diff --git a/docs/chapters/01_getting-started.html b/docs/chapters/01_getting-started.html
index 2000276..0da1409 100644
--- a/docs/chapters/01_getting-started.html
+++ b/docs/chapters/01_getting-started.html
@@ -1528,7 +1528,7 @@ <h3 data-number="1.7.3" class="anchored" data-anchor-id="exercise-2"><span class
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diff --git a/docs/chapters/02_data-structures.html b/docs/chapters/02_data-structures.html
index d498ca6..1110771 100644
--- a/docs/chapters/02_data-structures.html
+++ b/docs/chapters/02_data-structures.html
@@ -299,21 +299,22 @@ <h1 class="title"><span class="chapter-number">2</span>&nbsp; <span class="chapt
 <section id="sec-vectors" class="level2" data-number="2.1">
 <h2 data-number="2.1" class="anchored" data-anchor-id="sec-vectors"><span class="header-section-number">2.1</span> Vectors</h2>
 <p>A <strong>vector</strong> is a collection of values. Vectors are the fundamental unit of data in R, and you’ve already used them in the previous sections.</p>
-<p>For instance, each column in a data frame is a vector. So the <code>quarter</code> column in the earnings data from <a href="01_getting-started.html#sec-data-frames" class="quarto-xref"><span>Section 1.6</span></a> is a vector. Take a look at it now. You can use <code>head</code> to avoid printing too much. Set the second argument to <code>10</code> so that exactly 10 values are printed:</p>
+<p>For instance, each column in a data frame is a vector. So the <code>first_appearance_year</code> column in the banknotes data from <a href="01_getting-started.html#sec-data-frames" class="quarto-xref"><span>Section 1.6</span></a> is a vector. Take a look at it now. You can use <code>head</code> to avoid printing too much. Set the second argument to <code>10</code> so that exactly 10 values are printed:</p>
 <div class="cell">
-<div class="sourceCode cell-code" id="cb1"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb1-1"><a href="#cb1-1" aria-hidden="true" tabindex="-1"></a><span class="fu">head</span>(earn<span class="sc">$</span>quarter, <span class="dv">10</span>)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
+<div class="sourceCode cell-code" id="cb1"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb1-1"><a href="#cb1-1" aria-hidden="true" tabindex="-1"></a><span class="fu">head</span>(banknotes<span class="sc">$</span>first_appearance_year, <span class="dv">10</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-stdout">
-<pre><code> [1] 1 2 3 4 1 2 3 4 1 2</code></pre>
+<pre><code> [1] 2012 1988 1999 1992 1970 1995 1993 1994 1993 1995</code></pre>
 </div>
 </div>
-<p>Like all vectors, this vector is <strong>ordered</strong>, which just means the values, or <strong>elements</strong>, have specific positions. The value of the 1st element is <code>1</code>, the 2nd is <code>2</code>, the 5th is also <code>1</code>, and so on.</p>
-<p>Notice that the elements of this vector are all integers. This isn’t just a quirk of the earnings data set. In R, the elements of a vector must all be the same type of data (we say the elements are <strong>homogeneous</strong>). A vector can contain integers, decimal numbers, strings, or several other types of data, but not a mix these all at once.</p>
-<p>The other columns in the earnings data frame are also vectors. For instance, the <code>age</code> column is a vector of strings:</p>
+<p>Like all vectors, this vector is <strong>ordered</strong>, which just means the values, or <strong>elements</strong>, have specific positions. The value of the 1st element is <code>2012</code>, the 2nd is <code>1988</code>, the 5th is <code>1970</code>, and so on.</p>
+<p>Notice that the elements of this vector are all integers. In R, the elements of a vector must all be the same type of data (we say the elements are <strong>homogeneous</strong>). A vector can contain integers, decimal numbers, strings, or several other types of data, but not a mix these all at once.</p>
+<p>The other columns in the banknotes data frame are also vectors. For instance, the <code>name</code> column is a vector of strings:</p>
 <div class="cell">
-<div class="sourceCode cell-code" id="cb3"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb3-1"><a href="#cb3-1" aria-hidden="true" tabindex="-1"></a><span class="fu">head</span>(earn<span class="sc">$</span>age)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
+<div class="sourceCode cell-code" id="cb3"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb3-1"><a href="#cb3-1" aria-hidden="true" tabindex="-1"></a><span class="fu">head</span>(banknotes<span class="sc">$</span>name)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
 <div class="cell-output cell-output-stdout">
-<pre><code>[1] "16 years and over" "16 years and over" "16 years and over"
-[4] "16 years and over" "16 years and over" "16 years and over"</code></pre>
+<pre><code>[1] "Eva Perón"                  "Julio Argentino Roca"      
+[3] "Domingo Faustino Sarmiento" "Juan Manuel de Rosas"      
+[5] "Manuel Belgrano"            "David Unaipon"             </code></pre>
 </div>
 </div>
 <p>Vectors can contain any number of elements, including 0 or 1 element. Unlike mathematics, R does not distinguish between vectors and <strong>scalars</strong> (solitary values). So as far as R is concerned, a solitary value, like <code>3</code>, is a vector with 1 element.</p>
@@ -327,12 +328,12 @@ <h2 data-number="2.1" class="anchored" data-anchor-id="sec-vectors"><span class=
 <div class="cell-output cell-output-stdout">
 <pre><code>[1] 1</code></pre>
 </div>
-<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><span class="fu">length</span>(earn<span class="sc">$</span>age)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
+<div class="sourceCode cell-code" id="cb9"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb9-1"><a href="#cb9-1" aria-hidden="true" tabindex="-1"></a><span class="fu">length</span>(banknotes<span class="sc">$</span>first_appearance_year)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
 <div class="cell-output cell-output-stdout">
-<pre><code>[1] 4224</code></pre>
+<pre><code>[1] 279</code></pre>
 </div>
 </div>
-<p>Since the last of these is a column from the data frame <code>earn</code>, the length is the same as the number of rows in <code>earn</code>.</p>
+<p>Since the last of these is a column from the data frame <code>banknotes</code>, the length is the same as the number of rows in <code>banknotes</code>.</p>
 <section id="creating-vectors" class="level3" data-number="2.1.1">
 <h3 data-number="2.1.1" class="anchored" data-anchor-id="creating-vectors"><span class="header-section-number">2.1.1</span> Creating Vectors</h3>
 <p>Sometimes you’ll want to create your own vectors. You can do this by concatenating several vectors together with the <code>c</code> function. It accepts any number of vector arguments, and combines them into a single vector:</p>
@@ -666,13 +667,13 @@ <h3 data-number="2.2.1" class="anchored" data-anchor-id="sec-lists"><span class=
 </div>
 </div>
 <p>For ordinary lists, the type and the class are both <code>list</code>. In <a href="#sec-indexing" class="quarto-xref"><span>Section 2.4</span></a>, we’ll learn how to get and set list elements, and in later sections we’ll learn more about when and why to use lists.</p>
-<p>You’ve already seen one list, the earnings data frame:</p>
+<p>You’ve already seen one list, the banknotes data frame:</p>
 <div class="cell">
-<div class="sourceCode cell-code" id="cb76"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb76-1"><a href="#cb76-1" aria-hidden="true" tabindex="-1"></a><span class="fu">class</span>(earn)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
+<div class="sourceCode cell-code" id="cb76"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb76-1"><a href="#cb76-1" aria-hidden="true" tabindex="-1"></a><span class="fu">class</span>(banknotes)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
 <div class="cell-output cell-output-stdout">
 <pre><code>[1] "data.frame"</code></pre>
 </div>
-<div class="sourceCode cell-code" id="cb78"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb78-1"><a href="#cb78-1" aria-hidden="true" tabindex="-1"></a><span class="fu">typeof</span>(earn)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
+<div class="sourceCode cell-code" id="cb78"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb78-1"><a href="#cb78-1" aria-hidden="true" tabindex="-1"></a><span class="fu">typeof</span>(banknotes)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
 <div class="cell-output cell-output-stdout">
 <pre><code>[1] "list"</code></pre>
 </div>
@@ -785,93 +786,122 @@ <h3 data-number="2.2.4" class="anchored" data-anchor-id="factors"><span class="h
 <p>For example, if we want to know how many songs are in the <code>rock</code> genre, we first need to divide the songs by genre, and then count the number of songs in each group (or at least the <code>rock</code> group).</p>
 <p>As a second example, months recorded as numbers can be categorical or not, depending on how you want to use them. You might want to treat them as categorical (for example, to compute max rainfall in each month) or you might want to treat them as numbers (for example, to compute the number of months time between two events).</p>
 <p>The bottom line is that you have to think about what you’ll be doing in the analysis. In some cases, you might treat a feature as categorical only for part of the analysis.</p>
-<p>Let’s think about which features are categorical in earnings data set. To refresh our memory of what’s in the data set, we can look at the structural summary:</p>
-<div class="cell">
-<div class="sourceCode cell-code" id="cb102"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb102-1"><a href="#cb102-1" aria-hidden="true" tabindex="-1"></a><span class="fu">str</span>(earn)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
-<div class="cell-output cell-output-stdout">
-<pre><code>'data.frame':   4224 obs. of  8 variables:
- $ sex               : chr  "Both Sexes" "Both Sexes" "Both Sexes" "Both Sexes" ...
