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Resolucao.html
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<!DOCTYPE html>
<html>
<head>
<meta charset="utf-8" />
<meta name="generator" content="pandoc" />
<meta http-equiv="X-UA-Compatible" content="IE=EDGE" />
<meta name="viewport" content="width=device-width, initial-scale=1" />
<meta name="author" content="Caio Gomes Alves" />
<title>Resolução Lista de Exercícios 1</title>
<script>// Pandoc 2.9 adds attributes on both header and div. We remove the former (to
// be compatible with the behavior of Pandoc < 2.8).
document.addEventListener('DOMContentLoaded', function(e) {
var hs = document.querySelectorAll("div.section[class*='level'] > :first-child");
var i, h, a;
for (i = 0; i < hs.length; i++) {
h = hs[i];
if (!/^h[1-6]$/i.test(h.tagName)) continue; // it should be a header h1-h6
a = h.attributes;
while (a.length > 0) h.removeAttribute(a[0].name);
}
});
</script>
<style type="text/css">code{white-space: pre;}</style>
<style type="text/css" data-origin="pandoc">
pre > code.sourceCode { white-space: pre; position: relative; }
pre > code.sourceCode > span { display: inline-block; line-height: 1.25; }
pre > code.sourceCode > span:empty { height: 1.2em; }
.sourceCode { overflow: visible; }
code.sourceCode > span { color: inherit; text-decoration: inherit; }
div.sourceCode { margin: 1em 0; }
pre.sourceCode { margin: 0; }
@media screen {
div.sourceCode { overflow: auto; }
}
@media print {
pre > code.sourceCode { white-space: pre-wrap; }
pre > code.sourceCode > span { text-indent: -5em; padding-left: 5em; }
}
pre.numberSource code
{ counter-reset: source-line 0; }
pre.numberSource code > span
{ position: relative; left: -4em; counter-increment: source-line; }
pre.numberSource code > span > a:first-child::before
{ content: counter(source-line);
position: relative; left: -1em; text-align: right; vertical-align: baseline;
border: none; display: inline-block;
-webkit-touch-callout: none; -webkit-user-select: none;
-khtml-user-select: none; -moz-user-select: none;
-ms-user-select: none; user-select: none;
padding: 0 4px; width: 4em;
color: #aaaaaa;
}
pre.numberSource { margin-left: 3em; border-left: 1px solid #aaaaaa; padding-left: 4px; }
div.sourceCode
{ }
@media screen {
pre > code.sourceCode > span > a:first-child::before { text-decoration: underline; }
}
code span.al { color: #ff0000; font-weight: bold; }
code span.an { color: #60a0b0; font-weight: bold; font-style: italic; }
code span.at { color: #7d9029; }
code span.bn { color: #40a070; }
code span.bu { color: #008000; }
code span.cf { color: #007020; font-weight: bold; }
code span.ch { color: #4070a0; }
code span.cn { color: #880000; }
code span.co { color: #60a0b0; font-style: italic; }
code span.cv { color: #60a0b0; font-weight: bold; font-style: italic; }
code span.do { color: #ba2121; font-style: italic; }
code span.dt { color: #902000; }
code span.dv { color: #40a070; }
code span.er { color: #ff0000; font-weight: bold; }
code span.ex { }
code span.fl { color: #40a070; }
code span.fu { color: #06287e; }
code span.im { color: #008000; font-weight: bold; }
code span.in { color: #60a0b0; font-weight: bold; font-style: italic; }
code span.kw { color: #007020; font-weight: bold; }
code span.op { color: #666666; }
code span.ot { color: #007020; }
code span.pp { color: #bc7a00; }
code span.sc { color: #4070a0; }
code span.ss { color: #bb6688; }
code span.st { color: #4070a0; }
code span.va { color: #19177c; }
code span.vs { color: #4070a0; }
code span.wa { color: #60a0b0; font-weight: bold; font-style: italic; }
a.sourceLine {
pointer-events: auto;
}
</style>
<script>
// apply pandoc div.sourceCode style to pre.sourceCode instead
(function() {
var sheets = document.styleSheets;
for (var i = 0; i < sheets.length; i++) {
if (sheets[i].ownerNode.dataset["origin"] !== "pandoc") continue;
try { var rules = sheets[i].cssRules; } catch (e) { continue; }
for (var j = 0; j < rules.length; j++) {
var rule = rules[j];
// check if there is a div.sourceCode rule
if (rule.type !== rule.STYLE_RULE || rule.selectorText !== "div.sourceCode") continue;
var style = rule.style.cssText;
// check if color or background-color is set
if (rule.style.color === '' && rule.style.backgroundColor === '') continue;
// replace div.sourceCode by a pre.sourceCode rule
sheets[i].deleteRule(j);
sheets[i].insertRule('pre.sourceCode{' + style + '}', j);
}
}
})();
</script>
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<body>
<section class="page-header">
<h1 class="title toc-ignore project-name">Resolução Lista de Exercícios
1</h1>
<h4 class="author project-author">Caio Gomes Alves</h4>
<h4 class="date project-date">14/11/2022</h4>
</section>
<div id="TOC" class="toc">
<div class="toc-box">
<ul>
<li><a href="#aritmética" id="toc-aritmética">1 - Aritmética</a>
<ul>
<li><a href="#calculando-expressões-no-r" id="toc-calculando-expressões-no-r">1.1 - Calculando expressões no
R</a></li>
</ul></li>
<li><a href="#vetores" id="toc-vetores">2 - Vetores</a>
<ul>
<li><a href="#criação-de-vetores" id="toc-criação-de-vetores">2.1 -
Criação de vetores</a></li>
<li><a href="#análise-de-vetores" id="toc-análise-de-vetores">2.2 -
Análise de vetores</a></li>
<li><a href="#criação-de-vetores-por-sequências" id="toc-criação-de-vetores-por-sequências">2.3 - Criação de vetores por
sequências</a></li>
<li><a href="#manipulação-de-vetores" id="toc-manipulação-de-vetores">2.4 - Manipulação de vetores</a>
<ul>
