ETC3250/5250: Introduction to Machine Learning

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# .monash-blue[ETC3250/5250: Introduction to Machine Learning]

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<h2 style="font-weight:900!important;">Hierarchical clustering</h2>

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Lecturer: *Professor Di Cook*

Department of Econometrics and Business Statistics

<i class="fas fa-envelope"></i>  ETC3250.Clayton-x@monash.edu

<i class="fas fa-calendar-alt"></i> Week 10a

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## Hierarchical clustering

<br>

- .monash-orange2[Agglomeration]: Begin with all observations in singleton clusters. Sequentially .monash-orange2[join] points into clusters, until all are in one cluster. 
- .monash-orange2[Divisive]: Begin with all observtions in one cluster, adn sequentially .monash-orange2[divide] until all observations are in singleton clusters. 
- Produces a tree diagram illustrating the process, called a .monash-orange2[dendrogram].

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Some new data 🤸

<img src="images/lecture-10a/unnamed-chunk-3-1.png" width="100%" style="display: block; margin: auto;" />
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`\(n\times n\)` distance matrix 📏

<table class="table table-striped" style="font-size: 24px; margin-left: auto; margin-right: auto;">
 <thead>
  <tr>
   <th style="text-align:left;color: white !important;background-color: #3F9F7A !important;">   </th>
   <th style="text-align:right;color: white !important;background-color: #3F9F7A !important;"> a </th>
   <th style="text-align:right;color: white !important;background-color: #3F9F7A !important;"> b </th>
   <th style="text-align:right;color: white !important;background-color: #3F9F7A !important;"> c </th>
   <th style="text-align:right;color: white !important;background-color: #3F9F7A !important;"> d </th>
   <th style="text-align:right;color: white !important;background-color: #3F9F7A !important;"> e </th>
   <th style="text-align:right;color: white !important;background-color: #3F9F7A !important;"> f </th>
   <th style="text-align:right;color: white !important;background-color: #3F9F7A !important;"> g </th>
   <th style="text-align:right;color: white !important;background-color: #3F9F7A !important;"> h </th>
   <th style="text-align:right;color: white !important;background-color: #3F9F7A !important;"> i </th>
   <th style="text-align:right;color: white !important;background-color: #3F9F7A !important;"> j </th>
   <th style="text-align:right;color: white !important;background-color: #3F9F7A !important;"> k </th>
   <th style="text-align:right;color: white !important;background-color: #3F9F7A !important;"> l </th>
  </tr>
 </thead>
<tbody>
  <tr>
   <td style="text-align:left;color: white !important;background-color: #3F9F7A !important;width: 1cm; border-right:1px solid;"> a </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 0.0 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 8.1 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 5.0 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 3.6 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 14.9 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 13.0 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 19.8 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 13.4 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 9.2 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 14.3 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 8.9 </td>
   <td style="text-align:right;"> 11.0 </td>
  </tr>
  <tr>
   <td style="text-align:left;color: white !important;background-color: #3F9F7A !important;width: 1cm; border-right:1px solid;"> b </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 8.1 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 0.0 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 4.5 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 5.8 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 19.8 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 18.4 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 26.4 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 19.1 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 8.2 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 15.8 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 9.8 </td>
   <td style="text-align:right;"> 14.4 </td>
  </tr>
  <tr>
   <td style="text-align:left;color: white !important;background-color: #3F9F7A !important;width: 1cm; border-right:1px solid;"> c </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 5.0 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 4.5 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 0.0 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 5.1 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 19.2 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 17.5 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 24.8 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 18.0 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 10.2 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 17.0 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 11.0 </td>
   <td style="text-align:right;"> 14.6 </td>
  </tr>
  <tr>
   <td style="text-align:left;color: white !important;background-color: #3F9F7A !important;width: 1cm; border-right:1px solid;"> d </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 3.6 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 5.8 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 5.1 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 0.0 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 14.4 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 12.8 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 20.6 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 13.5 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 5.8 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 12.0 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 6.1 </td>
   <td style="text-align:right;"> 9.5 </td>
  </tr>
  <tr>
   <td style="text-align:left;color: white !important;background-color: #3F9F7A !important;width: 1cm; border-right:1px solid;"> e </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 14.9 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 19.8 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 19.2 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 14.4 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 0.0 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 2.0 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 8.1 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 2.2 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 13.0 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 8.0 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 10.8 </td>