- $ race              : chr  "All Races" "All Races" "All Races" "All Races" ...
- $ ethnic_origin     : chr  "All Origins" "All Origins" "All Origins" "All Origins" ...
- $ age               : chr  "16 years and over" "16 years and over" "16 years and over" "16 years and over" ...
- $ year              : int  2010 2010 2010 2010 2011 2011 2011 2011 2012 2012 ...
- $ quarter           : int  1 2 3 4 1 2 3 4 1 2 ...
- $ n_persons         : int  96821000 99798000 101385000 100120000 98329000 100593000 101447000 101458000 100830000 102769000 ...
- $ median_weekly_earn: int  754 740 740 752 755 753 753 764 769 771 ...</code></pre>
-</div>
-</div>
-<p>The columns <code>n_persons</code> and <code>median_weekly_earn</code> are quantitative rather than categorical, since they measure quantities of people and dollars, respectively.</p>
-<p>The <code>sex</code>, <code>race</code>, <code>ethnic_origin</code>, and <code>age</code> columns are all categorical, since they are all qualitative measurements. We can see this better if we use the <code>table</code> function to compute frequencies for the values in the columns:</p>
-<div class="cell">
-<div class="sourceCode cell-code" id="cb104"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb104-1"><a href="#cb104-1" aria-hidden="true" tabindex="-1"></a><span class="fu">table</span>(earn<span class="sc">$</span>sex)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
+<p>Let’s think about which features are categorical in banknotes data set. To refresh our memory of what’s in the data set, we can look at the structural summary:</p>
+<div class="cell">
+<div class="sourceCode cell-code" id="cb102"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb102-1"><a href="#cb102-1" aria-hidden="true" tabindex="-1"></a><span class="fu">str</span>(banknotes)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
+<div class="cell-output cell-output-stdout">
+<pre><code>'data.frame':   279 obs. of  17 variables:
+ $ currency_code        : chr  "ARS" "ARS" "ARS" "ARS" ...
+ $ country              : chr  "Argentina" "Argentina" "Argentina" "Argentina" ...
+ $ currency_name        : chr  "Argentinian Peso" "Argentinian Peso" "Argentinian Peso" "Argentinian Peso" ...
+ $ name                 : chr  "Eva Perón" "Julio Argentino Roca" "Domingo Faustino Sarmiento" "Juan Manuel de Rosas" ...
+ $ gender               : chr  "F" "M" "M" "M" ...
+ $ bill_count           : num  1 1 1 1 1 0.5 0.5 0.5 0.5 0.5 ...
+ $ profession           : chr  "Activist" "Head of Gov't" "Head of Gov't" "Politician" ...
+ $ known_for_being_first: chr  "No" "No" "No" "No" ...
+ $ current_bill_value   : int  100 100 50 20 10 50 10 20 10 50 ...
+ $ prop_total_bills     : num  NA NA NA NA NA 0.48 0.08 0.1 0.08 0.48 ...
+ $ first_appearance_year: int  2012 1988 1999 1992 1970 1995 1993 1994 1993 1995 ...
+ $ death_year           : chr  "1952" "1914" "1888" "1877" ...
+ $ comments             : chr  "" "" "" "" ...
+ $ hover_text           : chr  "" "" "" "" ...
+ $ has_portrait         : chr  "true" "true" "true" "true" ...
+ $ id                   : chr  "ARS_Evita" "ARS_Argentino" "ARS_Domingo" "ARS_Rosas" ...
+ $ scaled_bill_value    : num  1 1 0.444 0.111 0 ...</code></pre>
+</div>
+</div>
+<p>The columns <code>bill_count</code>, <code>current_bill_value</code>, and <code>prop_total_bills</code> are quantitative rather than categorical, since they measure values and proportions of bills.</p>
+<p>The <code>currency_code</code>, <code>country</code>, <code>currency_name</code>, <code>gender</code>, <code>profession</code>, <code>known_for_being_first</code>, and <code>has_portrait</code> columns are all categorical. We can see this better if we use the <code>table</code> function to compute frequencies for the values in the columns:</p>
+<div class="cell">
+<div class="sourceCode cell-code" id="cb104"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb104-1"><a href="#cb104-1" aria-hidden="true" tabindex="-1"></a><span class="fu">table</span>(banknotes<span class="sc">$</span>currency_code)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
 <div class="cell-output cell-output-stdout">
 <pre><code>
-Both Sexes        Men      Women 
-      1408       1408       1408 </code></pre>
+ARS AUD BDT BOB CAD CLP COP CRC CVE CZK DOP GBP GEL IDR ILS ISK JMD JPY KGS KRW 
+  5   9   9  15   9   5  11   6   5   6  11   8   9  12   4   5   5   3   7   4 
+MWK MXN NGN NZD PEN PGK PHP RMB RSD SEK STD TND TRY UAH USD UYU VES​ VES ZAR 
+  7  11   9   5   7   1   9   6   9   6   8   4  12  10   7   7   2   6   5 </code></pre>
 </div>
-<div class="sourceCode cell-code" id="cb106"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb106-1"><a href="#cb106-1" aria-hidden="true" tabindex="-1"></a><span class="fu">table</span>(earn<span class="sc">$</span>race)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
+<div class="sourceCode cell-code" id="cb106"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb106-1"><a href="#cb106-1" aria-hidden="true" tabindex="-1"></a><span class="fu">table</span>(banknotes<span class="sc">$</span>country)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
 <div class="cell-output cell-output-stdout">
 <pre><code>
-                All Races                     Asian Black or African American 
-                     2244                       660                       660 
-                    White 
-                      660 </code></pre>
-</div>
-<div class="sourceCode cell-code" id="cb108"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb108-1"><a href="#cb108-1" aria-hidden="true" tabindex="-1"></a><span class="fu">table</span>(earn<span class="sc">$</span>ethnic_origin)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
+            Argentina             Australia            Bangladesh 
+                    5                     9                     9 
+              Bolivia                Canada            Cape Verde 
+                   15                     9                     5 
+                Chile                 China              Colombia 
+                    5                     6                    11 
+           Costa Rica        Czech Republic    Dominican Republic 
+                    6                     6                    11 
+              England               Georgia               Iceland 
+                    8                     9                     5 
+            Indonesia                Israel               Jamaica 
+                   12                     4                     5 
+                Japan            Kyrgyzstan                Malawi 
+                    3                     7                     7 
+               Mexico           New Zealand               Nigeria 
+                   11                     5                     9 
+     Papua New Guinea                  Peru           Philippines 
+                    1                     7                     9 
+São Tomé and Príncipe                Serbia          South Africa 
+                    8                     9                     5 
+          South Korea                Sweden               Tunisia 
+                    4                     6                     4 
+               Turkey               Ukraine         United States 
+                   12                    10                     7 
+              Uruguay             Venezuela 
+                    7                     8 </code></pre>
+</div>
+<div class="sourceCode cell-code" id="cb108"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb108-1"><a href="#cb108-1" aria-hidden="true" tabindex="-1"></a><span class="fu">table</span>(banknotes<span class="sc">$</span>gender)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
 <div class="cell-output cell-output-stdout">
 <pre><code>