<li><a href="#usando-dois-vetores" id="toc-usando-dois-vetores">2.4.1 -
Usando dois vetores</a></li>
<li><a href="#usando-um-vetor-nomeado" id="toc-usando-um-vetor-nomeado">2.4.2 - Usando um vetor
nomeado</a></li>
</ul></li>
</ul></li>
</ul>
</div>
</div>
<section class="main-content">
<div id="aritmética" class="section level1">
<h1>1 - Aritmética</h1>
<div id="calculando-expressões-no-r" class="section level2">
<h2>1.1 - Calculando expressões no R</h2>
<ul>
<li><span class="math inline">\(\frac{32}{2}+4\)</span></li>
</ul>
<div class="sourceCode" id="cb1"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb1-1"><a href="#cb1-1" aria-hidden="true" tabindex="-1"></a>(<span class="dv">32</span><span class="sc">/</span><span class="dv">2</span>) <span class="sc">+</span> <span class="dv">4</span></span></code></pre></div>
<pre><code>## [1] 20</code></pre>
<ul>
<li><span class="math inline">\(3^2 \cdot 5+2\)</span></li>
</ul>
<div class="sourceCode" id="cb3"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb3-1"><a href="#cb3-1" aria-hidden="true" tabindex="-1"></a>((<span class="dv">3</span><span class="sc">^</span><span class="dv">2</span>)<span class="sc">*</span><span class="dv">5</span>)<span class="sc">+</span><span class="dv">2</span></span></code></pre></div>
<pre><code>## [1] 47</code></pre>
<ul>
<li><span class="math inline">\(2+5 \cdot 3^2\)</span></li>
</ul>
<div class="sourceCode" id="cb5"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb5-1"><a href="#cb5-1" aria-hidden="true" tabindex="-1"></a><span class="dv">2</span> <span class="sc">+</span> (<span class="dv">5</span><span class="sc">*</span>(<span class="dv">3</span><span class="sc">^</span><span class="dv">2</span>))</span></code></pre></div>
<pre><code>## [1] 47</code></pre>
<ul>
<li><span class="math inline">\(\frac{39-4^2}{5}\)</span></li>
</ul>
<div class="sourceCode" id="cb7"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb7-1"><a href="#cb7-1" aria-hidden="true" tabindex="-1"></a>(<span class="dv">39</span><span class="sc">-</span>(<span class="dv">4</span><span class="sc">^</span><span class="dv">2</span>))<span class="sc">/</span><span class="dv">5</span></span></code></pre></div>
<pre><code>## [1] 4.6</code></pre>
<ul>
<li><span class="math inline">\(\frac{39-4^2}{5\cdot6}\)</span></li>
</ul>
<div class="sourceCode" id="cb9"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb9-1"><a href="#cb9-1" aria-hidden="true" tabindex="-1"></a>(<span class="dv">39</span><span class="sc">-</span>(<span class="dv">4</span><span class="sc">^</span><span class="dv">2</span>))<span class="sc">/</span>(<span class="dv">5</span><span class="sc">*</span><span class="dv">6</span>)</span></code></pre></div>
<pre><code>## [1] 0.7666667</code></pre>
<ul>
<li><span class="math inline">\(\frac{39-4^2}{5}\cdot 6\)</span></li>
</ul>
<div class="sourceCode" id="cb11"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb11-1"><a href="#cb11-1" aria-hidden="true" tabindex="-1"></a>((<span class="dv">39</span><span class="sc">-</span>(<span class="dv">4</span><span class="sc">^</span><span class="dv">2</span>))<span class="sc">/</span><span class="dv">5</span>)<span class="sc">*</span><span class="dv">6</span></span></code></pre></div>
<pre><code>## [1] 27.6</code></pre>
<ul>
<li><span class="math inline">\(1-\frac{20}{20}\frac{19}{20}\frac{18}{20}\frac{17}{20}\frac{16}{20}\)</span></li>
</ul>
<div class="sourceCode" id="cb13"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb13-1"><a href="#cb13-1" aria-hidden="true" tabindex="-1"></a><span class="co"># Temos diversas maneiras de fazer essa conta.</span></span>
<span id="cb13-2"><a href="#cb13-2" aria-hidden="true" tabindex="-1"></a><span class="co"># Deixarei dois exemplos:</span></span>
<span id="cb13-3"><a href="#cb13-3" aria-hidden="true" tabindex="-1"></a><span class="dv">1</span><span class="sc">-</span>((<span class="dv">20</span><span class="sc">/</span><span class="dv">20</span>)<span class="sc">*</span>(<span class="dv">19</span><span class="sc">/</span><span class="dv">20</span>)<span class="sc">*</span>(<span class="dv">18</span><span class="sc">/</span><span class="dv">20</span>)<span class="sc">*</span>(<span class="dv">17</span><span class="sc">/</span><span class="dv">20</span>)<span class="sc">*</span>(<span class="dv">16</span><span class="sc">/</span><span class="dv">20</span>))</span></code></pre></div>
<pre><code>## [1] 0.4186</code></pre>
<div class="sourceCode" id="cb15"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb15-1"><a href="#cb15-1" aria-hidden="true" tabindex="-1"></a><span class="dv">1</span><span class="sc">-</span>(<span class="fu">prod</span>(<span class="dv">16</span><span class="sc">:</span><span class="dv">20</span>)<span class="sc">/</span>(<span class="dv">20</span><span class="sc">^</span><span class="dv">5</span>))</span></code></pre></div>
<pre><code>## [1] 0.4186</code></pre>
<ul>
<li><span class="math inline">\(\frac{e^{-2}-2^3}{3!}\)</span></li>
</ul>
<div class="sourceCode" id="cb17"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb17-1"><a href="#cb17-1" aria-hidden="true" tabindex="-1"></a>(<span class="fu">exp</span>(<span class="sc">-</span><span class="dv">2</span>)<span class="sc">-</span>(<span class="dv">2</span><span class="sc">^</span><span class="dv">3</span>))<span class="sc">/</span><span class="fu">factorial</span>(<span class="dv">3</span>)</span></code></pre></div>
<pre><code>## [1] -1.310777</code></pre>
<ul>
