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<!DOCTYPE html>
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<title>Chapter 5 Mean, mode, median, and resistance | Statistical Techniques for Biological and Environmental Sciences</title>
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<meta name="twitter:title" content="Chapter 5 Mean, mode, median, and resistance | Statistical Techniques for Biological and Environmental Sciences" />
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<meta name="author" content="Brad Duthie" />
<meta name="date" content="2022-10-21" />
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<nav role="navigation">
<ul class="summary">
<li><a href="./">A Minimal Book Example</a></li>
<li class="divider"></li>
<li class="chapter" data-level="" data-path="index.html"><a href="index.html"><i class="fa fa-check"></i>Preface</a>
<ul>
<li class="chapter" data-level="0.1" data-path="index.html"><a href="index.html#what-is-statistics"><i class="fa fa-check"></i><b>0.1</b> What is statistics?</a></li>
<li class="chapter" data-level="0.2" data-path="index.html"><a href="index.html#why-this-module-is-important"><i class="fa fa-check"></i><b>0.2</b> Why this module is important</a></li>
<li class="chapter" data-level="0.3" data-path="index.html"><a href="index.html#teaching-overview"><i class="fa fa-check"></i><b>0.3</b> Teaching overview</a></li>
<li class="chapter" data-level="0.4" data-path="index.html"><a href="index.html#assessment-overview"><i class="fa fa-check"></i><b>0.4</b> Assessment overview</a>
<ul>
<li class="chapter" data-level="0.4.1" data-path="index.html"><a href="index.html#test-1f"><i class="fa fa-check"></i><b>0.4.1</b> Test 1F</a></li>
<li class="chapter" data-level="0.4.2" data-path="index.html"><a href="index.html#test-1s"><i class="fa fa-check"></i><b>0.4.2</b> Test 1S</a></li>
<li class="chapter" data-level="0.4.3" data-path="index.html"><a href="index.html#test-2s"><i class="fa fa-check"></i><b>0.4.3</b> Test 2S</a></li>
<li class="chapter" data-level="0.4.4" data-path="index.html"><a href="index.html#mock-exam"><i class="fa fa-check"></i><b>0.4.4</b> Mock Exam</a></li>
<li class="chapter" data-level="0.4.5" data-path="index.html"><a href="index.html#exam"><i class="fa fa-check"></i><b>0.4.5</b> Exam</a></li>
</ul></li>
<li class="chapter" data-level="0.5" data-path="index.html"><a href="index.html#intro_jamovi"><i class="fa fa-check"></i><b>0.5</b> Jamovi statistical software</a></li>
<li class="chapter" data-level="0.6" data-path="index.html"><a href="index.html#textbooks"><i class="fa fa-check"></i><b>0.6</b> Textbooks</a></li>
<li class="chapter" data-level="0.7" data-path="index.html"><a href="index.html#canvas"><i class="fa fa-check"></i><b>0.7</b> Canvas</a></li>
<li class="chapter" data-level="0.8" data-path="index.html"><a href="index.html#timetable"><i class="fa fa-check"></i><b>0.8</b> Timetable</a></li>
</ul></li>
<li class="part"><span><b>I Background mathematics and data organisation</b></span></li>
<li class="chapter" data-level="" data-path="week-1-overview.html"><a href="week-1-overview.html"><i class="fa fa-check"></i>Week 1 Overview</a>
<ul>
<li class="chapter" data-level="0.9" data-path="week-1-overview.html"><a href="week-1-overview.html#numbers-and-operations"><i class="fa fa-check"></i><b>0.9</b> Numbers and operations</a></li>
<li class="chapter" data-level="0.10" data-path="week-1-overview.html"><a href="week-1-overview.html#order-of-operations"><i class="fa fa-check"></i><b>0.10</b> Order of operations</a></li>
<li class="chapter" data-level="0.11" data-path="week-1-overview.html"><a href="week-1-overview.html#tidy-data"><i class="fa fa-check"></i><b>0.11</b> Tidy data</a></li>
