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45 lines
1.5 KiB
HTML
45 lines
1.5 KiB
HTML
<div class="book-prose">
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<p>
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Dispersion describes how spread out data is. Two datasets can have the same average but very
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different variability.
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</p>
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<h2 id="range-iqr" class="book-prose__heading">Range and interquartile range</h2>
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<p class="book-formula">\[
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\text{Range}=\text{max}-\text{min},\qquad
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\text{IQR}=Q_3-Q_1.
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\]</p>
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<p>
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IQR is less affected by outliers than range.
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</p>
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<h2 id="variance-sd" class="book-prose__heading">Variance and standard deviation</h2>
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<p>
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Variance measures average squared distance from mean.
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Standard deviation is square root of variance and has same unit as data.
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</p>
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<p class="book-formula">\[
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\sigma=\sqrt{\frac{\sum (x-\bar{x})^2}{n}}
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\]</p>
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<h2 id="comparing-data" class="book-prose__heading">Comparing datasets</h2>
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<ul>
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<li>Smaller spread statistics \(\Rightarrow\) more consistent data.</li>
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<li>Use median + IQR for skewed data.</li>
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<li>Use mean + standard deviation for roughly symmetric data.</li>
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</ul>
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<h2 id="boxplot-reading" class="book-prose__heading">Box plot interpretation</h2>
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<p>
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Box shows middle 50% (\(Q_1\) to \(Q_3\)); median line marks center.
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Longer whisker/box indicates larger spread.
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</p>
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<h2 id="exam-strategy" class="book-prose__heading">Exam strategy</h2>
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<ul>
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<li>State both center and spread when comparing sets.</li>
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<li>Do not confuse variance with standard deviation.</li>
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<li>Check if grouped-data values are estimates.</li>
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<li>Interpret spread in context (consistency/risk).</li>
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</ul>
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</div>
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