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<p>There are at least 9 different ways to calculate the first quartile in this case, and different statistical software package will sometimes use different default methods <spanclass="citation">(<ahref="#ref-Hyndman1996" role="doc-biblioref">Hyndman and Fan 1996</a>)</span>.
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One logical way is to calculate the mean between the second (3.5) and third (3.8) position as you would do for the median <spanclass="citation">(<ahref="#ref-Rowntree2018" role="doc-biblioref">Rowntree 2018</a>)</span>, <spanclass="math inline">\((3.5 + 3.8) / 2 = 3.65\)</span>.
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Jamovi uses a slightly more complex method, which will give a value of <spanclass="math inline">\(3.725\)</span>.</p>
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Jamovi uses a slightly more complex method, which will give a value of <spanclass="math inline">\(3.725\)</span><spanclass="citation">(<ahref="#ref-Jamovi2022" role="doc-biblioref">The Jamovi Project 2022</a>)</span>.</p>
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<p>It is important to emphasise that no one way of calculating quantiles is the one and only correct way.
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Statisticians have just proposed different approaches to calculating quantiles from data, and these different approaches sometimes give slightly different results.
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This can be unsatisfying when first learning statistics because it would be nice to have a single approach that is demonstrably correct, i.e., the <em>right</em> answer under all circumstances.
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