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<!DOCTYPE html>
<html lang="en"><head>
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<meta name="author" content="Nicola Rennie">
<title>Introduction to Statistics</title>
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div.callout-warning {
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div.callout-warning.callout-style-default .callout-title {
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}
div.callout-tip {
border-left-color: #02b875 !important;
}
div.callout-tip .callout-icon::before {
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div.callout-caution {
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<style type="text/css">
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}
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<link rel="stylesheet" href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/6.5.1/css/all.min.css" integrity="sha512-DTOQO9RWCH3ppGqcWaEA1BIZOC6xxalwEsw9c2QQeAIftl+Vegovlnee1c9QX4TctnWMn13TZye+giMm8e2LwA==" crossorigin="anonymous" referrerpolicy="no-referrer">
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background-color: unset !important;
}
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width: 100%;
display: flex;
justify-content: space-between;
box-sizing: border-box;
}
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display: flex;
}
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display: flex;
background-color: rgba(250, 250, 250, 0.65);
border: 1px solid rgba(233, 236, 239, 0.65);
border-radius: 0.5rem;
margin-top: 15px;
margin-bottom: 15px;
}
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color: #2767B0; /* R Project's blue color */
}
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color: #7894c4;
}
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color: #0d9c29
}
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color: #111;
}
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color: #db4133;
}
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border: 1px solid #EEEEEE;
}
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background-color: #EEEEEE;
padding: 0.2rem 0.5rem;
}
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background-color: #EEEEEE;
display: inline-block;
font-weight: 400;
line-height: 1;
text-decoration: none;
text-align: center;
color: #000;
border-color: #dee2e6;
border: 1px solid rgba(0,0,0,0);
padding: 0.375rem 0.75rem;
font-size: .9rem;
border-radius: 0.25rem;
transition: color .15s ease-in-out,background-color .15s ease-in-out,border-color .15s ease-in-out,box-shadow .15s ease-in-out;
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color: #000;
background-color: #d9dce0;
border-color: #c8ccd0;
}
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pointer-events: none;
opacity: .65
}
.qpyodide-button-reset {
color: #696969; /*#4682b4;*/
}
.qpyodide-button-copy {
color: #696969;
}
/* Custom styling for RevealJS Presentations*/
/* Reset the style of the interactive area */
.reveal div.qpyodide-interactive-area {
display: block;
box-shadow: none;
max-width: 100%;
max-height: 100%;
margin: 0;
padding: 0;
}
/* Provide space to entries */
.reveal div.qpyodide-output-code-area pre div {
margin: 1px 2px 1px 10px;
}
/* Collapse the inside code tags to avoid extra space between line outputs */
.reveal pre div code.qpyodide-output-code-stdout, .reveal pre div code.qpyodide-output-code-stderr {
padding: 0;
display: contents;
}
.reveal pre div code.qpyodide-output-code-stdout {
color: #111;
}
.reveal pre div code.qpyodide-output-code-stderr {
color: #db4133;
}
/* Create a border around console and output (does not effect graphs) */
.reveal div.qpyodide-console-area {
border: 1px solid #EEEEEE;
box-shadow: 2px 2px 10px #EEEEEE;
}
/* Cap output height and allow text to scroll */
/* TODO: Is there a better way to fit contents/max it parallel to the monaco editor size? */
.reveal div.qpyodide-output-code-area pre {
max-height: 400px;
overflow: scroll;
}
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<script type="module">
// Declare startupMessageqpyodide globally
globalThis.qpyodideStartupMessage = document.createElement("p");
// Function to set the button text
globalThis.qpyodideSetInteractiveButtonState = function(buttonText, enableCodeButton = true) {
document.querySelectorAll(".qpyodide-button-run").forEach((btn) => {
btn.innerHTML = buttonText;
btn.disabled = !enableCodeButton;
});
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<section id="title-slide" class="quarto-title-block center">