<li class="chapter" data-level="0.12" data-path="week-1-overview.html"><a href="week-1-overview.html#data-files"><i class="fa fa-check"></i><b>0.12</b> Data files</a></li>
<li class="chapter" data-level="0.13" data-path="week-1-overview.html"><a href="week-1-overview.html#libreoffice-calc"><i class="fa fa-check"></i><b>0.13</b> LibreOffice Calc</a></li>
<li class="chapter" data-level="0.14" data-path="week-1-overview.html"><a href="week-1-overview.html#exercise-organising-data-1"><i class="fa fa-check"></i><b>0.14</b> Exercise Organising data 1</a></li>
<li class="chapter" data-level="0.15" data-path="week-1-overview.html"><a href="week-1-overview.html#exercise-organising-data-2"><i class="fa fa-check"></i><b>0.15</b> Exercise Organising data 2</a></li>
<li class="chapter" data-level="0.16" data-path="week-1-overview.html"><a href="week-1-overview.html#exercise-organising-data-3"><i class="fa fa-check"></i><b>0.16</b> Exercise Organising data 3</a></li>
<li class="chapter" data-level="0.17" data-path="week-1-overview.html"><a href="week-1-overview.html#summary-of-exercises-and-why-they-are-useful."><i class="fa fa-check"></i><b>0.17</b> Summary of exercises and why they are useful.</a></li>
</ul></li>
<li class="part"><span><b>II Statistical concepts</b></span></li>
<li class="chapter" data-level="" data-path="week-2-overview.html"><a href="week-2-overview.html"><i class="fa fa-check"></i>Week 2 Overview</a>
<ul>
<li class="chapter" data-level="0.18" data-path="week-2-overview.html"><a href="week-2-overview.html#accuracy"><i class="fa fa-check"></i><b>0.18</b> Accuracy</a></li>
<li class="chapter" data-level="0.19" data-path="week-2-overview.html"><a href="week-2-overview.html#precision"><i class="fa fa-check"></i><b>0.19</b> Precision</a></li>
<li class="chapter" data-level="0.20" data-path="week-2-overview.html"><a href="week-2-overview.html#systems-of-units"><i class="fa fa-check"></i><b>0.20</b> Systems of units</a></li>
<li class="chapter" data-level="0.21" data-path="week-2-overview.html"><a href="week-2-overview.html#other-examples-of-units"><i class="fa fa-check"></i><b>0.21</b> Other examples of units</a>
<ul>
<li class="chapter" data-level="0.21.1" data-path="week-2-overview.html"><a href="week-2-overview.html#units-of-density"><i class="fa fa-check"></i><b>0.21.1</b> Units of density</a></li>
<li class="chapter" data-level="0.21.2" data-path="week-2-overview.html"><a href="week-2-overview.html#mass-of-metal-discharged-from-a-catchment"><i class="fa fa-check"></i><b>0.21.2</b> Mass of metal discharged from a catchment</a></li>
<li class="chapter" data-level="0.21.3" data-path="week-2-overview.html"><a href="week-2-overview.html#soil-carbon-inventories"><i class="fa fa-check"></i><b>0.21.3</b> Soil carbon inventories</a></li>
</ul></li>
<li class="chapter" data-level="0.22" data-path="week-2-overview.html"><a href="week-2-overview.html#adding-or-subtracting-errors"><i class="fa fa-check"></i><b>0.22</b> Adding or subtracting errors</a></li>
<li class="chapter" data-level="0.23" data-path="week-2-overview.html"><a href="week-2-overview.html#multiplying-or-dividing-errors"><i class="fa fa-check"></i><b>0.23</b> Multiplying or dividing errors</a></li>
<li class="chapter" data-level="0.24" data-path="week-2-overview.html"><a href="week-2-overview.html#applying-formulas-for-combining-errors"><i class="fa fa-check"></i><b>0.24</b> Applying formulas for combining errors</a></li>
<li class="chapter" data-level="0.25" data-path="week-2-overview.html"><a href="week-2-overview.html#summary_statistics_02"><i class="fa fa-check"></i><b>0.25</b> Exercise for summary statistics</a></li>