-       All Origins Hispanic or Latino 
-              3564                660 </code></pre>
+  F   M 
+ 59 220 </code></pre>
 </div>
-<div class="sourceCode cell-code" id="cb110"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb110-1"><a href="#cb110-1" aria-hidden="true" tabindex="-1"></a><span class="fu">table</span>(earn<span class="sc">$</span>age)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
+<div class="sourceCode cell-code" id="cb110"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb110-1"><a href="#cb110-1" aria-hidden="true" tabindex="-1"></a><span class="fu">table</span>(banknotes<span class="sc">$</span>known_for_being_first)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
 <div class="cell-output cell-output-stdout">
 <pre><code>
-   16 to 19 years    16 to 24 years 16 years and over    20 to 24 years 
-              132               660               660               132 
-   25 to 34 years    25 to 54 years 25 years and over    35 to 44 years 
-              132               660               660               132 
-   45 to 54 years    55 to 64 years 55 years and over 65 years and over 
-              132               132               660               132 </code></pre>
+ No Yes 
+185  94 </code></pre>
 </div>
 </div>
 <p>Each column has only a few unique values, repeated many times. These are ideal for grouping the data. If age had been recorded as a number, rather than a range, it would probably be better to treat it as quantitative, since there would be far more unique values. Columns with many unique values don’t make good categorical features, because each group will only have a few elements!</p>
-<p>That leaves us with the <code>year</code> and <code>quarter</code> columns. It’s easy to imagine grouping the data by year or quarter, but these are also clearly numbers. These columns can be treated as quantitative or categorical data, depending on how we want to use them to analyze the data.</p>
-<p>Let’s convert the <code>age</code> column to a factor. To do this, use the <code>factor</code> function:</p>
+<p>The <code>name</code>, <code>comments</code>, <code>hover_text</code>, and <code>id</code> columns contain qualitative strings rather than categories, where values are rarely or never repeated. This means using them for grouping is generally unhelpful, since most of the groups will just be single observations.</p>
+<p>That leaves us with the <code>first_appearance_year</code> and <code>death_year</code> columns. It’s easy to imagine grouping the data by year, but these are also clearly numbers. These columns can be treated as quantitative or categorical data, depending on how we want to use them to analyze the data.</p>
+<p>Let’s convert the <code>currency_code</code> column to a factor. To do this, use the <code>factor</code> function:</p>
 <div class="cell">
-<div class="sourceCode cell-code" id="cb112"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb112-1"><a href="#cb112-1" aria-hidden="true" tabindex="-1"></a>age <span class="ot">=</span> <span class="fu">factor</span>(earn<span class="sc">$</span>age)</span>
-<span id="cb112-2"><a href="#cb112-2" aria-hidden="true" tabindex="-1"></a><span class="fu">head</span>(age)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
+<div class="sourceCode cell-code" id="cb112"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb112-1"><a href="#cb112-1" aria-hidden="true" tabindex="-1"></a>currency_codes <span class="ot">=</span> <span class="fu">factor</span>(banknotes<span class="sc">$</span>currency_code)</span>
+<span id="cb112-2"><a href="#cb112-2" aria-hidden="true" tabindex="-1"></a><span class="fu">head</span>(currency_codes)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
 <div class="cell-output cell-output-stdout">
-<pre><code>[1] 16 years and over 16 years and over 16 years and over 16 years and over
-[5] 16 years and over 16 years and over
-12 Levels: 16 to 19 years 16 to 24 years 16 years and over ... 65 years and over</code></pre>
+<pre><code>[1] ARS ARS ARS ARS ARS AUD
+39 Levels: ARS AUD BDT BOB CAD CLP COP CRC CVE CZK DOP GBP GEL IDR ILS ... ZAR</code></pre>
 </div>
 </div>
 <p>Notice that factors are printed differently than strings.</p>
 <p>The categories of a factor are called <strong>levels</strong>. You can list the levels with the <code>levels</code> function:</p>
 <div class="cell">
-<div class="sourceCode cell-code" id="cb114"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb114-1"><a href="#cb114-1" aria-hidden="true" tabindex="-1"></a><span class="fu">levels</span>(age)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
+<div class="sourceCode cell-code" id="cb114"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb114-1"><a href="#cb114-1" aria-hidden="true" tabindex="-1"></a><span class="fu">levels</span>(currency_codes)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
 <div class="cell-output cell-output-stdout">
-<pre><code> [1] "16 to 19 years"    "16 to 24 years"    "16 years and over"
- [4] "20 to 24 years"    "25 to 34 years"    "25 to 54 years"   
- [7] "25 years and over" "35 to 44 years"    "45 to 54 years"   
-[10] "55 to 64 years"    "55 years and over" "65 years and over"</code></pre>
+<pre><code> [1] "ARS" "AUD" "BDT" "BOB" "CAD" "CLP" "COP" "CRC" "CVE" "CZK" "DOP" "GBP"
+[13] "GEL" "IDR" "ILS" "ISK" "JMD" "JPY" "KGS" "KRW" "MWK" "MXN" "NGN" "NZD"
+[25] "PEN" "PGK" "PHP" "RMB" "RSD" "SEK" "STD" "TND" "TRY" "UAH" "USD" "UYU"
+[37] "VES​" "VES" "ZAR"</code></pre>
 </div>
 </div>
 <p>Factors remember all possible levels even if you take a subset:</p>
 <div class="cell">
-<div class="sourceCode cell-code" id="cb116"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb116-1"><a href="#cb116-1" aria-hidden="true" tabindex="-1"></a>age[<span class="dv">1</span><span class="sc">:</span><span class="dv">3</span>]</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
+<div class="sourceCode cell-code" id="cb116"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb116-1"><a href="#cb116-1" aria-hidden="true" tabindex="-1"></a>currency_codes[<span class="dv">1</span><span class="sc">:</span><span class="dv">3</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-stdout">
-<pre><code>[1] 16 years and over 16 years and over 16 years and over
-12 Levels: 16 to 19 years 16 to 24 years 16 years and over ... 65 years and over</code></pre>
+<pre><code>[1] ARS ARS ARS
+39 Levels: ARS AUD BDT BOB CAD CLP COP CRC CVE CZK DOP GBP GEL IDR ILS ... ZAR</code></pre>
 </div>
 </div>
 <p>This is another way factors are different from strings. Factors “remember” all possible levels even if they aren’t present. This ensures that if you plot a factor, the missing levels will still be represented on the plot.</p>
 <p>You can make a factor forget levels that aren’t present with the <code>droplevels</code> function:</p>
 <div class="cell">
-<div class="sourceCode cell-code" id="cb118"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb118-1"><a href="#cb118-1" aria-hidden="true" tabindex="-1"></a><span class="fu">droplevels</span>(age[<span class="dv">1</span><span class="sc">:</span><span class="dv">3</span>])</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
+<div class="sourceCode cell-code" id="cb118"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb118-1"><a href="#cb118-1" aria-hidden="true" tabindex="-1"></a><span class="fu">droplevels</span>(currency_codes[<span class="dv">1</span><span class="sc">:</span><span class="dv">3</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-stdout">
-<pre><code>[1] 16 years and over 16 years and over 16 years and over
-Levels: 16 years and over</code></pre>
+<pre><code>[1] ARS ARS ARS
+Levels: ARS</code></pre>
 </div>
 </div>
 </section>
@@ -1379,8 +1409,8 @@ <h3 data-number="2.5.3" class="anchored" data-anchor-id="exercise-2"><span class