<li><span class="math inline">\(5 + \log_{2}8\)</span></li>
</ul>
<div class="sourceCode" id="cb19"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb19-1"><a href="#cb19-1" aria-hidden="true" tabindex="-1"></a><span class="dv">5</span><span class="sc">+</span><span class="fu">log2</span>(<span class="dv">8</span>)</span></code></pre></div>
<pre><code>## [1] 8</code></pre>
<ul>
<li><span class="math inline">\(3 \cdot \log_{10}1000\)</span></li>
</ul>
<div class="sourceCode" id="cb21"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb21-1"><a href="#cb21-1" aria-hidden="true" tabindex="-1"></a><span class="dv">3</span><span class="sc">*</span><span class="fu">log10</span>(<span class="dv">1000</span>)</span></code></pre></div>
<pre><code>## [1] 9</code></pre>
<ul>
<li><span class="math inline">\(-2 \cdot \log_{e}4\)</span></li>
</ul>
<div class="sourceCode" id="cb23"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb23-1"><a href="#cb23-1" aria-hidden="true" tabindex="-1"></a><span class="sc">-</span><span class="dv">2</span><span class="sc">*</span><span class="fu">log</span>(<span class="dv">4</span>)</span></code></pre></div>
<pre><code>## [1] -2.772589</code></pre>
<ul>
<li><span class="math inline">\(\log_{5}80\)</span></li>
</ul>
<div class="sourceCode" id="cb25"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb25-1"><a href="#cb25-1" aria-hidden="true" tabindex="-1"></a><span class="co"># Temos duas maneiras de fazer isso:</span></span>
<span id="cb25-2"><a href="#cb25-2" aria-hidden="true" tabindex="-1"></a><span class="fu">log</span>(<span class="dv">80</span>, <span class="at">base =</span> <span class="dv">5</span>)</span></code></pre></div>
<pre><code>## [1] 2.722706</code></pre>
<div class="sourceCode" id="cb27"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb27-1"><a href="#cb27-1" aria-hidden="true" tabindex="-1"></a>(<span class="fu">log</span>(<span class="dv">80</span>))<span class="sc">/</span>(<span class="fu">log</span>(<span class="dv">5</span>))</span></code></pre></div>
<pre><code>## [1] 2.722706</code></pre>
</div>
</div>
<div id="vetores" class="section level1">
<h1>2 - Vetores</h1>
<div id="criação-de-vetores" class="section level2">
<h2>2.1 - Criação de vetores</h2>
<div class="sourceCode" id="cb29"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb29-1"><a href="#cb29-1" aria-hidden="true" tabindex="-1"></a>a <span class="ot"><-</span> <span class="fu">c</span>(<span class="dv">12</span>,<span class="dv">14</span>,<span class="dv">16</span>,<span class="dv">11</span>,<span class="dv">12</span>,<span class="dv">18</span>,<span class="dv">15</span>,<span class="dv">12</span>,<span class="dv">15</span>)</span>
<span id="cb29-2"><a href="#cb29-2" aria-hidden="true" tabindex="-1"></a>b <span class="ot"><-</span> <span class="fu">c</span>(<span class="dv">3</span>,<span class="dv">7</span>,<span class="dv">11</span>,<span class="dv">15</span>,<span class="dv">19</span>,<span class="dv">23</span>)</span>
<span id="cb29-3"><a href="#cb29-3" aria-hidden="true" tabindex="-1"></a>c <span class="ot"><-</span> <span class="fu">c</span>(<span class="dv">1</span>,<span class="dv">2</span>,<span class="dv">4</span>,<span class="dv">7</span>,<span class="dv">11</span>,<span class="dv">16</span>,<span class="dv">22</span>,<span class="dv">29</span>,<span class="dv">37</span>,<span class="dv">46</span>,<span class="dv">56</span>,<span class="dv">67</span>)</span>
<span id="cb29-4"><a href="#cb29-4" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb29-5"><a href="#cb29-5" aria-hidden="true" tabindex="-1"></a><span class="co"># Alternativamente, podemos utilizar as seguintes leis de formação para b e c:</span></span>
<span id="cb29-6"><a href="#cb29-6" aria-hidden="true" tabindex="-1"></a>(b <span class="ot"><-</span> <span class="fu">seq</span>(<span class="at">from =</span> <span class="dv">3</span>, <span class="at">to =</span> <span class="dv">23</span>, <span class="at">by =</span> <span class="dv">4</span>))</span></code></pre></div>
<pre><code>## [1] 3 7 11 15 19 23</code></pre>
<div class="sourceCode" id="cb31"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb31-1"><a href="#cb31-1" aria-hidden="true" tabindex="-1"></a>c <span class="ot"><-</span> <span class="fu">numeric</span>(<span class="dv">12</span>)</span>
<span id="cb31-2"><a href="#cb31-2" aria-hidden="true" tabindex="-1"></a>c[<span class="dv">1</span>] <span class="ot"><-</span> <span class="dv">1</span></span>
<span id="cb31-3"><a href="#cb31-3" aria-hidden="true" tabindex="-1"></a><span class="cf">for</span>(i <span class="cf">in</span> <span class="dv">2</span><span class="sc">:</span><span class="dv">12</span>){</span>
<span id="cb31-4"><a href="#cb31-4" aria-hidden="true" tabindex="-1"></a> c[i] <span class="ot"><-</span> c[i<span class="dv">-1</span>]<span class="sc">+</span>(i<span class="dv">-1</span>)</span>
<span id="cb31-5"><a href="#cb31-5" aria-hidden="true" tabindex="-1"></a>}</span>
<span id="cb31-6"><a href="#cb31-6" aria-hidden="true" tabindex="-1"></a>c</span></code></pre></div>
<pre><code>## [1] 1 2 4 7 11 16 22 29 37 46 56 67</code></pre>
</div>
<div id="análise-de-vetores" class="section level2">
<h2>2.2 - Análise de vetores</h2>
<ol style="list-style-type: lower-alpha">
<li>Valores únicos em <strong>a</strong>:</li>
</ol>
<div class="sourceCode" id="cb33"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb33-1"><a href="#cb33-1" aria-hidden="true" tabindex="-1"></a><span class="co"># A função unique retorna os valores em um vetor, eliminando valores repetidos:</span></span>
