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@ -136,7 +136,10 @@ For a continuous probability distribution, the median is the value such that a n
<h2>Implementation in python without using the scientific libraries</h2>
<div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">median</span><span class="p">(</span><span class="n">l</span><span class="p">):</span>
<span class="n">l</span> <span class="o">=</span> <span class="nb">sorted</span><span class="p">(</span><span class="n">l</span><span class="p">)</span>
<span class="k">return</span> <span class="p">(</span><span class="n">l</span><span class="p">[</span><span class="nb">len</span><span class="p">(</span><span class="n">l</span><span class="p">)</span> <span class="o">//</span> <span class="mi">2</span><span class="p">]</span> <span class="o">+</span> <span class="n">l</span><span class="p">[(</span><span class="nb">len</span><span class="p">(</span><span class="n">l</span><span class="p">)</span><span class="o">//</span><span class="mi">2</span> <span class="o">-</span> <span class="mi">1</span><span class="p">)])</span> <span class="o">/</span> <span class="mi">2</span>
<span class="k">if</span> <span class="nb">len</span><span class="p">(</span><span class="n">l</span><span class="p">)</span> <span class="o">%</span> <span class="mi">2</span> <span class="o">==</span> <span class="mi">0</span><span class="p">:</span>
<span class="k">return</span> <span class="p">(</span><span class="n">l</span><span class="p">[</span><span class="nb">len</span><span class="p">(</span><span class="n">l</span><span class="p">)</span> <span class="o">//</span> <span class="mi">2</span><span class="p">]</span> <span class="o">+</span> <span class="n">l</span><span class="p">[(</span><span class="nb">len</span><span class="p">(</span><span class="n">l</span><span class="p">)</span><span class="o">//</span><span class="mi">2</span> <span class="o">-</span> <span class="mi">1</span><span class="p">)])</span> <span class="o">/</span> <span class="mi">2</span>
<span class="k">else</span><span class="p">:</span>
<span class="k">return</span> <span class="n">l</span><span class="p">[</span><span class="nb">len</span><span class="p">(</span><span class="n">l</span><span class="p">)</span><span class="o">//</span><span class="mi">2</span><span class="p">]</span>
<span class="k">def</span> <span class="nf">mean</span><span class="p">(</span><span class="n">l</span><span class="p">):</span>
<span class="k">return</span> <span class="nb">sum</span><span class="p">(</span><span class="n">l</span><span class="p">)</span><span class="o">/</span><span class="nb">len</span><span class="p">(</span><span class="n">l</span><span class="p">)</span>
@ -182,7 +185,7 @@ Mean : 43117.75, Median : 44627.5, Mode : 4978
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<h1>
Day 1 - Quartiles, Interquartile Range and standard deviation
</h1>
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<time class="published" datetime="2018-11-08T22:22:00+01:00">
08 novembre 2018
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<h2>Quartile</h2>
<h3>Definition</h3>
<p>A quartile is a type of quantile. The first quartile (Q1) is defined as the middle number between the smallest number and the median of the data set. The second quartile (Q2) is the median of the data. The third quartile (Q3) is the middle value between the median and the highest value of the data set. </p>
<h3>Implementation in python without using the scientific libraries</h3>
<div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">median</span><span class="p">(</span><span class="n">l</span><span class="p">):</span>
<span class="n">l</span> <span class="o">=</span> <span class="nb">sorted</span><span class="p">(</span><span class="n">l</span><span class="p">)</span>
<span class="k">if</span> <span class="nb">len</span><span class="p">(</span><span class="n">l</span><span class="p">)</span> <span class="o">%</span> <span class="mi">2</span> <span class="o">==</span> <span class="mi">0</span><span class="p">:</span>
<span class="k">return</span> <span class="p">(</span><span class="n">l</span><span class="p">[</span><span class="nb">len</span><span class="p">(</span><span class="n">l</span><span class="p">)</span> <span class="o">//</span> <span class="mi">2</span><span class="p">]</span> <span class="o">+</span> <span class="n">l</span><span class="p">[(</span><span class="nb">len</span><span class="p">(</span><span class="n">l</span><span class="p">)</span><span class="o">//</span><span class="mi">2</span> <span class="o">-</span> <span class="mi">1</span><span class="p">)])</span> <span class="o">/</span> <span class="mi">2</span>