<li class="chapter" data-level="0.26" data-path="week-2-overview.html"><a href="week-2-overview.html#transforming_variables_02"><i class="fa fa-check"></i><b>0.26</b> Exercise on transforming variables</a></li>
<li class="chapter" data-level="0.27" data-path="week-2-overview.html"><a href="week-2-overview.html#computing_variables_02"><i class="fa fa-check"></i><b>0.27</b> Exercise on computing variables</a></li>
</ul></li>
<li class="part"><span><b>III Summary statistics</b></span></li>
<li class="chapter" data-level="" data-path="week-3-overview.html"><a href="week-3-overview.html"><i class="fa fa-check"></i>Week 3 Overview</a></li>
<li class="chapter" data-level="1" data-path="Chapter_9.html"><a href="Chapter_9.html"><i class="fa fa-check"></i><b>1</b> Decimal places, significant figures, and rounding</a>
<ul>
<li class="chapter" data-level="1.1" data-path="Chapter_9.html"><a href="Chapter_9.html#decimal-places-and-significant-figures"><i class="fa fa-check"></i><b>1.1</b> Decimal places and significant figures</a></li>
<li class="chapter" data-level="1.2" data-path="Chapter_9.html"><a href="Chapter_9.html#rounding"><i class="fa fa-check"></i><b>1.2</b> Rounding</a></li>
</ul></li>
<li class="chapter" data-level="2" data-path="the-mean.html"><a href="the-mean.html"><i class="fa fa-check"></i><b>2</b> The mean</a></li>
<li class="chapter" data-level="3" data-path="the-mode.html"><a href="the-mode.html"><i class="fa fa-check"></i><b>3</b> The mode</a></li>
<li class="chapter" data-level="4" data-path="the-median-and-quantiles.html"><a href="the-median-and-quantiles.html"><i class="fa fa-check"></i><b>4</b> The median and quantiles</a></li>
<li class="chapter" data-level="5" data-path="mean-mode-median-and-resistance.html"><a href="mean-mode-median-and-resistance.html"><i class="fa fa-check"></i><b>5</b> Mean, mode, median, and resistance</a></li>
<li class="chapter" data-level="6" data-path="plots.html"><a href="plots.html"><i class="fa fa-check"></i><b>6</b> Plots</a>
<ul>
<li class="chapter" data-level="6.1" data-path="plots.html"><a href="plots.html#general-principles"><i class="fa fa-check"></i><b>6.1</b> General principles</a></li>
<li class="chapter" data-level="6.2" data-path="plots.html"><a href="plots.html#histograms"><i class="fa fa-check"></i><b>6.2</b> Histograms</a></li>
<li class="chapter" data-level="6.3" data-path="plots.html"><a href="plots.html#box-whisker-plots"><i class="fa fa-check"></i><b>6.3</b> Box-whisker plots</a></li>
</ul></li>
<li class="chapter" data-level="7" data-path="practical.-real-data-with-jamovi.html"><a href="practical.-real-data-with-jamovi.html"><i class="fa fa-check"></i><b>7</b> <em>Practical</em>. Real data with Jamovi</a>
<ul>
<li class="chapter" data-level="7.1" data-path="practical.-real-data-with-jamovi.html"><a href="practical.-real-data-with-jamovi.html#some-biological-example"><i class="fa fa-check"></i><b>7.1</b> Some biological example</a></li>
<li class="chapter" data-level="7.2" data-path="practical.-real-data-with-jamovi.html"><a href="practical.-real-data-with-jamovi.html#some-environmental-example"><i class="fa fa-check"></i><b>7.2</b> Some environmental example</a></li>
<li class="chapter" data-level="7.3" data-path="practical.-real-data-with-jamovi.html"><a href="practical.-real-data-with-jamovi.html#summary-of-exercises-and-why-they-are-useful.-1"><i class="fa fa-check"></i><b>7.3</b> Summary of exercises and why they are useful.</a></li>
</ul></li>
<li class="part"><span><b>IV Probability models and the Central Limit Theorem</b></span></li>
<li class="chapter" data-level="" data-path="week-4-overview.html"><a href="week-4-overview.html"><i class="fa fa-check"></i>Week 4 Overview</a>
<ul>
<li class="chapter" data-level="7.4" data-path="week-4-overview.html"><a href="week-4-overview.html#a-practical-example"><i class="fa fa-check"></i><b>7.4</b> A practical example</a></li>
