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var DOCUMENTATION_OPTIONS = {
URL_ROOT: document.getElementById("documentation_options").getAttribute('data-url_root'),
VERSION: '[v0.5.2]',
VERSION: '[v1.0.0]',
LANGUAGE: 'None',
COLLAPSE_INDEX: false,
BUILDER: 'html',
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<a href="../index.html"> Minimalist Data Wrangling with Python [v0.5.2]
<a href="../index.html"> Minimalist Data Wrangling with Python [v1.0.0]



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Expand Down Expand Up @@ -797,7 +797,7 @@ <h2>Acknowledgements<a class="headerlink" href="#acknowledgements" title="Permal
<p>
Copyright &#169; 2022 by <a href="https://www.gagolewski.com">Marek Gagolewski</a>. Some rights reserved. Licensed under <a href='https://creativecommons.org/licenses/by-nc-nd/4.0/'>CC BY-NC-ND 4.0</a>.
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<a href="../index.html"> Minimalist Data Wrangling with Python [v0.5.2]
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Expand Down Expand Up @@ -732,7 +732,7 @@ <h2><span class="section-number">1.5. </span>Exercises<a class="headerlink" href
<p>
Copyright &#169; 2022 by <a href="https://www.gagolewski.com">Marek Gagolewski</a>. Some rights reserved. Licensed under <a href='https://creativecommons.org/licenses/by-nc-nd/4.0/'>CC BY-NC-ND 4.0</a>.
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<a href="../index.html"> Minimalist Data Wrangling with Python [v0.5.2]
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Expand Down Expand Up @@ -966,7 +966,7 @@ <h2><span class="section-number">2.5. </span>Exercises<a class="headerlink" href
<p>
Copyright &#169; 2022 by <a href="https://www.gagolewski.com">Marek Gagolewski</a>. Some rights reserved. Licensed under <a href='https://creativecommons.org/licenses/by-nc-nd/4.0/'>CC BY-NC-ND 4.0</a>.
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<a href="../index.html"> Minimalist Data Wrangling with Python [v0.5.2]
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Expand Down Expand Up @@ -204,7 +204,7 @@
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Expand Down Expand Up @@ -1019,7 +1019,7 @@ <h3><span class="section-number">3.5.3. </span>Object Copies<a class="headerlink
<span class="kn">import</span> <span class="nn">random</span>
<span class="n">random</span><span class="o">.</span><span class="n">shuffle</span><span class="p">(</span><span class="n">x</span><span class="p">)</span> <span class="c1"># modifies x in place, returns nothing</span>
<span class="nb">print</span><span class="p">(</span><span class="n">x</span><span class="p">)</span>
<span class="c1">## [5, 4, 2, 3, 1]</span>
<span class="c1">## [1, 4, 5, 3, 2]</span>
</pre></div>
</div>
<p>Later we will learn about the <code class="docutils literal notranslate"><span class="pre">Series</span></code> class in <strong class="program">pandas</strong>,
Expand Down Expand Up @@ -1166,7 +1166,7 @@ <h2><span class="section-number">3.7. </span>Exercises<a class="headerlink" href
<p>
Copyright &#169; 2022 by <a href="https://www.gagolewski.com">Marek Gagolewski</a>. Some rights reserved. Licensed under <a href='https://creativecommons.org/licenses/by-nc-nd/4.0/'>CC BY-NC-ND 4.0</a>.
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Expand Down Expand Up @@ -1342,7 +1342,7 @@ <h2><span class="section-number">4.4. </span>Exercises<a class="headerlink" href
<p>
Copyright &#169; 2022 by <a href="https://www.gagolewski.com">Marek Gagolewski</a>. Some rights reserved. Licensed under <a href='https://creativecommons.org/licenses/by-nc-nd/4.0/'>CC BY-NC-ND 4.0</a>.
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Expand Down Expand Up @@ -221,7 +221,7 @@
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Expand Down Expand Up @@ -621,7 +621,7 @@ <h4><span class="section-number">5.1.2.1. </span>Standard Deviation (and Varianc
\frac{ (x_1-\bar{x})^2 + (x_2-\bar{x})^2 + \dots + (x_n-\bar{x})^2 }{n}
} =
\sqrt{
\frac{1}{n} \sum_{i=1}^n (x_i-\bar{x})^2,
\frac{1}{n} \sum_{i=1}^n (x_i-\bar{x})^2.
}
\]</div>
<p>Computing the above with <strong class="program">numpy</strong>:</p>
Expand Down Expand Up @@ -876,7 +876,7 @@ <h3><span class="section-number">5.1.5. </span>Further Methods (*)<a class="head
convert between metres and centimetres).</p>
<p>The <em>Gini index</em>,
widely used in economics, can also serve as a measure of relative
dispersion, but assumes that all data points are nonnegative.</p>
dispersion, but assumes that all data points are nonnegative:</p>
<div class="math notranslate nohighlight">
\[
G = \frac{
Expand Down Expand Up @@ -1243,7 +1243,7 @@ <h4><span class="section-number">5.3.2.2. </span>Min-Max Scaling and Clipping<a
x_1^2 + x_2^2 + \dots + x_n^2
} = \sqrt{
\sum_{i=1}^n x_i^2
},
}.