<span class="k">else</span><span class="p">:</span>
<span class="k">return</span> <span class="n">l</span><span class="p">[</span><span class="nb">len</span><span class="p">(</span><span class="n">l</span><span class="p">)</span><span class="o">//</span><span class="mi">2</span><span class="p">]</span>
<span class="k">def</span> <span class="nf">quartiles</span><span class="p">(</span><span class="n">l</span><span class="p">):</span>
<span class="c1"># check the input is not empty</span>
<span class="k">if</span> <span class="ow">not</span> <span class="n">l</span><span class="p">:</span>
<span class="k">raise</span> <span class="n">StatsError</span><span class="p">(</span><span class="s1">&#39;no data points passed&#39;</span><span class="p">)</span>
<span class="c1"># 1. order the data set</span>
<span class="n">l</span> <span class="o">=</span> <span class="nb">sorted</span><span class="p">(</span><span class="n">l</span><span class="p">)</span>
<span class="c1"># 2. divide the data set in two halves</span>
<span class="n">mid</span> <span class="o">=</span> <span class="nb">int</span><span class="p">(</span><span class="nb">len</span><span class="p">(</span><span class="n">l</span><span class="p">)</span> <span class="o">/</span> <span class="mi">2</span><span class="p">)</span>
<span class="n">Q2</span> <span class="o">=</span> <span class="n">median</span><span class="p">(</span><span class="n">l</span><span class="p">)</span>
<span class="k">if</span> <span class="p">(</span><span class="nb">len</span><span class="p">(</span><span class="n">l</span><span class="p">)</span> <span class="o">%</span> <span class="mi">2</span> <span class="o">==</span> <span class="mi">0</span><span class="p">):</span>
<span class="c1"># even</span>
<span class="n">Q1</span> <span class="o">=</span> <span class="n">median</span><span class="p">(</span><span class="n">l</span><span class="p">[:</span><span class="n">mid</span><span class="p">])</span>
<span class="n">Q3</span> <span class="o">=</span> <span class="n">median</span><span class="p">(</span><span class="n">l</span><span class="p">[</span><span class="n">mid</span><span class="p">:])</span>
<span class="k">else</span><span class="p">:</span>
<span class="c1"># odd</span>
<span class="n">Q1</span> <span class="o">=</span> <span class="n">median</span><span class="p">(</span><span class="n">l</span><span class="p">[:</span><span class="n">mid</span><span class="p">])</span> <span class="c1"># same as even</span>
<span class="n">Q3</span> <span class="o">=</span> <span class="n">median</span><span class="p">(</span><span class="n">l</span><span class="p">[</span><span class="n">mid</span><span class="o">+</span><span class="mi">1</span><span class="p">:])</span>
<span class="k">return</span> <span class="p">(</span><span class="n">Q1</span><span class="p">,</span> <span class="n">Q2</span><span class="p">,</span> <span class="n">Q3</span><span class="p">)</span>
</pre></div>
<div class="highlight"><pre><span></span><span class="n">L</span> <span class="o">=</span> <span class="p">[</span><span class="mi">3</span><span class="p">,</span><span class="mi">7</span><span class="p">,</span><span class="mi">8</span><span class="p">,</span><span class="mi">5</span><span class="p">,</span><span class="mi">12</span><span class="p">,</span><span class="mi">14</span><span class="p">,</span><span class="mi">21</span><span class="p">,</span><span class="mi">13</span><span class="p">,</span><span class="mi">18</span><span class="p">]</span>
<span class="n">Q1</span><span class="p">,</span> <span class="n">Q2</span><span class="p">,</span> <span class="n">Q3</span> <span class="o">=</span> <span class="n">quartiles</span><span class="p">(</span><span class="n">L</span><span class="p">)</span>
<span class="k">print</span><span class="p">(</span><span class="n">f</span><span class="s2">&quot;Sample : {L}</span><span class="se">\n</span><span class="s2">Q1 : {Q1}, Q2 : {Q2}, Q3 : {Q3}&quot;</span><span class="p">)</span>
</pre></div>
<div class="highlight"><pre><span></span>Sample : [3, 7, 8, 5, 12, 14, 21, 13, 18]
Q1 : 6.0, Q2 : 12, Q3 : 16.0
</pre></div>
<h2>Interquartile Range</h2>
<h3>Definition</h3>