<h1 class="title">Introduction to Statistics</h1>
<div class="quarto-title-authors">
<div class="quarto-title-author">
<div class="quarto-title-author-name">
Nicola Rennie
</div>
</div>
</div>
</section>
<section>
<section id="descriptive-statistics" class="title-slide slide level1 center" data-background-color="#1A936F">
<h1>Descriptive statistics</h1>
<p>Descriptive statistics provide a summary that quantitatively describes a sample of data.</p>
</section>
<section id="population" class="slide level2">
<h2>Population</h2>
<p><strong>Population</strong> refers to the entire group of individuals that we want to draw conclusions about.</p>
<img data-src="index_files/figure-revealjs/pop-people-1.png" class="quarto-figure quarto-figure-center r-stretch" width="960"></section>
<section id="sample" class="slide level2">
<h2>Sample</h2>
<p><strong>Sample</strong> refers to the (usually smaller) group of people for which we have collected data on.</p>
<img data-src="index_files/figure-revealjs/samp-people-1.png" class="quarto-figure quarto-figure-center r-stretch" width="960"></section>
<section id="generate-sample-data" class="slide level2 scrollable">
<h2>Generate sample data</h2>
<p>For the examples later, let’s create a population of data in Python:</p>
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</section>
<section id="generate-sample-data-1" class="slide level2 scrollable">
<h2>Generate sample data</h2>
<p>… and draw a sample from it:</p>
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<p><br></p>
<div class="fragment">
<p>What do the values look like?</p>
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</section>
<section id="mean" class="slide level2">
<h2>Mean</h2>
<p>The mean, often simply called the <em>average</em>, is defined as <em>the sum of all values divided by the number of values</em>. It’s a measure of central tendency that tells us what’s happening near the middle of the data.</p>
<div style="text-align: center;">
<p><span class="math inline">\(\bar{x} = \frac{1}{n} \sum_{i=i}^{n} x_{i}\)</span></p>
</div>
<p><br></p>
<div class="fragment">
<p>In Python, we use the <code>mean()</code> function from <code>numpy</code>:</p>
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</section>
<section id="median" class="slide level2">
<h2>Median</h2>
<p>The median of a dataset is the middle value when the data is arranged in ascending order, or the average of the two middle values if the dataset has an even number of observations.</p>
<p><br></p>
<div class="fragment">
<p>In Python, we use the <code>median()</code> function from <code>numpy</code>:</p>
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</section>
<section id="mode" class="slide level2">
<h2>Mode</h2>
<p>The mode statistic represents the value that appears most frequently in a dataset.</p>
<p><br></p>
<div class="fragment">
<p>In Python, we use the <code>mode()</code> function from <code>statistics</code>:</p>
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</section>
<section id="range" class="slide level2">
<h2>Range</h2>
<p>The range is the difference between the maximum and minimum values in a dataset.</p>
<p><br></p>
<div class="fragment">
<p>In Python, we can use the <code>max()</code> and <code>min()</code> function and subtract the values:</p>
<div id="qpyodide-insertion-location-7"></div>
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<p>Or, we can use the <code>ptp()</code> function from <code>numpy</code>:</p>
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</div>
</section>
<section id="sample-variance" class="slide level2">
<h2>Sample variance</h2>
<p>The sample variance tells us about how spread out the data is. A lower variance indicates that values tend to be close to the mean, and a higher variance indicates that the values are spread out over a wider range.</p>
<div style="text-align: center;">
<p><span class="math inline">\(s^2 = \frac{\Sigma_{i= 1}^{N} (x_i - \bar{x})^2}{n-1}\)</span></p>
</div>
<p><br></p>
<div class="fragment">
<p>In Python, we use the <code>var()</code> function from <code>numpy</code>:</p>
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</section>
<section id="sample-standard-deviation" class="slide level2">
<h2>Sample standard deviation</h2>
<p>The sample standard deviation is the square root of the variance. It also tells us about how spread out the data is.</p>
<div style="text-align: center;">