 <h3 data-number="2.5.4" class="anchored" data-anchor-id="exercise-3"><span class="header-section-number">2.5.4</span> Exercise</h3>
 <p>The <code>table</code> function is useful for counting all sorts of things, not just level frequencies for a factor. For instance, you can use <code>table</code> to count how many <code>TRUE</code> and <code>FALSE</code> values there are in a logical vector.</p>
 <ol type="1">
-<li>For the earnings data, how many rows had median weekly earnings below $750?</li>
-<li>Based on how the data is structured, is your answer in part 1 the same as the number of quarters that had median weekly earnings below $750? Explain.</li>
+<li>For the banknotes data, how many bills have value below 1,000?</li>
+<li>How many bills with value above 1,000 depict women?</li>
 </ol>
 
 
diff --git a/docs/index.html b/docs/index.html
index 5ac9dc9..4dbec06 100644
--- a/docs/index.html
+++ b/docs/index.html
@@ -8,7 +8,7 @@
 
 <meta name="author" content="Nick Ulle">
 <meta name="author" content="Wesley Brooks">
-<meta name="dcterms.date" content="2024-11-17">
+<meta name="dcterms.date" content="2024-12-04">
 
 <title>R Basics</title>
 <style>
@@ -205,7 +205,7 @@ <h1 class="title">R Basics</h1>
     <div>
     <div class="quarto-title-meta-heading">Published</div>
     <div class="quarto-title-meta-contents">
-      <p class="date">November 17, 2024</p>
+      <p class="date">December 4, 2024</p>
     </div>
   </div>
   
diff --git a/docs/search.json b/docs/search.json
index ea66412..2d27626 100644
--- a/docs/search.json
+++ b/docs/search.json
@@ -84,7 +84,7 @@
     "href": "chapters/02_data-structures.html",
     "title": "2  Data Structures",
     "section": "",
-    "text": "2.1 Vectors\nA vector is a collection of values. Vectors are the fundamental unit of data in R, and you’ve already used them in the previous sections.\nFor instance, each column in a data frame is a vector. So the quarter column in the earnings data from Section 1.6 is a vector. Take a look at it now. You can use head to avoid printing too much. Set the second argument to 10 so that exactly 10 values are printed:\nhead(earn$quarter, 10)\n\n [1] 1 2 3 4 1 2 3 4 1 2\nLike all vectors, this vector is ordered, which just means the values, or elements, have specific positions. The value of the 1st element is 1, the 2nd is 2, the 5th is also 1, and so on.\nNotice that the elements of this vector are all integers. This isn’t just a quirk of the earnings data set. In R, the elements of a vector must all be the same type of data (we say the elements are homogeneous). A vector can contain integers, decimal numbers, strings, or several other types of data, but not a mix these all at once.\nThe other columns in the earnings data frame are also vectors. For instance, the age column is a vector of strings:\nhead(earn$age)\n\n[1] \"16 years and over\" \"16 years and over\" \"16 years and over\"\n[4] \"16 years and over\" \"16 years and over\" \"16 years and over\"\nVectors can contain any number of elements, including 0 or 1 element. Unlike mathematics, R does not distinguish between vectors and scalars (solitary values). So as far as R is concerned, a solitary value, like 3, is a vector with 1 element.\nYou can check the length of a vector (and other objects) with the length function:\nlength(3)\n\n[1] 1\n\nlength(\"hello\")\n\n[1] 1\n\nlength(earn$age)\n\n[1] 4224\nSince the last of these is a column from the data frame earn, the length is the same as the number of rows in earn.",
+    "text": "2.1 Vectors\nA vector is a collection of values. Vectors are the fundamental unit of data in R, and you’ve already used them in the previous sections.\nFor instance, each column in a data frame is a vector. So the first_appearance_year column in the banknotes data from Section 1.6 is a vector. Take a look at it now. You can use head to avoid printing too much. Set the second argument to 10 so that exactly 10 values are printed:\nhead(banknotes$first_appearance_year, 10)\n\n [1] 2012 1988 1999 1992 1970 1995 1993 1994 1993 1995\nLike all vectors, this vector is ordered, which just means the values, or elements, have specific positions. The value of the 1st element is 2012, the 2nd is 1988, the 5th is 1970, and so on.\nNotice that the elements of this vector are all integers. In R, the elements of a vector must all be the same type of data (we say the elements are homogeneous). A vector can contain integers, decimal numbers, strings, or several other types of data, but not a mix these all at once.\nThe other columns in the banknotes data frame are also vectors. For instance, the name column is a vector of strings:\nhead(banknotes$name)\n\n[1] \"Eva Perón\"                  \"Julio Argentino Roca\"      \n[3] \"Domingo Faustino Sarmiento\" \"Juan Manuel de Rosas\"      \n[5] \"Manuel Belgrano\"            \"David Unaipon\"\nVectors can contain any number of elements, including 0 or 1 element. Unlike mathematics, R does not distinguish between vectors and scalars (solitary values). So as far as R is concerned, a solitary value, like 3, is a vector with 1 element.\nYou can check the length of a vector (and other objects) with the length function:\nlength(3)\n\n[1] 1\n\nlength(\"hello\")\n\n[1] 1\n\nlength(banknotes$first_appearance_year)\n\n[1] 279\nSince the last of these is a column from the data frame banknotes, the length is the same as the number of rows in banknotes.",
     "crumbs": [
       "<span class='chapter-number'>2</span>  <span class='chapter-title'>Data Structures</span>"
     ]
@@ -104,7 +104,7 @@
     "href": "chapters/02_data-structures.html#sec-data-types-classes",
     "title": "2  Data Structures",
     "section": "2.2 Data Types & Classes",
-    "text": "2.2 Data Types & Classes\nData can be categorized into different types based on sets of shared characteristics. For instance, statisticians tend to think about whether data are numeric or categorical:\n\nnumeric\n\ncontinuous (real or complex numbers)\ndiscrete (integers)\n\ncategorical\n\nnominal (categories with no ordering)\nordinal (categories with some ordering)\n\n\nOf course, other types of data, like graphs (networks) and natural language (books, speech, and so on), are also possible. Categorizing data this way is useful for reasoning about which methods to apply to which data.\nIn R, data objects are categorized in two different ways:\n\nThe class of an R object describes what the object does, or the role that it plays. Sometimes objects can do more than one thing, so objects can have more than one class. The class function, which debuted in Section 1.6, returns the classes of its argument.\nThe type of an R object describes what the object is. Technically, the type corresponds to how the object is stored in your computer’s memory. Each object has exactly one type. The typeof function returns the type of its argument.\n\nOf the two, classes tend to be more important than types. If you aren’t sure what an object is, checking its classes should be the first thing you do.\nThe built-in classes you’ll use all the time correspond to vectors and lists (which we’ll learn more about in Section 2.2.1):\n\n\n\n\n\n\n\n\nClass\nExample\nDescription\n\n\n\n\nlogical\nTRUE, FALSE\nLogical (or Boolean) values\n\n\ninteger\n-1L, 1L, 2L\nInteger numbers\n\n\nnumeric\n-2.1, 7, 34.2\nReal numbers\n\n\ncomplex\n3-2i, -8+0i\nComplex numbers\n\n\ncharacter\n\"hi\", \"YAY\"\nText strings\n\n\nlist\nlist(TRUE, 1, \"hi\")\nOrdered collection of heterogeneous elements\n\n\n\nR doesn’t distinguish between scalars and vectors, so the class of a vector is the same as the class of its elements:\n\nclass(\"hi\")\n\n[1] \"character\"\n\nclass(c(\"hello\", \"hi\"))\n\n[1] \"character\"\n\n\nIn addition, for most vectors, the class and the type are the same:\n\nx = c(TRUE, FALSE)\nclass(x)\n\n[1] \"logical\"\n\ntypeof(x)\n\n[1] \"logical\"\n\n\nThe exception to this rule is numeric vectors, which have type double for historical reasons:\n\nclass(pi)\n\n[1] \"numeric\"\n\ntypeof(pi)\n\n[1] \"double\"\n\ntypeof(3)\n\n[1] \"double\"\n\n\nThe word “double” here stands for double-precision floating point number, a standard way to represent real numbers on computers.