<li class="chapter" data-level="7.5" data-path="week-4-overview.html"><a href="week-4-overview.html#probability-distributions"><i class="fa fa-check"></i><b>7.5</b> Probability distributions</a>
<ul>
<li class="chapter" data-level="7.5.1" data-path="week-4-overview.html"><a href="week-4-overview.html#binomial-distribution"><i class="fa fa-check"></i><b>7.5.1</b> Binomial distribution</a></li>
<li class="chapter" data-level="7.5.2" data-path="week-4-overview.html"><a href="week-4-overview.html#poisson-distribution"><i class="fa fa-check"></i><b>7.5.2</b> Poisson distribution</a></li>
<li class="chapter" data-level="7.5.3" data-path="week-4-overview.html"><a href="week-4-overview.html#normal-distribution"><i class="fa fa-check"></i><b>7.5.3</b> Normal distribution</a></li>
</ul></li>
<li class="chapter" data-level="7.6" data-path="week-4-overview.html"><a href="week-4-overview.html#examples-of-the-clt-in-action"><i class="fa fa-check"></i><b>7.6</b> Examples of the CLT in action</a></li>
<li class="chapter" data-level="7.7" data-path="week-4-overview.html"><a href="week-4-overview.html#the-standard-normal-distribution"><i class="fa fa-check"></i><b>7.7</b> The standard normal distribution</a></li>
<li class="chapter" data-level="7.8" data-path="week-4-overview.html"><a href="week-4-overview.html#what-are-z-scores"><i class="fa fa-check"></i><b>7.8</b> What are z-scores?</a></li>
<li class="chapter" data-level="7.9" data-path="week-4-overview.html"><a href="week-4-overview.html#calculating-probability-exercise-1"><i class="fa fa-check"></i><b>7.9</b> Calculating probability exercise 1</a></li>
<li class="chapter" data-level="7.10" data-path="week-4-overview.html"><a href="week-4-overview.html#calculating-probability-exercise-2"><i class="fa fa-check"></i><b>7.10</b> Calculating probability exercise 2</a></li>
<li class="chapter" data-level="7.11" data-path="week-4-overview.html"><a href="week-4-overview.html#calculating-probability-from-normal-distribution"><i class="fa fa-check"></i><b>7.11</b> Calculating probability from normal distribution</a></li>
<li class="chapter" data-level="7.12" data-path="week-4-overview.html"><a href="week-4-overview.html#normal-distribution-and-sample-size"><i class="fa fa-check"></i><b>7.12</b> Normal distribution and sample size</a></li>
<li class="chapter" data-level="7.13" data-path="week-4-overview.html"><a href="week-4-overview.html#simulating-the-central-limit-theorem"><i class="fa fa-check"></i><b>7.13</b> Simulating the central limit theorem</a></li>
</ul></li>
<li class="part"><span><b>V Statistical inference</b></span></li>
<li class="chapter" data-level="" data-path="week-5-overview.html"><a href="week-5-overview.html"><i class="fa fa-check"></i>Week 5 Overview</a>
<ul>
<li class="chapter" data-level="7.14" data-path="week-5-overview.html"><a href="week-5-overview.html#example-constructing-confidence-intervals"><i class="fa fa-check"></i><b>7.14</b> Example constructing confidence intervals</a></li>
<li class="chapter" data-level="7.15" data-path="week-5-overview.html"><a href="week-5-overview.html#confidence-interval-for-different-levels-t--and-z-"><i class="fa fa-check"></i><b>7.15</b> Confidence interval for different levels (t- and z-)</a></li>
<li class="chapter" data-level="7.16" data-path="week-5-overview.html"><a href="week-5-overview.html#proportion-confidence-intervals"><i class="fa fa-check"></i><b>7.16</b> Proportion confidence intervals</a></li>
<li class="chapter" data-level="7.17" data-path="week-5-overview.html"><a href="week-5-overview.html#another-confidence-interval-example"><i class="fa fa-check"></i><b>7.17</b> Another confidence interval example?</a></li>