\]</div>
<p>Its special case for <em>n=2</em> we know well from high school:
the length of a vector <span class="math notranslate nohighlight">\((a,b)\)</span>
Expand All @@ -1260,7 +1260,7 @@ <h4><span class="section-number">5.3.2.2. </span>Min-Max Scaling and Clipping<a
\frac{x_2}{\| \boldsymbol{x} \|},
\dots,
\frac{x_n}{\| \boldsymbol{x} \|}
\right)
\right),
\]</div>
<p>can be determined via:</p>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">x</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">([</span><span class="mi">1</span><span class="p">,</span> <span class="mi">5</span><span class="p">,</span> <span class="o">-</span><span class="mi">4</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mf">2.5</span><span class="p">])</span> <span class="c1"># example vector</span>
Expand Down Expand Up @@ -1404,12 +1404,11 @@ <h3><span class="section-number">5.3.3. </span>Vector-Vector Case<a class="heade
<span class="proof-type">Exercise 5.14</span>

</div><div class="proof-content">
<p>Based on the
<p>Using a single line of code, compute the vector of BMIs of all persons
based on the
<a class="reference external" href="https://github.com/gagolews/teaching_data/blob/master/marek/nhanes_adult_female_height_2020.txt"><code class="docutils literal notranslate"><span class="pre">nhanes_adult_female_height_2020</span></code></a>
and
<a class="reference external" href="https://github.com/gagolews/teaching_data/blob/master/marek/nhanes_adult_female_weight_2020.txt"><code class="docutils literal notranslate"><span class="pre">nhanes_adult_female_weight_2020</span></code></a>
datasets (discussed in the part on histograms), using a single line of code,
compute the vector of BMIs of all persons.
<a class="reference external" href="https://github.com/gagolews/teaching_data/blob/master/marek/nhanes_adult_female_weight_2020.txt"><code class="docutils literal notranslate"><span class="pre">nhanes_adult_female_weight_2020</span></code></a> datasets.
It is assumed that the <em>i</em>-th elements therein both refer to the same
person.</p>
</div></div></div>
Expand Down Expand Up @@ -1727,7 +1726,7 @@ <h3><span class="section-number">5.5.5. </span>Searching for Certain Indexes (Ar
<p>Using mathematical notation, we can denote the former with:</p>
<div class="math notranslate nohighlight">
\[
i = \mathrm{arg}\min_j x_j
i = \mathrm{arg}\min_j x_j,
\]</div>
<p>and read it as: let <span class="math notranslate nohighlight">\(i\)</span> be the index of the smallest element in the sequence.
Alternatively, it is the <em>argument of the minimum</em>, whenever:</p>
Expand Down Expand Up @@ -1806,20 +1805,19 @@ <h3><span class="section-number">5.5.5. </span>Searching for Certain Indexes (Ar
</div>
<p>When a comparison is needed, we need to take some error margin
into account. Ideally, instead of testing <code class="docutils literal notranslate"><span class="pre">x</span> <span class="pre">==</span> <span class="pre">y</span></code>, we should either
inspect the absolute error</p>
inspect the <em>absolute error</em>:</p>
<div class="math notranslate nohighlight">
\[
|x-y| \le \varepsilon
|x-y| \le \varepsilon,
\]</div>
<p>or, assuming <span class="math notranslate nohighlight">\(y\neq 0\)</span>, the relative error</p>
<p>or, assuming <span class="math notranslate nohighlight">\(y\neq 0\)</span>, the <em>relative error</em>:</p>
<div class="math notranslate nohighlight">
\[
\frac{|x-y|}{|y|} \le \varepsilon,
\]</div>
<p>where <span class="math notranslate nohighlight">\(\varepsilon\)</span> is some small error margin.</p>
<p>For instance, <strong class="command">numpy.allclose</strong><code class="code docutils literal notranslate"><span class="pre">(x,</span> <span class="pre">y)</span></code>
checks (by default) if for all corresponding elements in both vectors
it holds
<p>For instance, <strong class="command">numpy.allclose</strong><code class="code docutils literal notranslate"><span class="pre">(x,</span> <span class="pre">y)</span></code> checks (by default)
if for all corresponding elements in both vectors it holds
<strong class="command">numpy.abs</strong><code class="code docutils literal notranslate"><span class="pre">(x-y)</span> <span class="pre">&lt;=</span> <span class="pre">1e-8</span> <span class="pre">+</span> <span class="pre">1e-5*</span></code><strong class="command">numpy.abs</strong><code class="code docutils literal notranslate"><span class="pre">(y)</span></code>,
which is a combination of both tests.</p>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">np</span><span class="o">.</span><span class="n">allclose</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">mean</span><span class="p">(</span><span class="n">heights_centred</span><span class="p">),</span> <span class="mi">0</span><span class="p">)</span>
Expand Down Expand Up @@ -2190,7 +2188,7 @@ <h2><span class="section-number">5.6. </span>Exercises<a class="headerlink" href
<p>
Copyright &#169; 2022 by <a href="https://www.gagolewski.com">Marek Gagolewski</a>. Some rights reserved. Licensed under <a href='https://creativecommons.org/licenses/by-nc-nd/4.0/'>CC BY-NC-ND 4.0</a>.
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