   <td style="text-align:right;"> 5.8 </td>
  </tr>
  <tr>
   <td style="text-align:left;color: white !important;background-color: #3F9F7A !important;width: 1cm; border-right:1px solid;"> f </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 13.0 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 18.4 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 17.5 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 12.8 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 2.0 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 0.0 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 8.5 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 1.0 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 12.1 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 8.2 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 9.8 </td>
   <td style="text-align:right;"> 5.1 </td>
  </tr>
  <tr>
   <td style="text-align:left;color: white !important;background-color: #3F9F7A !important;width: 1cm; border-right:1px solid;"> g </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 19.8 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 26.4 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 24.8 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 20.6 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 8.1 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 8.5 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 0.0 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 7.6 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 20.6 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 16.0 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 18.4 </td>
   <td style="text-align:right;"> 13.6 </td>
  </tr>
  <tr>
   <td style="text-align:left;color: white !important;background-color: #3F9F7A !important;width: 1cm; border-right:1px solid;"> h </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 13.4 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 19.1 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 18.0 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 13.5 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 2.2 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 1.0 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 7.6 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 0.0 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 13.0 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 9.2 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 10.8 </td>
   <td style="text-align:right;"> 6.1 </td>
  </tr>
  <tr>
   <td style="text-align:left;color: white !important;background-color: #3F9F7A !important;width: 1cm; border-right:1px solid;"> i </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 9.2 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 8.2 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 10.2 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 5.8 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 13.0 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 12.1 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 20.6 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 13.0 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 0.0 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 7.6 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 2.2 </td>
   <td style="text-align:right;"> 7.2 </td>
  </tr>
  <tr>
   <td style="text-align:left;color: white !important;background-color: #3F9F7A !important;width: 1cm; border-right:1px solid;"> j </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 14.3 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 15.8 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 17.0 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 12.0 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 8.0 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 8.2 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 16.0 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 9.2 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 7.6 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 0.0 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 6.1 </td>
   <td style="text-align:right;"> 4.2 </td>
  </tr>
  <tr>
   <td style="text-align:left;color: white !important;background-color: #3F9F7A !important;width: 1cm; border-right:1px solid;"> k </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 8.9 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 9.8 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 11.0 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 6.1 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 10.8 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 9.8 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 18.4 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 10.8 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 2.2 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 6.1 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 0.0 </td>
   <td style="text-align:right;"> 5.0 </td>
  </tr>
  <tr>
   <td style="text-align:left;color: white !important;background-color: #3F9F7A !important;width: 1cm; border-right:1px solid;"> l </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 11.0 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 14.4 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 14.6 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 9.5 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 5.8 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 5.1 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 13.6 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 6.1 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 7.2 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 4.2 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 5.0 </td>
   <td style="text-align:right;"> 0.0 </td>
  </tr>
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class: middle center

# 🤔

What is the .monash-orange2[distance] between the new .monash-orange2[cluster (f,h)] and all of the other observations?

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## Linkage

Between points .monash-orange2[in] the cluster to points .monash-orange2[not in] the cluster.