</ul></li>
<li class="part"><span><b>VI Review of parts I-V</b></span></li>
<li class="chapter" data-level="" data-path="week-6-overview-reading-week.html"><a href="week-6-overview-reading-week.html"><i class="fa fa-check"></i>Week 6 Overview (Reading week)</a></li>
<li class="part"><span><b>VII Hypothesis testing</b></span></li>
<li class="chapter" data-level="" data-path="week-7-overview.html"><a href="week-7-overview.html"><i class="fa fa-check"></i>Week 7 Overview</a>
<ul>
<li class="chapter" data-level="7.18" data-path="week-7-overview.html"><a href="week-7-overview.html#exercise-on-a-simple-one-sample-t-test"><i class="fa fa-check"></i><b>7.18</b> Exercise on a simple one sample t-test</a></li>
<li class="chapter" data-level="7.19" data-path="week-7-overview.html"><a href="week-7-overview.html#exercise-on-an-independent-sample-t-test"><i class="fa fa-check"></i><b>7.19</b> Exercise on an independent sample t-test</a></li>
<li class="chapter" data-level="7.20" data-path="week-7-overview.html"><a href="week-7-overview.html#exercise-involving-multiple-comparisons"><i class="fa fa-check"></i><b>7.20</b> Exercise involving multiple comparisons</a></li>
<li class="chapter" data-level="7.21" data-path="week-7-overview.html"><a href="week-7-overview.html#exercise-with-non-parametric"><i class="fa fa-check"></i><b>7.21</b> Exercise with non-parametric</a></li>
<li class="chapter" data-level="7.22" data-path="week-7-overview.html"><a href="week-7-overview.html#another-exercise-with-non-parametric"><i class="fa fa-check"></i><b>7.22</b> Another exercise with non-parametric</a></li>
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<li class="part"><span><b>VIII Analysis of Variance (ANOVA)</b></span></li>
<li class="chapter" data-level="" data-path="week-8-overview.html"><a href="week-8-overview.html"><i class="fa fa-check"></i>Week 8 Overview</a>
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<li class="chapter" data-level="7.23" data-path="week-8-overview.html"><a href="week-8-overview.html#anova-exercise-1"><i class="fa fa-check"></i><b>7.23</b> ANOVA Exercise 1</a></li>
<li class="chapter" data-level="7.24" data-path="week-8-overview.html"><a href="week-8-overview.html#anova-exercise-2"><i class="fa fa-check"></i><b>7.24</b> ANOVA Exercise 2</a></li>
<li class="chapter" data-level="7.25" data-path="week-8-overview.html"><a href="week-8-overview.html#anova-exercise-3"><i class="fa fa-check"></i><b>7.25</b> ANOVA Exercise 3</a></li>
<li class="chapter" data-level="7.26" data-path="week-8-overview.html"><a href="week-8-overview.html#anova-exercise-4"><i class="fa fa-check"></i><b>7.26</b> ANOVA Exercise 4</a></li>
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<li class="part"><span><b>IX Counts and Correlation</b></span></li>
<li class="chapter" data-level="" data-path="week-9-overview.html"><a href="week-9-overview.html"><i class="fa fa-check"></i>Week 9 Overview</a>
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<li class="chapter" data-level="7.27" data-path="week-9-overview.html"><a href="week-9-overview.html#chi-square-exercise-1"><i class="fa fa-check"></i><b>7.27</b> Chi-Square Exercise 1</a></li>
<li class="chapter" data-level="7.28" data-path="week-9-overview.html"><a href="week-9-overview.html#chi-square-association-exercise-2"><i class="fa fa-check"></i><b>7.28</b> Chi-Square association Exercise 2</a></li>
<li class="chapter" data-level="7.29" data-path="week-9-overview.html"><a href="week-9-overview.html#correlation-exercise-3"><i class="fa fa-check"></i><b>7.29</b> Correlation Exercise 3</a></li>
<li class="chapter" data-level="7.30" data-path="week-9-overview.html"><a href="week-9-overview.html#correlation-exercise-4"><i class="fa fa-check"></i><b>7.30</b> Correlation Exercise 4</a></li>
