">:</span> <span class="bu">JSON</span><span class="op">.</span><span class="fu">parse</span>(localStorage<span class="op">.</span><span class="fu">getItem</span>(<span class="st">"q8_selected_t10"</span>) <span class="op">??</span> <span class="st">"null"</span>)}</span>
<span id="cb22-566"><a href="#cb22-566" aria-hidden="true" tabindex="-1"></a>)<span class="op">;</span></span>
<span id="cb22-567"><a href="#cb22-567" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb22-568"><a href="#cb22-568" aria-hidden="true" tabindex="-1"></a>{</span>
<span id="cb22-569"><a href="#cb22-569" aria-hidden="true" tabindex="-1"></a> localStorage<span class="op">.</span><span class="fu">setItem</span>(<span class="st">"q8_selected_t10"</span><span class="op">,</span> <span class="bu">JSON</span><span class="op">.</span><span class="fu">stringify</span>(q8))<span class="op">;</span></span>
<span id="cb22-570"><a href="#cb22-570" aria-hidden="true" tabindex="-1"></a> localStorage<span class="op">.</span><span class="fu">setItem</span>(<span class="st">"q8_correct_t10"</span><span class="op">,</span> <span class="st">"1"</span>)<span class="op">;</span></span>
<span id="cb22-571"><a href="#cb22-571" aria-hidden="true" tabindex="-1"></a> localStorage<span class="op">.</span><span class="fu">setItem</span>(<span class="st">"q8_result_t10"</span><span class="op">,</span> q8 <span class="op">===</span> <span class="kw">null</span> <span class="op">?</span> <span class="st">"unattempted"</span> <span class="op">:</span> (q8 <span class="op">==</span> <span class="dv">1</span> <span class="op">?</span> <span class="st">"correct"</span> <span class="op">:</span> <span class="st">"incorrect"</span>))<span class="op">;</span></span>
<span id="cb22-572"><a href="#cb22-572" aria-hidden="true" tabindex="-1"></a>}</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
<div class="cell-output cell-output-display">
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<div id="ojs-cell-10-1" data-nodetype="declaration">
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<div class="sourceCode cell-code hidden" id="cb23" data-startfrom="573" data-source-offset="-443"><pre class="sourceCode js code-with-copy"><code class="sourceCode javascript" style="counter-reset: source-line 572;"><span id="cb23-573"><a href="#cb23-573" aria-hidden="true" tabindex="-1"></a><span class="fu">ok_response</span>(q8<span class="op">,</span> <span class="st">"1"</span>)<span class="op">;</span></span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
<div class="cell-output cell-output-display">
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<div id="ojs-cell-10-3" data-nodetype="expression">
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<div class="callout callout-style-default callout-caution callout-titled">
<div class="callout-header d-flex align-content-center">
<div class="callout-icon-container">
<i class="callout-icon"></i>
</div>
<div class="callout-title-container flex-fill">
Check Your Understanding: Summary Statistics VI
</div>
</div>
<div class="callout-body-container callout-body">
<p>What does the relationship between the mean and median tell you about the distribution of <code>area</code>?</p>
<div class="cell">
<div class="sourceCode cell-code hidden" id="cb24" data-startfrom="586" data-source-offset="-1"><pre class="sourceCode js code-with-copy"><code class="sourceCode javascript" style="counter-reset: source-line 585;"><span id="cb24-586"><a href="#cb24-586" aria-hidden="true" tabindex="-1"></a>viewof q9 <span class="op">=</span> Inputs<span class="op">.</span><span class="fu">radio</span>(</span>
<span id="cb24-587"><a href="#cb24-587" aria-hidden="true" tabindex="-1"></a> <span class="kw">new</span> <span class="bu">Map</span>([</span>
<span id="cb24-588"><a href="#cb24-588" aria-hidden="true" tabindex="-1"></a> [<span class="st">"The `area` variable is skewed right."</span><span class="op">,</span> <span class="dv">1</span>]<span class="op">,</span></span>
<span id="cb24-589"><a href="#cb24-589" aria-hidden="true" tabindex="-1"></a> [<span class="st">"The `area` variable is skewed left."</span><span class="op">,</span> <span class="dv">2</span>]<span class="op">,</span></span>
<span id="cb24-590"><a href="#cb24-590" aria-hidden="true" tabindex="-1"></a> [<span class="st">"The `area` variable is bimodal."</span><span class="op">,</span> <span class="dv">3</span>]<span class="op">,</span></span>
<span id="cb24-591"><a href="#cb24-591" aria-hidden="true" tabindex="-1"></a> [<span class="st">"The `area` variable is symmetric."</span><span class="op">,</span> <span class="dv">4</span>]</span>
<span id="cb24-592"><a href="#cb24-592" aria-hidden="true" tabindex="-1"></a> ])<span class="op">,</span></span>
<span id="cb24-593"><a href="#cb24-593" aria-hidden="true" tabindex="-1"></a> {<span class="dt">value</span><span class="op">:</span> <span class="bu">JSON</span><span class="op">.</span><span class="fu">parse</span>(localStorage<span class="op">.</span><span class="fu">getItem</span>(<span class="st">"q9_selected_t10"</span>) <span class="op">??</span> <span class="st">"null"</span>)}</span>
<span id="cb24-594"><a href="#cb24-594" aria-hidden="true" tabindex="-1"></a>)<span class="op">;</span></span>
<span id="cb24-595"><a href="#cb24-595" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb24-596"><a href="#cb24-596" aria-hidden="true" tabindex="-1"></a>{</span>
<span id="cb24-597"><a href="#cb24-597" aria-hidden="true" tabindex="-1"></a> localStorage<span class="op">.</span><span class="fu">setItem</span>(<span class="st">"q9_selected_t10"</span><span class="op">,</span> <span class="bu">JSON</span><span class="op">.</span><span class="fu">stringify</span>(q9))<span class="op">;</span></span>