\nBy default, R assumes any numbers you enter in code are numeric, even if they’re integer-valued.\nThe class integer also represents integer numbers, but it’s not used as often as numeric. A few functions, such as the sequence operator : and the length function, return integers. You can also force R to create an integer by adding the suffix L to a number, but there are no major drawbacks to using the double default:\n\nclass(1:3)\n\n[1] \"integer\"\n\nclass(3)\n\n[1] \"numeric\"\n\nclass(3L)\n\n[1] \"integer\"\n\n\nBesides the classes for vectors and lists, there are several built-in classes that represent more sophisticated data structures:\n\n\n\n\n\n\n\nClass\nDescription\n\n\n\n\nfunction\nFunctions\n\n\nfactor\nCategorical values\n\n\nmatrix\nTwo-dimensional ordered collection of homogeneous elements\n\n\narray\nMulti-dimensional ordered collection of homogeneous elements\n\n\ndata.frame\nData frames\n\n\n\nFor these, the class is usually different from the type. We’ll learn more about most of these later on.\n\n2.2.1 Lists\nA list is an ordered data structure where the elements can have different types (they are heterogeneous). This differs from a vector, where the elements all have to have the same type, as we saw in Section 2.1. The tradeoff is that most vectorized functions do not work with lists.\nYou can make an ordinary list with the list function:\n\nx = list(1, c(\"hi\", \"bye\"))\nclass(x)\n\n[1] \"list\"\n\ntypeof(x)\n\n[1] \"list\"\n\n\nFor ordinary lists, the type and the class are both list. In Section 2.4, we’ll learn how to get and set list elements, and in later sections we’ll learn more about when and why to use lists.\nYou’ve already seen one list, the earnings data frame:\n\nclass(earn)\n\n[1] \"data.frame\"\n\ntypeof(earn)\n\n[1] \"list\"\n\n\nUnder the hood, data frames are lists, and each column is a list element. Because the class is data.frame rather than list, R treats data frames differently from ordinary lists. This difference is apparent in how data frames are printed compared to ordinary lists.\n\n\n2.2.2 Implicit Coercion\nR’s types fall into a natural hierarchy of expressiveness:\n\n\n\nR’s hierarchy of types.\n\n\nEach type on the right is more expressive than the ones to its left. That is, with the convention that FALSE is 0 and TRUE is 1, we can represent any logical value as an integer. In turn, we can represent any integer as a double, and any double as a complex number. By writing the number out, we can also represent any complex number as a string.\nThe point is that no information is lost as we follow the arrows from left to right along the types in the hierarchy. In fact, R will automatically and silently convert from types on the left to types on the right as needed. This is called implicit coercion.\nAs an example, consider what happens if we add a logical value to a number:\n\nTRUE + 2\n\n[1] 3\n\n\nR automatically converts the TRUE to the numeric value 1, and then carries out the arithmetic as usual.\nWe’ve already seen implicit coercion at work once before, when we learned the c function. Since the elements of a vector all have to have the same type, if you pass several different types to c, then R tries to use implicit coercion to make them the same:\n\nx = c(TRUE, \"hi\", 1, 1+3i)\nclass(x)\n\n[1] \"character\"\n\nx\n\n[1] \"TRUE\" \"hi\"   \"1\"    \"1+3i\"\n\n\nImplicit coercion is strictly one-way; it never occurs in the other direction. If you want to coerce a type on the right to one on the left, you can do it explicitly with one of the as.TYPE functions. For instance, the as.numeric (or as.double) function coerces to numeric:\n\nas.numeric(\"3.1\")\n\n[1] 3.1\n\n\nThere are a few types that fall outside of the hierarchy entirely, like functions. Implicit coercion doesn’t apply to these. If you try to use these types where it doesn’t make sense to, R generally returns an error:\n\nsin + 3\n\nError in sin + 3: non-numeric argument to binary operator\n\n\nIf you try to use these types as elements of a vector, you get back a list instead:\n\nx = c(1, 2, sum)\nclass(x)\n\n[1] \"list\"\n\n\nUnderstanding how implicit coercion works will help you avoid bugs, and can also be a time-saver. For example, we can use implicit coercion to succinctly count how many elements of a vector satisfy a some condition:\n\nx = c(1, 3, -1, 10, -2, 3, 8, 2)\ncondition = x &lt; 4\nsum(condition)    # or sum(x &lt; 4)\n\n[1] 6\n\n\nIf you still don’t quite understand how the code above works, try inspecting each variable. In general, inspecting each step or variable is a good strategy for understanding why a piece of code works (or doesn’t work!). Here the implicit coercion happens in the third line.\n\n\n2.2.3 Matrices & Arrays\nA matrix is the two-dimensional analogue of a vector. The elements, which are arranged into rows and columns, are ordered and homogeneous.\nYou can create a matrix from a vector with the matrix function. By default, the columns are filled first:\n\n# A matrix with 2 rows and 3 columns:\nmatrix(1:6, 2, 3)\n\n     [,1] [,2] [,3]\n[1,]    1    3    5\n[2,]    2    4    6\n\n\nThe class of a matrix is always matrix, and the type matches the type of the elements:\n\nx = matrix(c(\"a\", \"b\", NA, \"c\"), 2, 2)\nx\n\n     [,1] [,2]\n[1,] \"a\"  NA  \n[2,] \"b\"  \"c\" \n\nclass(x)\n\n[1] \"matrix\" \"array\" \n\ntypeof(x)\n\n[1] \"character\"\n\n\nYou can use the matrix multiplication operator %*% to multiply two matrices with compatible dimensions.\nAn array is a further generalization of matrices to higher dimensions. You can create an array from a vector with the array function. The characteristics of arrays are almost identical to matrices, but the class of an array is always array.\n\n\n2.2.4 Factors\nA feature is categorical if it measures a qualitative category. For example, the genres rock, blues, alternative, folk, pop are categories.\nR uses the class factor to represent categorical data. Visualizations and statistical models sometimes treat factors differently than other data types, so it’s important to make sure you have the right data type. If you’re ever unsure, remember that you can check the class of an object with the class function.\nWhen you load a data set, R usually can’t tell which features are categorical. That means identifying and converting the categorical features is up to you. For beginners, it can be difficult to understand whether a feature is categorical or not. The key is to think about whether you want to use the feature to divide the data into groups.\nFor example, if we want to know how many songs are in the rock genre, we first need to divide the songs by genre, and then count the number of songs in each group (or at least the rock group).\nAs a second example, months recorded as numbers can be categorical or not, depending on how you want to use them. You might want to treat them as categorical (for example, to compute max rainfall in each month) or you might want to treat them as numbers (for example, to compute the number of months time between two events).\nThe bottom line is that you have to think about what you’ll be doing in the analysis. In some cases, you might treat a feature as categorical only for part of the analysis.\nLet’s think about which features are categorical in earnings data set. To refresh our memory of what’s in the data set, we can look at the structural summary:\n\nstr(earn)\n\n'data.frame':   4224 obs. of  8 variables:\n $ sex               : chr  \"Both Sexes\" \"Both Sexes\" \"Both Sexes\" \"Both Sexes\" ...