<span id="cb33-2"><a href="#cb33-2" aria-hidden="true" tabindex="-1"></a><span class="fu">unique</span>(a)</span></code></pre></div>
<pre><code>## [1] 12 14 16 11 18 15</code></pre>
<div class="sourceCode" id="cb35"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb35-1"><a href="#cb35-1" aria-hidden="true" tabindex="-1"></a><span class="co"># Para descobrirmos quantos valores únicos a tem, vemos o tamanho de unique(a):</span></span>
<span id="cb35-2"><a href="#cb35-2" aria-hidden="true" tabindex="-1"></a><span class="fu">length</span>(<span class="fu">unique</span>(a))</span></code></pre></div>
<pre><code>## [1] 6</code></pre>
<ol start="2" style="list-style-type: lower-alpha">
<li>Valores em <strong>a</strong> maiores que 13:</li>
</ol>
<div class="sourceCode" id="cb37"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb37-1"><a href="#cb37-1" aria-hidden="true" tabindex="-1"></a><span class="co"># Temos várias maneiras de fazer isso:</span></span>
<span id="cb37-2"><a href="#cb37-2" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb37-3"><a href="#cb37-3" aria-hidden="true" tabindex="-1"></a><span class="co"># A função which() nos retorna a posição dos valores que obedecem a comparação:</span></span>
<span id="cb37-4"><a href="#cb37-4" aria-hidden="true" tabindex="-1"></a><span class="fu">which</span>(a<span class="sc">></span><span class="dv">13</span>)</span></code></pre></div>
<pre><code>## [1] 2 3 6 7 9</code></pre>
<div class="sourceCode" id="cb39"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb39-1"><a href="#cb39-1" aria-hidden="true" tabindex="-1"></a><span class="co"># Com isso, podemos indezar os valores dentro de colchetes []:</span></span>
<span id="cb39-2"><a href="#cb39-2" aria-hidden="true" tabindex="-1"></a>a[<span class="fu">which</span>(a<span class="sc">></span><span class="dv">13</span>)]</span></code></pre></div>
<pre><code>## [1] 14 16 18 15 15</code></pre>
<div class="sourceCode" id="cb41"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb41-1"><a href="#cb41-1" aria-hidden="true" tabindex="-1"></a><span class="co"># Como a comparação é simples, podemos nos livrar do which(), sem perda de generalidade:</span></span>
<span id="cb41-2"><a href="#cb41-2" aria-hidden="true" tabindex="-1"></a>a[a<span class="sc">></span><span class="dv">13</span>]</span></code></pre></div>
<pre><code>## [1] 14 16 18 15 15</code></pre>
<ol start="3" style="list-style-type: lower-alpha">
<li>Soma de <strong>b</strong> e <strong>c</strong>:</li>
</ol>
<div class="sourceCode" id="cb43"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb43-1"><a href="#cb43-1" aria-hidden="true" tabindex="-1"></a>b<span class="sc">+</span>c</span></code></pre></div>
<pre><code>## [1] 4 9 15 22 30 39 25 36 48 61 75 90</code></pre>
<ol start="4" style="list-style-type: lower-alpha">
<li>Valores de <strong>a</strong> divisíveis por 3:</li>
</ol>
<div class="sourceCode" id="cb45"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb45-1"><a href="#cb45-1" aria-hidden="true" tabindex="-1"></a><span class="co"># Para verificar se um número é divisível por outro, o resto da divisão deve ser 0.</span></span>
<span id="cb45-2"><a href="#cb45-2" aria-hidden="true" tabindex="-1"></a><span class="co"># Com a divisão inteira, o resultado retornado é o resto da divisão:</span></span>
<span id="cb45-3"><a href="#cb45-3" aria-hidden="true" tabindex="-1"></a>a<span class="sc">%%</span><span class="dv">3</span></span></code></pre></div>
<pre><code>## [1] 0 2 1 2 0 0 0 0 0</code></pre>
<div class="sourceCode" id="cb47"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb47-1"><a href="#cb47-1" aria-hidden="true" tabindex="-1"></a><span class="co"># Agora usamos a comparação lógica de igualdade == para encontrar os valores que são divisiveis por 3:</span></span>
<span id="cb47-2"><a href="#cb47-2" aria-hidden="true" tabindex="-1"></a>a[a<span class="sc">%%</span><span class="dv">3</span> <span class="sc">==</span> <span class="dv">0</span>]</span></code></pre></div>
<pre><code>## [1] 12 12 18 15 12 15</code></pre>
<div class="sourceCode" id="cb49"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb49-1"><a href="#cb49-1" aria-hidden="true" tabindex="-1"></a><span class="co"># E para saber quantos são, somamos os valores em que essa comparação é verdadeira:</span></span>
<span id="cb49-2"><a href="#cb49-2" aria-hidden="true" tabindex="-1"></a><span class="fu">sum</span>(a<span class="sc">%%</span><span class="dv">3</span><span class="sc">==</span><span class="dv">0</span>)</span></code></pre></div>
<pre><code>## [1] 6</code></pre>
<ol start="5" style="list-style-type: lower-alpha">
<li>Quantas vezes cada valor de <strong>a</strong> aparece:</li>
</ol>
<div class="sourceCode" id="cb51"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb51-1"><a href="#cb51-1" aria-hidden="true" tabindex="-1"></a><span class="co"># Para retornar esse resultado, usamos a função table()</span></span>
<span id="cb51-2"><a href="#cb51-2" aria-hidden="true" tabindex="-1"></a><span class="co"># Que nos apresenta uma tabela de frequência de um dadd vetor:</span></span>
<span id="cb51-3"><a href="#cb51-3" aria-hidden="true" tabindex="-1"></a><span class="fu">table</span>(a)</span></code></pre></div>
<pre><code>## a
## 11 12 14 15 16 18
## 1 3 1 2 1 1</code></pre>
<ol start="6" style="list-style-type: lower-alpha">
<li>Valor mais frequente de <strong>a</strong>:</li>