<p>The interquartile range of an array is the difference between its first (Q1) and third (Q3) quartiles. Hence the interquartile range is Q3-Q1</p>
<h3>Implementation in python without using the scientific libraries</h3>
<div class="highlight"><pre><span></span><span class="k">print</span><span class="p">(</span><span class="n">f</span><span class="s2">&quot;Interquatile range : {Q3-Q1}&quot;</span><span class="p">)</span>
</pre></div>
<div class="highlight"><pre><span></span>Interquatile range : 10.0
</pre></div>
<h2>Standard deviation</h2>
<h3>Definition</h3>
<p>The standard deviation (σ) is a measure that is used to quantify the amount of variation or dispersion of a set of data values. A low standard deviation indicates that the data points tend to be close to the mean (also called the expected value) of the set, while a high standard deviation indicates that the data points are spread out over a wider range of values. </p>
<p>The standard deviation can be computed with the formula:</p>
<p><img alt="Standard deviation" src="../images/stat_challenge/day1/ecart_type.png"></p>
<p>where µ is the mean :</p>
<p><img alt="Mean" src="../images/stat_challenge/day1/moyenne.png"></p>
<h3>Implementation in python without using the scientific libraries</h3>
<div class="highlight"><pre><span></span><span class="kn">import</span> <span class="nn">math</span>
<span class="n">X</span> <span class="o">=</span> <span class="p">[</span><span class="mi">10</span><span class="p">,</span><span class="mi">40</span><span class="p">,</span><span class="mi">30</span><span class="p">,</span><span class="mi">50</span><span class="p">,</span><span class="mi">20</span><span class="p">]</span>
<span class="n">mean</span> <span class="o">=</span> <span class="nb">sum</span><span class="p">(</span><span class="n">X</span><span class="p">)</span><span class="o">/</span><span class="nb">len</span><span class="p">(</span><span class="n">X</span><span class="p">)</span>
<span class="n">X</span> <span class="o">=</span> <span class="p">[(</span><span class="n">x</span> <span class="o">-</span> <span class="n">mean</span><span class="p">)</span><span class="o">**</span><span class="mi">2</span> <span class="k">for</span> <span class="n">x</span> <span class="ow">in</span> <span class="n">X</span><span class="p">]</span>
<span class="n">std</span> <span class="o">=</span> <span class="n">math</span><span class="o">.</span><span class="n">sqrt</span><span class="p">(</span>
<span class="nb">sum</span><span class="p">(</span><span class="n">X</span><span class="p">)</span><span class="o">/</span><span class="nb">len</span><span class="p">(</span><span class="n">X</span><span class="p">)</span>
<span class="p">)</span>
<span class="k">print</span><span class="p">(</span><span class="n">f</span><span class="s2">&quot;The distribution {X} has a standard deviation of {std}&quot;</span><span class="p">)</span>
</pre></div>
<div class="highlight"><pre><span></span>The distribution [400.0, 100.0, 0.0, 400.0, 100.0] has a standard deviation of 14.142135623730951
</pre></div>
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linux/Reloading_.bashrc.html
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linux/free_disk_space_linux.html
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@ -167,7 +167,7 @@ none 0 0 0 - /config
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linux/get_ip_linux.html
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@ -256,7 +256,7 @@ wifi0 Link encap:UNSPEC HWaddr 5C-51-4F-41-7A-AD-00-00-00-00-00-00-00-00-00
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linux/linux_process_information.html
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@ -172,7 +172,7 @@ USER;PID;%CPU;%MEM;VSZ;RSS;TTY;STAT;START;TIME;COMMAND</p>
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@ -192,7 +192,7 @@ Sorted array : [0.13876208 0.19939047 0.40021786 0.43734158 0.46015169]
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@ -5,7 +5,7 @@ xmlns="http://www.sitemaps.org/schemas/sitemap/0.9">
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<p class="text-muted">
<center>This project contains 47 pages and is available on <a href="https://github.com/redoules/redoules.github.io">GitHub</a>.
<center>This project contains 48 pages and is available on <a href="https://github.com/redoules/redoules.github.io">GitHub</a>.
<br/>
Copyright &copy; Guillaume Redoulès,
<time datetime="2018">2018</time>.

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