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<h1>
Day 0 - Median, mean, mode and weighted mean
</h1>
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<time class="published" datetime="2018-11-07T22:12:00+01:00">
07 novembre 2018
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<h2>A reminder</h2>
<h3>The median</h3>
<p>The median is the value separating the higher half from the lower half of a data sample. For a data set, it may be thought of as the middle value.
For a continuous probability distribution, the median is the value such that a number is equally likely to fall above or below it. </p>
<h3>The mean</h3>
<p>The arithmetic mean (or simply mean) of a sample is the sum of the sampled values divided by the number of items.</p>
<h3>The mode</h3>
<p>The mode of a set of data values is the value that appears most often. It is the value x at which its probability mass function takes its maximum value. In other words, it is the value that is most likely to be sampled. </p>
<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">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>
<span class="k">def</span> <span class="nf">mode</span><span class="p">(</span><span class="n">data</span><span class="p">):</span>
<span class="n">dico</span> <span class="o">=</span> <span class="p">{</span><span class="n">x</span><span class="p">:</span><span class="n">data</span><span class="o">.</span><span class="n">count</span><span class="p">(</span><span class="n">x</span><span class="p">)</span> <span class="k">for</span> <span class="n">x</span> <span class="ow">in</span> <span class="nb">list</span><span class="p">(</span><span class="nb">set</span><span class="p">(</span><span class="n">data</span><span class="p">))}</span>
<span class="k">return</span> <span class="nb">sorted</span><span class="p">(</span><span class="nb">sorted</span><span class="p">(</span><span class="n">dico</span><span class="o">.</span><span class="n">items</span><span class="p">()),</span> <span class="n">key</span> <span class="o">=</span> <span class="k">lambda</span> <span class="n">x</span><span class="p">:</span> <span class="n">x</span><span class="p">[</span><span class="mi">1</span><span class="p">],</span> <span class="n">reverse</span> <span class="o">=</span> <span class="kc">True</span><span class="p">)[</span><span class="mi">0</span><span class="p">][</span><span class="mi">0</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">64630</span><span class="p">,</span><span class="mi">11735</span><span class="p">,</span><span class="mi">14216</span><span class="p">,</span><span class="mi">99233</span><span class="p">,</span><span class="mi">14470</span><span class="p">,</span><span class="mi">4978</span><span class="p">,</span><span class="mi">73429</span><span class="p">,</span><span class="mi">38120</span><span class="p">,</span><span class="mi">51135</span><span class="p">,</span><span class="mi">67060</span><span class="p">,</span> <span class="mi">4978</span><span class="p">,</span> <span class="mi">73429</span><span class="p">]</span>
<span class="nb">print</span><span class="p">(</span><span class="sa">f</span><span class="s2">&quot;Sample : </span><span class="si">{L}</span><span class="se">\n</span><span class="s2">Mean : {mean(L)}, Median : {median(L)}, Mode : {mode(L)}&quot;</span><span class="p">)</span>
</pre></div>
<div class="highlight"><pre><span></span><span class="err">Sample : [64630, 11735, 14216, 99233, 14470, 4978, 73429, 38120, 51135, 67060, 4978, 73429]</span>
<span class="err">Mean : 43117.75, Median : 44627.5, Mode : 4978</span>
</pre></div>
<h2>The weighted average</h2>
<p>The weighted arithmetic mean is similar to an ordinary arithmetic mean (the most common type of average), except that instead of each of the data points contributing equally to the final average, some data points contribute more than others.</p>
<div class="highlight"><pre><span></span><span class="n">data</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">weights</span> <span class="o">=</span> <span class="p">[</span><span class="mi">1</span><span class="p">,</span><span class="mi">2</span><span class="p">,</span><span class="mi">3</span><span class="p">,</span><span class="mi">4</span><span class="p">,</span><span class="mi">5</span><span class="p">]</span>
<span class="n">sum_X</span> <span class="o">=</span> <span class="nb">sum</span><span class="p">([</span><span class="n">x</span><span class="o">*</span><span class="n">w</span> <span class="k">for</span> <span class="n">x</span><span class="p">,</span><span class="n">w</span> <span class="ow">in</span> <span class="nb">zip</span><span class="p">(</span><span class="n">data</span><span class="p">,</span><span class="n">weights</span><span class="p">)])</span>
<span class="nb">print</span><span class="p">(</span><span class="nb">round</span><span class="p">((</span><span class="n">sum_X</span><span class="o">/</span><span class="nb">sum</span><span class="p">(</span><span class="n">weights</span><span class="p">)),</span><span class="mi">1</span><span class="p">))</span>
</pre></div>
<div class="highlight"><pre><span></span><span class="err">32.0</span>
</pre></div>
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