</ol>
<div class="sourceCode" id="cb53"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb53-1"><a href="#cb53-1" aria-hidden="true" tabindex="-1"></a><span class="co"># Usaremos a função which.max para isso:</span></span>
<span id="cb53-2"><a href="#cb53-2" aria-hidden="true" tabindex="-1"></a><span class="fu">which.max</span>(<span class="fu">table</span>(a))</span></code></pre></div>
<pre><code>## 12
## 2</code></pre>
<div class="sourceCode" id="cb55"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb55-1"><a href="#cb55-1" aria-hidden="true" tabindex="-1"></a><span class="co"># Percebe-se o problema, pois é retornado o número 12</span></span>
<span id="cb55-2"><a href="#cb55-2" aria-hidden="true" tabindex="-1"></a><span class="co"># Que é o valor que mais aparece, mas com o número 2 abaixo</span></span>
<span id="cb55-3"><a href="#cb55-3" aria-hidden="true" tabindex="-1"></a><span class="co"># Que não é a quantidade de vezes que ele aparece, mas sim a posição do 12.</span></span>
<span id="cb55-4"><a href="#cb55-4" aria-hidden="true" tabindex="-1"></a><span class="co"># Para encontrar o valor que mais aparece e quantas vezes, vamos indexar o vetor:</span></span>
<span id="cb55-5"><a href="#cb55-5" aria-hidden="true" tabindex="-1"></a><span class="fu">table</span>(a)[<span class="fu">which.max</span>(<span class="fu">table</span>(a))]</span></code></pre></div>
<pre><code>## 12
## 3</code></pre>
</div>
<div id="criação-de-vetores-por-sequências" class="section level2">
<h2>2.3 - Criação de vetores por sequências</h2>
<ol style="list-style-type: lower-alpha">
<li></li>
</ol>
<div class="sourceCode" id="cb57"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb57-1"><a href="#cb57-1" aria-hidden="true" tabindex="-1"></a><span class="co"># Usaremos o argumento each para especificar quantas vezes cada elemento será repetido</span></span>
<span id="cb57-2"><a href="#cb57-2" aria-hidden="true" tabindex="-1"></a><span class="fu">rep</span>(<span class="fu">c</span>(<span class="dv">1</span>,<span class="dv">2</span>,<span class="dv">3</span>,<span class="dv">4</span>,<span class="dv">5</span>), <span class="at">each =</span> <span class="dv">3</span>)</span></code></pre></div>
<pre><code>## [1] 1 1 1 2 2 2 3 3 3 4 4 4 5 5 5</code></pre>
<ol start="2" style="list-style-type: lower-alpha">
<li></li>
</ol>
<div class="sourceCode" id="cb59"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb59-1"><a href="#cb59-1" aria-hidden="true" tabindex="-1"></a><span class="co"># Usaremos o argumento times para especificar quantas vezes o vetor (inteiro) será repetido</span></span>
<span id="cb59-2"><a href="#cb59-2" aria-hidden="true" tabindex="-1"></a><span class="fu">rep</span>(<span class="fu">c</span>(<span class="dv">1</span>,<span class="dv">2</span>,<span class="dv">3</span>),<span class="at">times =</span> <span class="dv">5</span>)</span></code></pre></div>
<pre><code>## [1] 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3</code></pre>
<ol start="3" style="list-style-type: lower-alpha">
<li></li>
</ol>
<div class="sourceCode" id="cb61"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb61-1"><a href="#cb61-1" aria-hidden="true" tabindex="-1"></a><span class="co"># Podemos repetir um vetor criado por outra função, como o seq(), que cria uma sequência</span></span>
<span id="cb61-2"><a href="#cb61-2" aria-hidden="true" tabindex="-1"></a><span class="fu">rep</span>(<span class="fu">seq</span>(<span class="dv">1</span><span class="sc">:</span><span class="dv">10</span>),<span class="at">times =</span> <span class="dv">2</span>)</span></code></pre></div>
<pre><code>## [1] 1 2 3 4 5 6 7 8 9 10 1 2 3 4 5 6 7 8 9 10</code></pre>
<ol start="4" style="list-style-type: lower-alpha">
<li></li>
</ol>
<div class="sourceCode" id="cb63"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb63-1"><a href="#cb63-1" aria-hidden="true" tabindex="-1"></a><span class="co"># Na função seq podemos especificar o começo (from), o final (to) e o tamanho de cada "passo" (by)</span></span>
<span id="cb63-2"><a href="#cb63-2" aria-hidden="true" tabindex="-1"></a><span class="fu">seq</span>(<span class="at">from =</span> <span class="fl">0.5</span>, <span class="at">to =</span> <span class="fl">7.5</span>, <span class="at">by =</span> <span class="dv">1</span>)</span></code></pre></div>
<pre><code>## [1] 0.5 1.5 2.5 3.5 4.5 5.5 6.5 7.5</code></pre>
<ol start="5" style="list-style-type: lower-alpha">
<li></li>
</ol>
<div class="sourceCode" id="cb65"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb65-1"><a href="#cb65-1" aria-hidden="true" tabindex="-1"></a><span class="co"># Para valores inteiros, ao invés de usar a função seq, podemos usar : para criar a sequência:</span></span>
<span id="cb65-2"><a href="#cb65-2" aria-hidden="true" tabindex="-1"></a><span class="sc">-</span><span class="dv">3</span><span class="sc">:</span><span class="dv">3</span></span></code></pre></div>
<pre><code>## [1] -3 -2 -1 0 1 2 3</code></pre>
<ol start="6" style="list-style-type: lower-alpha">
<li></li>
</ol>
<div class="sourceCode" id="cb67"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb67-1"><a href="#cb67-1" aria-hidden="true" tabindex="-1"></a><span class="co"># Se quisermos repetir cada um dos valores uma quantidade de vezes diferente</span></span>
<span id="cb67-2"><a href="#cb67-2" aria-hidden="true" tabindex="-1"></a><span class="co"># Precisaremos colocar dois vetores: o primeiro é o vetor a ser repetido</span></span>