\n $ race              : chr  \"All Races\" \"All Races\" \"All Races\" \"All Races\" ...\n $ ethnic_origin     : chr  \"All Origins\" \"All Origins\" \"All Origins\" \"All Origins\" ...\n $ age               : chr  \"16 years and over\" \"16 years and over\" \"16 years and over\" \"16 years and over\" ...\n $ year              : int  2010 2010 2010 2010 2011 2011 2011 2011 2012 2012 ...\n $ quarter           : int  1 2 3 4 1 2 3 4 1 2 ...\n $ n_persons         : int  96821000 99798000 101385000 100120000 98329000 100593000 101447000 101458000 100830000 102769000 ...\n $ median_weekly_earn: int  754 740 740 752 755 753 753 764 769 771 ...\n\n\nThe columns n_persons and median_weekly_earn are quantitative rather than categorical, since they measure quantities of people and dollars, respectively.\nThe sex, race, ethnic_origin, and age columns are all categorical, since they are all qualitative measurements. We can see this better if we use the table function to compute frequencies for the values in the columns:\n\ntable(earn$sex)\n\n\nBoth Sexes        Men      Women \n      1408       1408       1408 \n\ntable(earn$race)\n\n\n                All Races                     Asian Black or African American \n                     2244                       660                       660 \n                    White \n                      660 \n\ntable(earn$ethnic_origin)\n\n\n       All Origins Hispanic or Latino \n              3564                660 \n\ntable(earn$age)\n\n\n   16 to 19 years    16 to 24 years 16 years and over    20 to 24 years \n              132               660               660               132 \n   25 to 34 years    25 to 54 years 25 years and over    35 to 44 years \n              132               660               660               132 \n   45 to 54 years    55 to 64 years 55 years and over 65 years and over \n              132               132               660               132 \n\n\nEach column has only a few unique values, repeated many times. These are ideal for grouping the data. If age had been recorded as a number, rather than a range, it would probably be better to treat it as quantitative, since there would be far more unique values. Columns with many unique values don’t make good categorical features, because each group will only have a few elements!\nThat leaves us with the year and quarter columns. It’s easy to imagine grouping the data by year or quarter, but these are also clearly numbers. These columns can be treated as quantitative or categorical data, depending on how we want to use them to analyze the data.\nLet’s convert the age column to a factor. To do this, use the factor function:\n\nage = factor(earn$age)\nhead(age)\n\n[1] 16 years and over 16 years and over 16 years and over 16 years and over\n[5] 16 years and over 16 years and over\n12 Levels: 16 to 19 years 16 to 24 years 16 years and over ... 65 years and over\n\n\nNotice that factors are printed differently than strings.\nThe categories of a factor are called levels. You can list the levels with the levels function:\n\nlevels(age)\n\n [1] \"16 to 19 years\"    \"16 to 24 years\"    \"16 years and over\"\n [4] \"20 to 24 years\"    \"25 to 34 years\"    \"25 to 54 years\"   \n [7] \"25 years and over\" \"35 to 44 years\"    \"45 to 54 years\"   \n[10] \"55 to 64 years\"    \"55 years and over\" \"65 years and over\"\n\n\nFactors remember all possible levels even if you take a subset:\n\nage[1:3]\n\n[1] 16 years and over 16 years and over 16 years and over\n12 Levels: 16 to 19 years 16 to 24 years 16 years and over ... 65 years and over\n\n\nThis is another way factors are different from strings. Factors “remember” all possible levels even if they aren’t present. This ensures that if you plot a factor, the missing levels will still be represented on the plot.\nYou can make a factor forget levels that aren’t present with the droplevels function:\n\ndroplevels(age[1:3])\n\n[1] 16 years and over 16 years and over 16 years and over\nLevels: 16 years and over",
+    "text": "2.2 Data Types & Classes\nData can be categorized into different types based on sets of shared characteristics. For instance, statisticians tend to think about whether data are numeric or categorical:\n\nnumeric\n\ncontinuous (real or complex numbers)\ndiscrete (integers)\n\ncategorical\n\nnominal (categories with no ordering)\nordinal (categories with some ordering)\n\n\nOf course, other types of data, like graphs (networks) and natural language (books, speech, and so on), are also possible. Categorizing data this way is useful for reasoning about which methods to apply to which data.\nIn R, data objects are categorized in two different ways:\n\nThe class of an R object describes what the object does, or the role that it plays. Sometimes objects can do more than one thing, so objects can have more than one class. The class function, which debuted in Section 1.6, returns the classes of its argument.\nThe type of an R object describes what the object is. Technically, the type corresponds to how the object is stored in your computer’s memory. Each object has exactly one type. The typeof function returns the type of its argument.\n\nOf the two, classes tend to be more important than types. If you aren’t sure what an object is, checking its classes should be the first thing you do.\nThe built-in classes you’ll use all the time correspond to vectors and lists (which we’ll learn more about in Section 2.2.1):\n\n\n\n\n\n\n\n\nClass\nExample\nDescription\n\n\n\n\nlogical\nTRUE, FALSE\nLogical (or Boolean) values\n\n\ninteger\n-1L, 1L, 2L\nInteger numbers\n\n\nnumeric\n-2.1, 7, 34.2\nReal numbers\n\n\ncomplex\n3-2i, -8+0i\nComplex numbers\n\n\ncharacter\n\"hi\", \"YAY\"\nText strings\n\n\nlist\nlist(TRUE, 1, \"hi\")\nOrdered collection of heterogeneous elements\n\n\n\nR doesn’t distinguish between scalars and vectors, so the class of a vector is the same as the class of its elements:\n\nclass(\"hi\")\n\n[1] \"character\"\n\nclass(c(\"hello\", \"hi\"))\n\n[1] \"character\"\n\n\nIn addition, for most vectors, the class and the type are the same:\n\nx = c(TRUE, FALSE)\nclass(x)\n\n[1] \"logical\"\n\ntypeof(x)\n\n[1] \"logical\"\n\n\nThe exception to this rule is numeric vectors, which have type double for historical reasons:\n\nclass(pi)\n\n[1] \"numeric\"\n\ntypeof(pi)\n\n[1] \"double\"\n\ntypeof(3)\n\n[1] \"double\"\n\n\nThe word “double” here stands for double-precision floating point number, a standard way to represent real numbers on computers.\nBy default, R assumes any numbers you enter in code are numeric, even if they’re integer-valued.\nThe class integer also represents integer numbers, but it’s not used as often as numeric. A few functions, such as the sequence operator : and the length function, return integers. You can also force R to create an integer by adding the suffix L to a number, but there are no major drawbacks to using the double default:\n\nclass(1:3)\n\n[1] \"integer\"\n\nclass(3)\n\n[1] \"numeric\"\n\nclass(3L)\n\n[1] \"integer\"\n\n\nBesides the classes for vectors and lists, there are several built-in classes that represent more sophisticated data structures:\n\n\n\n\n\n\n\nClass\nDescription\n\n\n\n\nfunction\nFunctions\n\n\nfactor\nCategorical values\n\n\nmatrix\nTwo-dimensional ordered collection of homogeneous elements\n\n\narray\nMulti-dimensional ordered collection of homogeneous elements\n\n\ndata.frame\nData frames\n\n\n\nFor these, the class is usually different from the type. We’ll learn more about most of these later on.\n\n2.2.1 Lists\nA list is an ordered data structure where the elements can have different types (they are heterogeneous). This differs from a vector, where the elements all have to have the same type, as we saw in Section 2.1. The tradeoff is that most vectorized functions do not work with lists.