artificial intelligence
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<article>
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<h1>Levels of Measurement</h1>
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<section>
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<address class="h-card">
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by
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<a rel="author" class="u-url" href="http://changelog.ca/"><span class="p-given-name">Charles</span> <span class="p-additional-name">Iliya</span> <span class="p-family-name">Krempeaux</span></a>
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</address>
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</section>
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<section>
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<p>
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The <strong>levels of measurement</strong> are a way of categorizing a <ziba-link>data</ziba-link> as one of four different categories:
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</p>
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<ul>
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<li><ziba-link>nominal data</ziba-link>,</li>
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<li><ziba-link>ordinal data</ziba-link>,</li>
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<li><ziba-link>interval data</ziba-link>, and</li>
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<li><ziba-link>ratio data</ziba-link>.</li>
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</ul>
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</section>
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<section>
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<h2>Ratio Data</h2>
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</section>
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<section>
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<h2>Interval Data</h2>
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</section>
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<section>
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<h2>Ordinal Data</h2>
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</section>
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<section>
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<h2>Nominal Data</h2>
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<section>
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<p>
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An example of <strong>nominal data</strong> is <em>blood types</em>:
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</p>
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<ul>
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<li>type A+</li>
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<li>type A-</li>
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<li>type B+</li>
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<li>type B-</li>
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<li>type AB+</li>
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<li>type AB-</li>
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<li>type O+</li>
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<li>type O-</li>
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</ul>
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</section>
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<section>
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<p>
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Another example of <strong>nominal data</strong> is <em>sex</em>:
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</p>
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<ul>
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<li>female</li>
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<li>male</li>
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</ul>
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</section>
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<section>
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<p>
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Another example of <strong>nominal data</strong> is <em>family names</em>:
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</p>
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<ul>
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<li>Alves</li>
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<li>Beg</li>
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<li>Chen</li>
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<li>Cho</li>
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<li>Choi</li>
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<li>da Silva</li>
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<li>Dickson</li>
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<li>dos Santos</li>
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<li>Esfahani</li>
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<li>Fernández</li>
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<li>Ferreira</li>
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<li>García</li>
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<li>Jung</li>
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<li>Kang</li>
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<li>Kerr</li>
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<li>Kim</li>
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<li>Krempeaux</li>
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<li>Li</li>
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<li>Liu</li>
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<li>Martin</li>
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<li>Müller</li>
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<li>Pahlavi</li>
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<li>Park</li>
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<li>Parsi</li>
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<li>Pereira</li>
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<li>Rodríguez</li>
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<li>Safavi</li>
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<li>Sasani</li>
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<li>Wang</li>
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<li>Yun</li>
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<li>Zhang</li>
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<li><em>etc</em></li>
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</ul>
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</section>
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<section>
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<p>
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Another example of <strong>nominal data</strong> is <em>hair color</em>:
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</p>
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<ul>
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<li>brown</li>
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<li>black</li>
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<li>blond</li>
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<li>gray</li>
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<li>red</li>
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<li><em>etc</em></li>
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</ul>
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</section>
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<section>
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<p>
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Another example of <strong>nominal data</strong> is <em>cities</em>:
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</p>
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<ul>
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<li>Beijing</li>
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<li>Bangalore</li>
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<li>Bangkok</li>
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<li>Bogotá</li>
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<li>Buenos Aires</li>
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<li>Cairo</li>
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<li>Chennai</li>
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<li>Chicago</li>
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<li>Chongqing</li>
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<li>Dallas</li>
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<li>Delhi</li>
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<li>Dhaka</li>
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<li>Guangzhou</li>
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<li>Hyderabad</li>
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<li>Kinshasa</li>
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<li>Kolkata</li>
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<li>Isfahan</li>
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<li>Istanbul</li>
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<li>Jakarta</li>
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<li>Karachi</li>
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<li>Lagos</li>
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<li>Lahore</li>
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<li>Lima</li>
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<li>London</li>
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<li>Los Angeles</li>
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<li>Moscow</li>
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<li>Nagoya</li>
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<li>New York City</li>
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<li>Osaka</li>
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<li>Manila</li>
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<li>Mexico City</li>
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<li>Mumbai</li>
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<li>Paris</li>
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<li>Rio de Janeiro</li>
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<li>São Paulo</li>
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<li>Seoul</li>
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<li>Shanghai</li>
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<li>Shenzhen</li>
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<li>Tehran</li>
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<li>Tianjin</li>
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<li>Tokyo</li>
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<li>Toronto</li>
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<li>Vancouver</li>
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<li><em>etc</em></li>
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</ul>
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</section>
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</section>
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<section>
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<h2>Operations</h2>
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<p>
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One way of understanding the <strong>levels of measurement</strong> is — what type of <strong>operations</strong> are meaningful and valid for that type of data‽
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</p>
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<p>
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Here is a table that summarizes what <strong>operations</strong> are and are <em>not</em >meaningful and valid for each <strong>levels of measurement</strong> category:
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</p>
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<table>
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<thead>
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<tr>
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<th></th>
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<th>nominal</th>
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<th>ordinal</th>
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<th>interval</th>
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<th>ratio</th>
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</tr>
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</thead>
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<tbody>
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<tr>
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<td>can × and ÷ ?</td>
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<td>no</td>
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<td>no</td>
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<td>no</td>
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<td>YES</td>
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</tr>
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<tr>
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<td>can + and - ?</td>
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<td>no</td>
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<td>no</td>
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<td>YES</td>
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<td>YES</td>
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</tr>
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<tr>
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<td>can < and > ?</td>
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<td>no</td>
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<td>YES</td>
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<td>YES</td>
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<td>YES</td>
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</tr>
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<tr>
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<td>can = and ≠ ?</td>
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<td>YES</td>
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<td>YES</td>
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<td>YES</td>
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<td>YES</td>
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</tr>
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</tbody>
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</table>
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</section>
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</article>
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