<span id="cb67-3"><a href="#cb67-3" aria-hidden="true" tabindex="-1"></a><span class="co"># E o segundo deve conter quantas vezes cada elemento será repetido (em ordem)</span></span>
<span id="cb67-4"><a href="#cb67-4" aria-hidden="true" tabindex="-1"></a><span class="fu">rep</span>(<span class="fu">c</span>(<span class="dv">10</span>,<span class="dv">15</span>,<span class="dv">13</span>),<span class="fu">c</span>(<span class="dv">2</span>,<span class="dv">5</span>,<span class="dv">3</span>))</span></code></pre></div>
<pre><code>## [1] 10 10 15 15 15 15 15 13 13 13</code></pre>
<ol start="7" style="list-style-type: lower-alpha">
<li></li>
</ol>
<div class="sourceCode" id="cb69"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb69-1"><a href="#cb69-1" aria-hidden="true" tabindex="-1"></a><span class="co"># Usaremos o mesmo princípio do item anterior, mas usaremos uma sequência ao invés de vetores feitos à mão:</span></span>
<span id="cb69-2"><a href="#cb69-2" aria-hidden="true" tabindex="-1"></a><span class="fu">rep</span>(<span class="dv">1</span><span class="sc">:</span><span class="dv">5</span>,<span class="dv">1</span><span class="sc">:</span><span class="dv">5</span>)</span></code></pre></div>
<pre><code>## [1] 1 2 2 3 3 3 4 4 4 4 5 5 5 5 5</code></pre>
<ol start="8" style="list-style-type: lower-alpha">
<li></li>
</ol>
<div class="sourceCode" id="cb71"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb71-1"><a href="#cb71-1" aria-hidden="true" tabindex="-1"></a><span class="co"># Podemos usar a função seq (ou :) tanto de maneira crescente, quanto decrescente:</span></span>
<span id="cb71-2"><a href="#cb71-2" aria-hidden="true" tabindex="-1"></a><span class="fu">rep</span>(<span class="dv">10</span><span class="sc">:</span><span class="dv">7</span>,<span class="dv">5</span><span class="sc">:</span><span class="dv">2</span>)</span></code></pre></div>
<pre><code>## [1] 10 10 10 10 10 9 9 9 9 8 8 8 7 7</code></pre>
</div>
<div id="manipulação-de-vetores" class="section level2">
<h2>2.4 - Manipulação de vetores</h2>
<div id="usando-dois-vetores" class="section level3">
<h3>2.4.1 - Usando dois vetores</h3>
<ol style="list-style-type: lower-alpha">
<li></li>
</ol>
<div class="sourceCode" id="cb73"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb73-1"><a href="#cb73-1" aria-hidden="true" tabindex="-1"></a>Estado <span class="ot"><-</span> <span class="fu">c</span>(<span class="st">"RS"</span>,<span class="st">"SC"</span>,<span class="st">"PR"</span>,<span class="st">"SP"</span>,<span class="st">"MG"</span>,<span class="st">"RJ"</span>,<span class="st">"ES"</span>)</span>
<span id="cb73-2"><a href="#cb73-2" aria-hidden="true" tabindex="-1"></a>PIB <span class="ot"><-</span> <span class="fu">c</span>(<span class="dv">42406</span>,<span class="dv">45118</span>,<span class="dv">40788</span>,<span class="dv">51140</span>,<span class="dv">30794</span>,<span class="dv">45174</span>,<span class="dv">34177</span>)</span></code></pre></div>
<ol start="2" style="list-style-type: lower-alpha">
<li></li>
</ol>
<div class="sourceCode" id="cb74"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb74-1"><a href="#cb74-1" aria-hidden="true" tabindex="-1"></a><span class="co"># Média</span></span>
<span id="cb74-2"><a href="#cb74-2" aria-hidden="true" tabindex="-1"></a><span class="fu">mean</span>(PIB)</span></code></pre></div>
<pre><code>## [1] 41371</code></pre>
<div class="sourceCode" id="cb76"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb76-1"><a href="#cb76-1" aria-hidden="true" tabindex="-1"></a><span class="co"># Mediana</span></span>
<span id="cb76-2"><a href="#cb76-2" aria-hidden="true" tabindex="-1"></a><span class="fu">median</span>(PIB)</span></code></pre></div>
<pre><code>## [1] 42406</code></pre>
<div class="sourceCode" id="cb78"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb78-1"><a href="#cb78-1" aria-hidden="true" tabindex="-1"></a><span class="co"># Desvio-Padrão</span></span>
<span id="cb78-2"><a href="#cb78-2" aria-hidden="true" tabindex="-1"></a><span class="fu">sd</span>(PIB)</span></code></pre></div>
<pre><code>## [1] 6939.907</code></pre>
<div class="sourceCode" id="cb80"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb80-1"><a href="#cb80-1" aria-hidden="true" tabindex="-1"></a><span class="co"># Coeficiente de Variação</span></span>
<span id="cb80-2"><a href="#cb80-2" aria-hidden="true" tabindex="-1"></a><span class="fu">sd</span>(PIB)<span class="sc">/</span><span class="fu">mean</span>(PIB)</span></code></pre></div>
<pre><code>## [1] 0.1677481</code></pre>
<ol start="3" style="list-style-type: lower-alpha">
<li></li>
</ol>
<div class="sourceCode" id="cb82"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb82-1"><a href="#cb82-1" aria-hidden="true" tabindex="-1"></a><span class="co"># Para encontrar os valores máximo e mínimo, usamos a função max() e min():</span></span>
<span id="cb82-2"><a href="#cb82-2" aria-hidden="true" tabindex="-1"></a><span class="fu">max</span>(PIB)</span></code></pre></div>
<pre><code>## [1] 51140</code></pre>
<div class="sourceCode" id="cb84"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb84-1"><a href="#cb84-1" aria-hidden="true" tabindex="-1"></a><span class="fu">min</span>(PIB)</span></code></pre></div>
<pre><code>## [1] 30794</code></pre>
<div class="sourceCode" id="cb86"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb86-1"><a href="#cb86-1" aria-hidden="true" tabindex="-1"></a><span class="co"># Para encontrar a quais estados esses valores correspondem, iremos indexar de maneira cruzada:</span></span>