\nYou can make an ordinary list with the list function:\n\nx = list(1, c(\"hi\", \"bye\"))\nclass(x)\n\n[1] \"list\"\n\ntypeof(x)\n\n[1] \"list\"\n\n\nFor ordinary lists, the type and the class are both list. In Section 2.4, we’ll learn how to get and set list elements, and in later sections we’ll learn more about when and why to use lists.\nYou’ve already seen one list, the banknotes data frame:\n\nclass(banknotes)\n\n[1] \"data.frame\"\n\ntypeof(banknotes)\n\n[1] \"list\"\n\n\nUnder the hood, data frames are lists, and each column is a list element. Because the class is data.frame rather than list, R treats data frames differently from ordinary lists. This difference is apparent in how data frames are printed compared to ordinary lists.\n\n\n2.2.2 Implicit Coercion\nR’s types fall into a natural hierarchy of expressiveness:\n\n\n\nR’s hierarchy of types.\n\n\nEach type on the right is more expressive than the ones to its left. That is, with the convention that FALSE is 0 and TRUE is 1, we can represent any logical value as an integer. In turn, we can represent any integer as a double, and any double as a complex number. By writing the number out, we can also represent any complex number as a string.\nThe point is that no information is lost as we follow the arrows from left to right along the types in the hierarchy. In fact, R will automatically and silently convert from types on the left to types on the right as needed. This is called implicit coercion.\nAs an example, consider what happens if we add a logical value to a number:\n\nTRUE + 2\n\n[1] 3\n\n\nR automatically converts the TRUE to the numeric value 1, and then carries out the arithmetic as usual.\nWe’ve already seen implicit coercion at work once before, when we learned the c function. Since the elements of a vector all have to have the same type, if you pass several different types to c, then R tries to use implicit coercion to make them the same:\n\nx = c(TRUE, \"hi\", 1, 1+3i)\nclass(x)\n\n[1] \"character\"\n\nx\n\n[1] \"TRUE\" \"hi\"   \"1\"    \"1+3i\"\n\n\nImplicit coercion is strictly one-way; it never occurs in the other direction. If you want to coerce a type on the right to one on the left, you can do it explicitly with one of the as.TYPE functions. For instance, the as.numeric (or as.double) function coerces to numeric:\n\nas.numeric(\"3.1\")\n\n[1] 3.1\n\n\nThere are a few types that fall outside of the hierarchy entirely, like functions. Implicit coercion doesn’t apply to these. If you try to use these types where it doesn’t make sense to, R generally returns an error:\n\nsin + 3\n\nError in sin + 3: non-numeric argument to binary operator\n\n\nIf you try to use these types as elements of a vector, you get back a list instead:\n\nx = c(1, 2, sum)\nclass(x)\n\n[1] \"list\"\n\n\nUnderstanding how implicit coercion works will help you avoid bugs, and can also be a time-saver. For example, we can use implicit coercion to succinctly count how many elements of a vector satisfy a some condition:\n\nx = c(1, 3, -1, 10, -2, 3, 8, 2)\ncondition = x &lt; 4\nsum(condition)    # or sum(x &lt; 4)\n\n[1] 6\n\n\nIf you still don’t quite understand how the code above works, try inspecting each variable. In general, inspecting each step or variable is a good strategy for understanding why a piece of code works (or doesn’t work!). Here the implicit coercion happens in the third line.\n\n\n2.2.3 Matrices & Arrays\nA matrix is the two-dimensional analogue of a vector. The elements, which are arranged into rows and columns, are ordered and homogeneous.\nYou can create a matrix from a vector with the matrix function. By default, the columns are filled first:\n\n# A matrix with 2 rows and 3 columns:\nmatrix(1:6, 2, 3)\n\n     [,1] [,2] [,3]\n[1,]    1    3    5\n[2,]    2    4    6\n\n\nThe class of a matrix is always matrix, and the type matches the type of the elements:\n\nx = matrix(c(\"a\", \"b\", NA, \"c\"), 2, 2)\nx\n\n     [,1] [,2]\n[1,] \"a\"  NA  \n[2,] \"b\"  \"c\" \n\nclass(x)\n\n[1] \"matrix\" \"array\" \n\ntypeof(x)\n\n[1] \"character\"\n\n\nYou can use the matrix multiplication operator %*% to multiply two matrices with compatible dimensions.\nAn array is a further generalization of matrices to higher dimensions. You can create an array from a vector with the array function. The characteristics of arrays are almost identical to matrices, but the class of an array is always array.\n\n\n2.2.4 Factors\nA feature is categorical if it measures a qualitative category. For example, the genres rock, blues, alternative, folk, pop are categories.\nR uses the class factor to represent categorical data. Visualizations and statistical models sometimes treat factors differently than other data types, so it’s important to make sure you have the right data type. If you’re ever unsure, remember that you can check the class of an object with the class function.\nWhen you load a data set, R usually can’t tell which features are categorical. That means identifying and converting the categorical features is up to you. For beginners, it can be difficult to understand whether a feature is categorical or not. The key is to think about whether you want to use the feature to divide the data into groups.\nFor example, if we want to know how many songs are in the rock genre, we first need to divide the songs by genre, and then count the number of songs in each group (or at least the rock group).\nAs a second example, months recorded as numbers can be categorical or not, depending on how you want to use them. You might want to treat them as categorical (for example, to compute max rainfall in each month) or you might want to treat them as numbers (for example, to compute the number of months time between two events).\nThe bottom line is that you have to think about what you’ll be doing in the analysis. In some cases, you might treat a feature as categorical only for part of the analysis.\nLet’s think about which features are categorical in banknotes data set. To refresh our memory of what’s in the data set, we can look at the structural summary:\n\nstr(banknotes)\n\n'data.frame':   279 obs. of  17 variables:\n $ currency_code        : chr  \"ARS\" \"ARS\" \"ARS\" \"ARS\" ...\n $ country              : chr  \"Argentina\" \"Argentina\" \"Argentina\" \"Argentina\" ...\n $ currency_name        : chr  \"Argentinian Peso\" \"Argentinian Peso\" \"Argentinian Peso\" \"Argentinian Peso\" ...\n $ name                 : chr  \"Eva Perón\" \"Julio Argentino Roca\" \"Domingo Faustino Sarmiento\" \"Juan Manuel de Rosas\" ...\n $ gender               : chr  \"F\" \"M\" \"M\" \"M\" ...\n $ bill_count           : num  1 1 1 1 1 0.5 0.5 0.5 0.5 0.5 ...\n $ profession           : chr  \"Activist\" \"Head of Gov't\" \"Head of Gov't\" \"Politician\" ...\n $ known_for_being_first: chr  \"No\" \"No\" \"No\" \"No\" ...\n $ current_bill_value   : int  100 100 50 20 10 50 10 20 10 50 ...\n $ prop_total_bills     : num  NA NA NA NA NA 0.48 0.08 0.1 0.08 0.48 ...\n $ first_appearance_year: int  2012 1988 1999 1992 1970 1995 1993 1994 1993 1995 ...\n $ death_year           : chr  \"1952\" \"1914\" \"1888\" \"1877\" ...\n $ comments             : chr  \"\" \"\" \"\" \"\" ...\n $ hover_text           : chr  \"\" \"\" \"\" \"\" ...\n $ has_portrait         : chr  \"true\" \"true\" \"true\" \"true\" ...\n $ id                   : chr  \"ARS_Evita\" \"ARS_Argentino\" \"ARS_Domingo\" \"ARS_Rosas\" ...\n $ scaled_bill_value    : num  1 1 0.444 0.111 0 ...\n\n\nThe columns bill_count, current_bill_value, and prop_total_bills are quantitative rather than categorical, since they measure values and proportions of bills.