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<li class="part"><span><b>X Linear Regression</b></span></li>
<li class="chapter" data-level="" data-path="week-10-overview.html"><a href="week-10-overview.html"><i class="fa fa-check"></i>Week 10 Overview</a>
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<li class="chapter" data-level="7.31" data-path="week-10-overview.html"><a href="week-10-overview.html#regression-exercise-1"><i class="fa fa-check"></i><b>7.31</b> Regression Exercise 1</a></li>
<li class="chapter" data-level="7.32" data-path="week-10-overview.html"><a href="week-10-overview.html#regression-exercise-2"><i class="fa fa-check"></i><b>7.32</b> Regression Exercise 2</a></li>
<li class="chapter" data-level="7.33" data-path="week-10-overview.html"><a href="week-10-overview.html#regression-exercise-3"><i class="fa fa-check"></i><b>7.33</b> Regression Exercise 3</a></li>
<li class="chapter" data-level="7.34" data-path="week-10-overview.html"><a href="week-10-overview.html#regression-exercise-4"><i class="fa fa-check"></i><b>7.34</b> Regression Exercise 4</a></li>
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<li class="part"><span><b>XI Randomisation approaches</b></span></li>
<li class="chapter" data-level="" data-path="week-11-overview.html"><a href="week-11-overview.html"><i class="fa fa-check"></i>Week 11 Overview</a>
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<li class="chapter" data-level="7.35" data-path="week-11-overview.html"><a href="week-11-overview.html#r-exercise-1"><i class="fa fa-check"></i><b>7.35</b> R Exercise 1</a></li>
<li class="chapter" data-level="7.36" data-path="week-11-overview.html"><a href="week-11-overview.html#r-exercise-2"><i class="fa fa-check"></i><b>7.36</b> R Exercise 2</a></li>
<li class="chapter" data-level="7.37" data-path="week-11-overview.html"><a href="week-11-overview.html#r-exercise-3"><i class="fa fa-check"></i><b>7.37</b> R Exercise 3</a></li>
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<li class="part"><span><b>XII Statistical Reporting</b></span></li>
<li class="chapter" data-level="" data-path="week-12-overview.html"><a href="week-12-overview.html"><i class="fa fa-check"></i>Week 12 Overview</a>
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<li class="chapter" data-level="7.38" data-path="week-12-overview.html"><a href="week-12-overview.html#r-exercise-1-1"><i class="fa fa-check"></i><b>7.38</b> R Exercise 1</a></li>
<li class="chapter" data-level="7.39" data-path="week-12-overview.html"><a href="week-12-overview.html#r-exercise-2-1"><i class="fa fa-check"></i><b>7.39</b> R Exercise 2</a></li>
<li class="chapter" data-level="7.40" data-path="week-12-overview.html"><a href="week-12-overview.html#r-exercise-3-1"><i class="fa fa-check"></i><b>7.40</b> R Exercise 3</a></li>
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<li class="part"><span><b>XIII Review of parts (VII-XII)</b></span></li>
<li class="chapter" data-level="" data-path="module-summary.html"><a href="module-summary.html"><i class="fa fa-check"></i>Module summary</a></li>
<li class="appendix"><span><b>Appendix</b></span></li>
<li class="chapter" data-level="A" data-path="appendixA_units.html"><a href="appendixA_units.html"><i class="fa fa-check"></i><b>A</b> Statistical units</a></li>
<li class="chapter" data-level="" data-path="references.html"><a href="references.html"><i class="fa fa-check"></i>References</a></li>
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<li><a href="https://github.com/rstudio/bookdown" target="blank">Published with bookdown</a></li>
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