<span id="cb86-2"><a href="#cb86-2" aria-hidden="true" tabindex="-1"></a>Estado[<span class="fu">which.max</span>(PIB)]</span></code></pre></div>
<pre><code>## [1] "SP"</code></pre>
<div class="sourceCode" id="cb88"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb88-1"><a href="#cb88-1" aria-hidden="true" tabindex="-1"></a>Estado[<span class="fu">which.min</span>(PIB)]</span></code></pre></div>
<pre><code>## [1] "MG"</code></pre>
<ol start="4" style="list-style-type: lower-alpha">
<li></li>
</ol>
<div class="sourceCode" id="cb90"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb90-1"><a href="#cb90-1" aria-hidden="true" tabindex="-1"></a><span class="co"># De maneira similar ao item anterior, vamos primeiro encontrar as posições e depois os estados:</span></span>
<span id="cb90-2"><a href="#cb90-2" aria-hidden="true" tabindex="-1"></a><span class="fu">which</span>(PIB<span class="sc">></span><span class="dv">40000</span>)</span></code></pre></div>
<pre><code>## [1] 1 2 3 4 6</code></pre>
<div class="sourceCode" id="cb92"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb92-1"><a href="#cb92-1" aria-hidden="true" tabindex="-1"></a>PIB[PIB<span class="sc">></span><span class="dv">40000</span>]</span></code></pre></div>
<pre><code>## [1] 42406 45118 40788 51140 45174</code></pre>
<div class="sourceCode" id="cb94"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb94-1"><a href="#cb94-1" aria-hidden="true" tabindex="-1"></a>Estado[<span class="fu">which</span>(PIB<span class="sc">></span><span class="dv">40000</span>)]</span></code></pre></div>
<pre><code>## [1] "RS" "SC" "PR" "SP" "RJ"</code></pre>
<div class="sourceCode" id="cb96"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb96-1"><a href="#cb96-1" aria-hidden="true" tabindex="-1"></a><span class="co"># Agora, para encontrar o valor mediano desses estados, podemos utilizar median() somente sobre os valores filtrados:</span></span>
<span id="cb96-2"><a href="#cb96-2" aria-hidden="true" tabindex="-1"></a><span class="fu">median</span>(PIB[PIB<span class="sc">></span><span class="dv">40000</span>])</span></code></pre></div>
<pre><code>## [1] 45118</code></pre>
<ol start="5" style="list-style-type: lower-alpha">
<li></li>
</ol>
<div class="sourceCode" id="cb98"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb98-1"><a href="#cb98-1" aria-hidden="true" tabindex="-1"></a><span class="co"># Para encontrarmos a proporção, vamos dividir o tamanho de um vetor filtrado pelo original:</span></span>
<span id="cb98-2"><a href="#cb98-2" aria-hidden="true" tabindex="-1"></a><span class="fu">length</span>(PIB[PIB<span class="sc"><</span><span class="dv">42000</span>]) <span class="sc">/</span> <span class="fu">length</span>(PIB)</span></code></pre></div>
<pre><code>## [1] 0.4285714</code></pre>
<div class="sourceCode" id="cb100"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb100-1"><a href="#cb100-1" aria-hidden="true" tabindex="-1"></a><span class="co"># Agora vamos encontrar os estados correspondentes:</span></span>
<span id="cb100-2"><a href="#cb100-2" aria-hidden="true" tabindex="-1"></a>Estado[<span class="fu">which</span>(PIB<span class="sc"><</span><span class="dv">42000</span>)]</span></code></pre></div>
<pre><code>## [1] "PR" "MG" "ES"</code></pre>
<div class="sourceCode" id="cb102"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb102-1"><a href="#cb102-1" aria-hidden="true" tabindex="-1"></a><span class="co"># Calculamos agora a média de maneira similar ao item anterior:</span></span>
<span id="cb102-2"><a href="#cb102-2" aria-hidden="true" tabindex="-1"></a><span class="fu">mean</span>(PIB[PIB<span class="sc"><</span><span class="dv">42000</span>])</span></code></pre></div>
<pre><code>## [1] 35253</code></pre>
<ol start="6" style="list-style-type: lower-alpha">
<li></li>
</ol>
<div class="sourceCode" id="cb104"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb104-1"><a href="#cb104-1" aria-hidden="true" tabindex="-1"></a><span class="co"># Podemos fazer a comparação com uma função no filtro:</span></span>
<span id="cb104-2"><a href="#cb104-2" aria-hidden="true" tabindex="-1"></a>PIB[PIB<span class="sc">></span><span class="fu">mean</span>(PIB)]</span></code></pre></div>
<pre><code>## [1] 42406 45118 51140 45174</code></pre>
<div class="sourceCode" id="cb106"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb106-1"><a href="#cb106-1" aria-hidden="true" tabindex="-1"></a><span class="co"># Agora para encontrar os estados:</span></span>
<span id="cb106-2"><a href="#cb106-2" aria-hidden="true" tabindex="-1"></a>Estado[<span class="fu">which</span>(PIB<span class="sc">></span><span class="fu">mean</span>(PIB))]</span></code></pre></div>
<pre><code>## [1] "RS" "SC" "SP" "RJ"</code></pre>
<ol start="7" style="list-style-type: lower-alpha">
<li></li>
</ol>
<div class="sourceCode" id="cb108"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb108-1"><a href="#cb108-1" aria-hidden="true" tabindex="-1"></a><span class="co"># Para reordenar os estados, vamos usar a função order(), que coloca vetores de strings (texto) em ordem alfabética:</span></span>
<span id="cb108-2"><a href="#cb108-2" aria-hidden="true" tabindex="-1"></a><span class="fu">order</span>(Estado)</span></code></pre></div>
<pre><code>## [1] 7 5 3 6 1 2 4</code></pre>