\nThe currency_code, country, currency_name, gender, profession, known_for_being_first, and has_portrait columns are all categorical. We can see this better if we use the table function to compute frequencies for the values in the columns:\n\ntable(banknotes$currency_code)\n\n\nARS AUD BDT BOB CAD CLP COP CRC CVE CZK DOP GBP GEL IDR ILS ISK JMD JPY KGS KRW \n  5   9   9  15   9   5  11   6   5   6  11   8   9  12   4   5   5   3   7   4 \nMWK MXN NGN NZD PEN PGK PHP RMB RSD SEK STD TND TRY UAH USD UYU VES​ VES ZAR \n  7  11   9   5   7   1   9   6   9   6   8   4  12  10   7   7   2   6   5 \n\ntable(banknotes$country)\n\n\n            Argentina             Australia            Bangladesh \n                    5                     9                     9 \n              Bolivia                Canada            Cape Verde \n                   15                     9                     5 \n                Chile                 China              Colombia \n                    5                     6                    11 \n           Costa Rica        Czech Republic    Dominican Republic \n                    6                     6                    11 \n              England               Georgia               Iceland \n                    8                     9                     5 \n            Indonesia                Israel               Jamaica \n                   12                     4                     5 \n                Japan            Kyrgyzstan                Malawi \n                    3                     7                     7 \n               Mexico           New Zealand               Nigeria \n                   11                     5                     9 \n     Papua New Guinea                  Peru           Philippines \n                    1                     7                     9 \nSão Tomé and Príncipe                Serbia          South Africa \n                    8                     9                     5 \n          South Korea                Sweden               Tunisia \n                    4                     6                     4 \n               Turkey               Ukraine         United States \n                   12                    10                     7 \n              Uruguay             Venezuela \n                    7                     8 \n\ntable(banknotes$gender)\n\n\n  F   M \n 59 220 \n\ntable(banknotes$known_for_being_first)\n\n\n No Yes \n185  94 \n\n\nEach column has only a few unique values, repeated many times. These are ideal for grouping the data. If age had been recorded as a number, rather than a range, it would probably be better to treat it as quantitative, since there would be far more unique values. Columns with many unique values don’t make good categorical features, because each group will only have a few elements!\nThe name, comments, hover_text, and id columns contain qualitative strings rather than categories, where values are rarely or never repeated. This means using them for grouping is generally unhelpful, since most of the groups will just be single observations.\nThat leaves us with the first_appearance_year and death_year columns. It’s easy to imagine grouping the data by year, but these are also clearly numbers. These columns can be treated as quantitative or categorical data, depending on how we want to use them to analyze the data.\nLet’s convert the currency_code column to a factor. To do this, use the factor function:\n\ncurrency_codes = factor(banknotes$currency_code)\nhead(currency_codes)\n\n[1] ARS ARS ARS ARS ARS AUD\n39 Levels: ARS AUD BDT BOB CAD CLP COP CRC CVE CZK DOP GBP GEL IDR ILS ... ZAR\n\n\nNotice that factors are printed differently than strings.\nThe categories of a factor are called levels. You can list the levels with the levels function:\n\nlevels(currency_codes)\n\n [1] \"ARS\" \"AUD\" \"BDT\" \"BOB\" \"CAD\" \"CLP\" \"COP\" \"CRC\" \"CVE\" \"CZK\" \"DOP\" \"GBP\"\n[13] \"GEL\" \"IDR\" \"ILS\" \"ISK\" \"JMD\" \"JPY\" \"KGS\" \"KRW\" \"MWK\" \"MXN\" \"NGN\" \"NZD\"\n[25] \"PEN\" \"PGK\" \"PHP\" \"RMB\" \"RSD\" \"SEK\" \"STD\" \"TND\" \"TRY\" \"UAH\" \"USD\" \"UYU\"\n[37] \"VES​\" \"VES\" \"ZAR\"\n\n\nFactors remember all possible levels even if you take a subset:\n\ncurrency_codes[1:3]\n\n[1] ARS ARS ARS\n39 Levels: ARS AUD BDT BOB CAD CLP COP CRC CVE CZK DOP GBP GEL IDR ILS ... ZAR\n\n\nThis is another way factors are different from strings. Factors “remember” all possible levels even if they aren’t present. This ensures that if you plot a factor, the missing levels will still be represented on the plot.\nYou can make a factor forget levels that aren’t present with the droplevels function:\n\ndroplevels(currency_codes[1:3])\n\n[1] ARS ARS ARS\nLevels: ARS",
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-    "text": "2.5 Exercises\n\n2.5.1 Exercise\nThe rep function is another way to create a vector. Read the help file for the rep function.\n\nWhat does the rep function do to create a vector? Give an example.\nThe rep function has parameters times and each. What does each do, and how do they differ? Give examples for both.\nCan you set both of times and each in a single call to rep? If the function raises an error, explain what the error message means. If the function returns a result, explain how the result corresponds to the arguments you chose.\n\n\n\n2.5.2 Exercise\nConsidering how implicit coercion works (Section 2.2.2):\n\nWhy does \"3\" + 4 raise an error?\nWhy does \"TRUE\" == TRUE return TRUE?\nWhy does \"FALSE\" &lt; TRUE return TRUE?\n\n\n\n2.5.3 Exercise\n\nSection 2.3.1 described the missing value as a “chameleon” because it can have many different types. Is Inf also a chameleon? Use examples to justify your answer.\nThe missing value is also “contagious” because using it as an argument usually produces another missing value. Is Inf contagious? Again, use examples to justify your answer.\n\n\n\n2.5.4 Exercise\nThe table function is useful for counting all sorts of things, not just level frequencies for a factor. For instance, you can use table to count how many TRUE and FALSE values there are in a logical vector.\n\nFor the earnings data, how many rows had median weekly earnings below $750?\nBased on how the data is structured, is your answer in part 1 the same as the number of quarters that had median weekly earnings below $750? Explain.",
+    "text": "2.5 Exercises\n\n2.5.1 Exercise\nThe rep function is another way to create a vector. Read the help file for the rep function.\n\nWhat does the rep function do to create a vector? Give an example.\nThe rep function has parameters times and each. What does each do, and how do they differ? Give examples for both.\nCan you set both of times and each in a single call to rep? If the function raises an error, explain what the error message means. If the function returns a result, explain how the result corresponds to the arguments you chose.\n\n\n\n2.5.2 Exercise\nConsidering how implicit coercion works (Section 2.2.2):\n\nWhy does \"3\" + 4 raise an error?\nWhy does \"TRUE\" == TRUE return TRUE?\nWhy does \"FALSE\" &lt; TRUE return TRUE?\n\n\n\n2.5.3 Exercise\n\nSection 2.3.1 described the missing value as a “chameleon” because it can have many different types. Is Inf also a chameleon? Use examples to justify your answer.\nThe missing value is also “contagious” because using it as an argument usually produces another missing value. Is Inf contagious? Again, use examples to justify your answer.\n\n\n\n2.5.4 Exercise\nThe table function is useful for counting all sorts of things, not just level frequencies for a factor. For instance, you can use table to count how many TRUE and FALSE values there are in a logical vector.\n\nFor the banknotes data, how many bills have value below 1,000?\nHow many bills with value above 1,000 depict women?",
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