<span id="cb24-598"><a href="#cb24-598" aria-hidden="true" tabindex="-1"></a> localStorage<span class="op">.</span><span class="fu">setItem</span>(<span class="st">"q9_correct_t10"</span><span class="op">,</span> <span class="st">"1"</span>)<span class="op">;</span></span>
<span id="cb24-599"><a href="#cb24-599" aria-hidden="true" tabindex="-1"></a> localStorage<span class="op">.</span><span class="fu">setItem</span>(<span class="st">"q9_result_t10"</span><span class="op">,</span> q9 <span class="op">===</span> <span class="kw">null</span> <span class="op">?</span> <span class="st">"unattempted"</span> <span class="op">:</span> (q9 <span class="op">==</span> <span class="dv">1</span> <span class="op">?</span> <span class="st">"correct"</span> <span class="op">:</span> <span class="st">"incorrect"</span>))<span class="op">;</span></span>
<span id="cb24-600"><a href="#cb24-600" aria-hidden="true" tabindex="-1"></a>}</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
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<div class="sourceCode cell-code hidden" id="cb25" data-startfrom="601" data-source-offset="-530"><pre class="sourceCode js code-with-copy"><code class="sourceCode javascript" style="counter-reset: source-line 600;"><span id="cb25-601"><a href="#cb25-601" aria-hidden="true" tabindex="-1"></a><span class="fu">ok_response</span>(q9<span class="op">,</span> <span class="st">"1"</span>)<span class="op">;</span></span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
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<p>Use the code block below to verify your answers about the shapes of the distributions. The code to produce the histogram and boxplot for <code>area</code> is already present. Add the code necessary to produce a histogram and boxplot for <code>price</code>. Are you able to see the skew in the distributions?</p>
<div class="cell" data-exercise="plot-area-price-dists" data-caption="Ungraded, Exploratory Only">
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<p>Start by copying and pasting the code for the existing plots. What needs to be changed?</p>
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<div class="sourceCode cell-code" id="cb26"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb26-1"><a href="#cb26-1" aria-hidden="true" tabindex="-1"></a><span class="fu">ggplot</span>() <span class="sc">+</span> </span>
<span id="cb26-2"><a href="#cb26-2" aria-hidden="true" tabindex="-1"></a> <span class="fu">geom_histogram</span>(<span class="fu">aes</span>(<span class="at">x =</span> area)) <span class="sc">+</span> </span>
<span id="cb26-3"><a href="#cb26-3" aria-hidden="true" tabindex="-1"></a> <span class="fu">labs</span>(<span class="at">title =</span> <span class="st">"Histogram of Home Size"</span>,</span>
<span id="cb26-4"><a href="#cb26-4" aria-hidden="true" tabindex="-1"></a> <span class="at">x =</span> <span class="st">"Size (sq ft)"</span>, <span class="at">y =</span> <span class="st">"Count"</span>)</span>
<span id="cb26-5"><a href="#cb26-5" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb26-6"><a href="#cb26-6" aria-hidden="true" tabindex="-1"></a><span class="fu">ggplot</span>() <span class="sc">+</span> </span>
<span id="cb26-7"><a href="#cb26-7" aria-hidden="true" tabindex="-1"></a> <span class="fu">geom_boxplot</span>(<span class="fu">aes</span>(<span class="at">x =</span> area)) <span class="sc">+</span> </span>
<span id="cb26-8"><a href="#cb26-8" aria-hidden="true" tabindex="-1"></a> <span class="fu">labs</span>(<span class="at">title =</span> <span class="st">"Boxplot of Home Sizes"</span>,</span>
<span id="cb26-9"><a href="#cb26-9" aria-hidden="true" tabindex="-1"></a> <span class="at">x =</span> <span class="st">"Size (sq ft)"</span>)</span>
<span id="cb26-10"><a href="#cb26-10" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb26-11"><a href="#cb26-11" aria-hidden="true" tabindex="-1"></a><span class="fu">ggplot</span>() <span class="sc">+</span> </span>
<span id="cb26-12"><a href="#cb26-12" aria-hidden="true" tabindex="-1"></a> <span class="fu">geom_histogram</span>(<span class="fu">aes</span>(<span class="at">x =</span> area)) <span class="sc">+</span> </span>
<span id="cb26-13"><a href="#cb26-13" aria-hidden="true" tabindex="-1"></a> <span class="fu">labs</span>(<span class="at">title =</span> <span class="st">"Histogram of Home Size"</span>,</span>
<span id="cb26-14"><a href="#cb26-14" aria-hidden="true" tabindex="-1"></a> <span class="at">x =</span> <span class="st">"Size (sq ft)"</span>, <span class="at">y =</span> <span class="st">"Count"</span>)</span>
<span id="cb26-15"><a href="#cb26-15" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb26-16"><a href="#cb26-16" aria-hidden="true" tabindex="-1"></a><span class="fu">ggplot</span>() <span class="sc">+</span> </span>
<span id="cb26-17"><a href="#cb26-17" aria-hidden="true" tabindex="-1"></a> <span class="fu">geom_boxplot</span>(<span class="fu">aes</span>(<span class="at">x =</span> area)) <span class="sc">+</span> </span>
<span id="cb26-18"><a href="#cb26-18" aria-hidden="true" tabindex="-1"></a> <span class="fu">labs</span>(<span class="at">title =</span> <span class="st">"Boxplot of Home Sizes"</span>,</span>
<span id="cb26-19"><a href="#cb26-19" aria-hidden="true" tabindex="-1"></a> <span class="at">x =</span> <span class="st">"Size (sq ft)"</span>)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
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