<p><span class="math inline">\(s = \sqrt{\frac{\Sigma_{i= 1}^{N} (x_i - \bar{x})^2}{n-1}}\)</span></p>
</div>
<p><br></p>
<div class="fragment">
<p>In Python, we use the <code>std()</code> function from <code>numpy</code>:</p>
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</div>
</section>
<section id="descriptive-statistics-1" class="slide level2">
<h2>Descriptive statistics</h2>
<p>Descriptive statistics provide a summary that quantitatively describes a sample of data.</p>
<ul>
<li>Mean: The sum of the values divided by the number of values.</li>
<li>Median: The middle value of the data when it’s sorted.</li>
<li>Mode: The value that appears most frequently.</li>
<li>Range: The difference between the maximum and minimum values.</li>
<li>Variance: The average of the squared differences from the mean.</li>
<li>Standard deviation: The square root of the variance.</li>
</ul>
</section>
<section id="exercise" class="slide level2">
<h2>Exercise</h2>
<p>In Python:</p>
<ul>
<li>Import <code>numpy</code> and <code>statistics</code>.</li>
<li>Import <code>data</code> from <code>pydataset</code> using <code>from pydataset import data</code></li>
<li>Load the <code>housing</code> data set using <code>housing = data('Housing')</code></li>
<li>Calculate the mean, median, mode, range, variance, and standard deviation of house prices.</li>
</ul>
<blockquote>
<p>Remember: you can extract a column in Python using <code>dataset['column_name']</code>.</p>
</blockquote>
</section>
<section id="exercise-solutions" class="slide level2">
<h2>Exercise solutions</h2>
<div class="cell">
<div class="sourceCode cell-code" id="cb1"><pre class="sourceCode numberSource python number-lines code-with-copy"><code class="sourceCode python"><span id="cb1-1"><a href=""></a><span class="im">import</span> numpy <span class="im">as</span> np</span>
<span id="cb1-2"><a href=""></a><span class="im">import</span> statistics</span>
<span id="cb1-3"><a href=""></a><span class="im">from</span> pydataset <span class="im">import</span> data</span>
<span id="cb1-4"><a href=""></a></span>
<span id="cb1-5"><a href=""></a><span class="co"># load data</span></span>
<span id="cb1-6"><a href=""></a>housing <span class="op">=</span> data(<span class="st">'Housing'</span>)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
</div>
</section>
<section id="exercise-solutions-1" class="slide level2">
<h2>Exercise solutions</h2>
<div class="cell">
<div class="sourceCode cell-code" id="cb2"><pre class="sourceCode numberSource python number-lines code-with-copy"><code class="sourceCode python"><span id="cb2-1"><a href=""></a><span class="co"># summary statistics</span></span>
<span id="cb2-2"><a href=""></a>np.mean(housing[<span class="st">'price'</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>68121.59706959708</code></pre>
</div>
<div class="sourceCode cell-code" id="cb4"><pre class="sourceCode numberSource python number-lines code-with-copy"><code class="sourceCode python"><span id="cb4-1"><a href=""></a>np.median(housing[<span class="st">'price'</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>62000.0</code></pre>
</div>
<div class="sourceCode cell-code" id="cb6"><pre class="sourceCode numberSource python number-lines code-with-copy"><code class="sourceCode python"><span id="cb6-1"><a href=""></a>statistics.mode(housing[<span class="st">'price'</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>60000.0</code></pre>
</div>
<div class="sourceCode cell-code" id="cb8"><pre class="sourceCode numberSource python number-lines code-with-copy"><code class="sourceCode python"><span id="cb8-1"><a href=""></a><span class="bu">max</span>(housing[<span class="st">'price'</span>]) <span class="op">-</span> <span class="bu">min</span>(housing[<span class="st">'price'</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>165000.0</code></pre>
</div>
<div class="sourceCode cell-code" id="cb10"><pre class="sourceCode numberSource python number-lines code-with-copy"><code class="sourceCode python"><span id="cb10-1"><a href=""></a>np.var(housing[<span class="st">'price'</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>711726713.9951562</code></pre>
</div>
<div class="sourceCode cell-code" id="cb12"><pre class="sourceCode numberSource python number-lines code-with-copy"><code class="sourceCode python"><span id="cb12-1"><a href=""></a>np.std(housing[<span class="st">'price'</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>26678.206723750307</code></pre>
</div>
</div>
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