<div class="sourceCode" id="cb110"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb110-1"><a href="#cb110-1" aria-hidden="true" tabindex="-1"></a><span class="co"># Agora que temos a ordem alfabética dos estados, podemos indexar os dois:</span></span>
<span id="cb110-2"><a href="#cb110-2" aria-hidden="true" tabindex="-1"></a>Estado[<span class="fu">order</span>(Estado)]</span></code></pre></div>
<pre><code>## [1] "ES" "MG" "PR" "RJ" "RS" "SC" "SP"</code></pre>
<div class="sourceCode" id="cb112"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb112-1"><a href="#cb112-1" aria-hidden="true" tabindex="-1"></a><span class="co"># Para os valores usamos o mesmo método anteriormente, ainda com relação aos estados:</span></span>
<span id="cb112-2"><a href="#cb112-2" aria-hidden="true" tabindex="-1"></a>PIB[<span class="fu">order</span>(Estado)]</span></code></pre></div>
<pre><code>## [1] 34177 30794 40788 45174 42406 45118 51140</code></pre>
<ol start="8" style="list-style-type: lower-alpha">
<li></li>
</ol>
<div class="sourceCode" id="cb114"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb114-1"><a href="#cb114-1" aria-hidden="true" tabindex="-1"></a><span class="co"># A função order() aplicada a vetores numéricos retorna a ordem crescente:</span></span>
<span id="cb114-2"><a href="#cb114-2" aria-hidden="true" tabindex="-1"></a><span class="fu">order</span>(PIB)</span></code></pre></div>
<pre><code>## [1] 5 7 3 1 2 6 4</code></pre>
<div class="sourceCode" id="cb116"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb116-1"><a href="#cb116-1" aria-hidden="true" tabindex="-1"></a><span class="co"># Para retornar de maneira decrescente, usamos o argumento decreasing = TRUE:</span></span>
<span id="cb116-2"><a href="#cb116-2" aria-hidden="true" tabindex="-1"></a><span class="fu">order</span>(PIB, <span class="at">decreasing =</span> <span class="cn">TRUE</span>)</span></code></pre></div>
<pre><code>## [1] 4 6 2 1 3 7 5</code></pre>
<div class="sourceCode" id="cb118"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb118-1"><a href="#cb118-1" aria-hidden="true" tabindex="-1"></a><span class="co"># Agora ordenamos os vetores como no exemplo anterior:</span></span>
<span id="cb118-2"><a href="#cb118-2" aria-hidden="true" tabindex="-1"></a>PIB[<span class="fu">order</span>(PIB, <span class="at">decreasing =</span> <span class="cn">TRUE</span>)]</span></code></pre></div>
<pre><code>## [1] 51140 45174 45118 42406 40788 34177 30794</code></pre>
<div class="sourceCode" id="cb120"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb120-1"><a href="#cb120-1" aria-hidden="true" tabindex="-1"></a>Estado[<span class="fu">order</span>(PIB, <span class="at">decreasing =</span> <span class="cn">TRUE</span>)]</span></code></pre></div>
<pre><code>## [1] "SP" "RJ" "SC" "RS" "PR" "ES" "MG"</code></pre>
</div>
<div id="usando-um-vetor-nomeado" class="section level3">
<h3>2.4.2 - Usando um vetor nomeado</h3>
<p>Para criarmos um vetor nomeado, temos dois métodos: adicionar nomes a
um vetor ou nomear o vetor na criação:</p>
<div class="sourceCode" id="cb122"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb122-1"><a href="#cb122-1" aria-hidden="true" tabindex="-1"></a><span class="co"># Vamos começar com a nomeação interna:</span></span>
<span id="cb122-2"><a href="#cb122-2" aria-hidden="true" tabindex="-1"></a>(PIB2 <span class="ot"><-</span> <span class="fu">c</span>(<span class="at">RS =</span> <span class="dv">42406</span>, <span class="at">SC =</span> <span class="dv">45118</span>, <span class="at">PR =</span> <span class="dv">40788</span>, <span class="at">SP =</span> <span class="dv">51140</span>, <span class="at">MG =</span> <span class="dv">30794</span>, <span class="at">RJ =</span> <span class="dv">45174</span>, <span class="at">ES =</span> <span class="dv">34177</span>))</span></code></pre></div>
<pre><code>## RS SC PR SP MG RJ ES
## 42406 45118 40788 51140 30794 45174 34177</code></pre>
<div class="sourceCode" id="cb124"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb124-1"><a href="#cb124-1" aria-hidden="true" tabindex="-1"></a><span class="co"># Outra maneira é definindo o argumento extermo names() do vetor:</span></span>
<span id="cb124-2"><a href="#cb124-2" aria-hidden="true" tabindex="-1"></a>PIB3 <span class="ot"><-</span> PIB</span>
<span id="cb124-3"><a href="#cb124-3" aria-hidden="true" tabindex="-1"></a><span class="fu">names</span>(PIB3) <span class="ot"><-</span> Estado</span>
<span id="cb124-4"><a href="#cb124-4" aria-hidden="true" tabindex="-1"></a>PIB3</span></code></pre></div>
<pre><code>## RS SC PR SP MG RJ ES
## 42406 45118 40788 51140 30794 45174 34177</code></pre>
<p>Como agora temos um vetor que possui nomes para os seus elementos, a
maioria dos exercícios anteriores é feita de maneira direta. Mas vale
lembrar que os valores desse vetor são os do PIB <em>per Capita</em>, e
que todas as operações serão feitas com eles. A título de exemplo,
faremos os exercícios <strong>f</strong> e <strong>g</strong>:</p>
<div class="sourceCode" id="cb126"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb126-1"><a href="#cb126-1" aria-hidden="true" tabindex="-1"></a><span class="co"># f:</span></span>
<span id="cb126-2"><a href="#cb126-2" aria-hidden="true" tabindex="-1"></a>PIB2[<span class="fu">which</span>(PIB2<span class="sc">></span><span class="fu">mean</span>(PIB2))]</span></code></pre></div>
<pre><code>## RS SC SP RJ
## 42406 45118 51140 45174</code></pre>
</div>
</div>
</div>
</section>
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