- .monash-orange2[Single]: minimum distance between points in the different clusters
- .monash-orange2[Complete]: maximum distance between points in the different clusters
- .monash-orange2[Average]: average of distances between points in the different clusters
- .monash-orange2[Centroid]: distances between the average of the different clusters
- .monash-orange2[Wards]: minimizes the total within-cluster variance

---

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<table class="table table-striped" style="font-size: 24px; margin-left: auto; margin-right: auto;">
 <thead>
  <tr>
   <th style="text-align:left;color: white !important;background-color: #3F9F7A !important;">   </th>
   <th style="text-align:right;color: white !important;background-color: #3F9F7A !important;"> a </th>
   <th style="text-align:right;color: white !important;background-color: #3F9F7A !important;"> b </th>
   <th style="text-align:right;color: white !important;background-color: #3F9F7A !important;"> c </th>
   <th style="text-align:right;color: white !important;background-color: #3F9F7A !important;"> d </th>
   <th style="text-align:right;color: white !important;background-color: #3F9F7A !important;"> e </th>
   <th style="text-align:right;color: white !important;background-color: #3F9F7A !important;"> f </th>
   <th style="text-align:right;color: white !important;background-color: #3F9F7A !important;"> g </th>
   <th style="text-align:right;color: white !important;background-color: #3F9F7A !important;"> h </th>
   <th style="text-align:right;color: white !important;background-color: #3F9F7A !important;"> i </th>
   <th style="text-align:right;color: white !important;background-color: #3F9F7A !important;"> j </th>
   <th style="text-align:right;color: white !important;background-color: #3F9F7A !important;"> k </th>
   <th style="text-align:right;color: white !important;background-color: #3F9F7A !important;"> l </th>
  </tr>
 </thead>
<tbody>
  <tr>
   <td style="text-align:left;color: white !important;background-color: #3F9F7A !important;width: 1cm; border-right:1px solid;"> a </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 0.0 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 8.1 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 5.0 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 3.6 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 14.9 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;color: #7570B3 !important;"> 13.0 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 19.8 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;color: #7570B3 !important;"> 13.4 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 9.2 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 14.3 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 8.9 </td>
   <td style="text-align:right;"> 11.0 </td>
  </tr>
  <tr>
   <td style="text-align:left;color: white !important;background-color: #3F9F7A !important;width: 1cm; border-right:1px solid;"> b </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 8.1 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 0.0 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 4.5 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 5.8 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 19.8 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;color: #7570B3 !important;"> 18.4 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 26.4 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;color: #7570B3 !important;"> 19.1 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 8.2 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 15.8 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 9.8 </td>
   <td style="text-align:right;"> 14.4 </td>
  </tr>
  <tr>
   <td style="text-align:left;color: white !important;background-color: #3F9F7A !important;width: 1cm; border-right:1px solid;"> c </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 5.0 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 4.5 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 0.0 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 5.1 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 19.2 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;color: #7570B3 !important;"> 17.5 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 24.8 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;color: #7570B3 !important;"> 18.0 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 10.2 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 17.0 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 11.0 </td>
   <td style="text-align:right;"> 14.6 </td>
  </tr>
  <tr>
   <td style="text-align:left;color: white !important;background-color: #3F9F7A !important;width: 1cm; border-right:1px solid;"> d </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 3.6 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 5.8 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 5.1 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 0.0 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 14.4 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;color: #7570B3 !important;"> 12.8 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 20.6 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;color: #7570B3 !important;"> 13.5 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 5.8 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 12.0 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 6.1 </td>
   <td style="text-align:right;"> 9.5 </td>
  </tr>
  <tr>
   <td style="text-align:left;color: white !important;background-color: #3F9F7A !important;width: 1cm; border-right:1px solid;"> e </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 14.9 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 19.8 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 19.2 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 14.4 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 0.0 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;color: #7570B3 !important;"> 2.0 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 8.1 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;color: #7570B3 !important;"> 2.2 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 13.0 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 8.0 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 10.8 </td>
   <td style="text-align:right;"> 5.8 </td>
  </tr>
  <tr>
   <td style="text-align:left;color: white !important;background-color: #3F9F7A !important;width: 1cm; border-right:1px solid;color: #7570B3 !important;"> f </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;color: #7570B3 !important;"> 13.0 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;color: #7570B3 !important;"> 18.4 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;color: #7570B3 !important;"> 17.5 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;color: #7570B3 !important;"> 12.8 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;color: #7570B3 !important;"> 2.0 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;color: #7570B3 !important;color: #7570B3 !important;"> 0.0 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;color: #7570B3 !important;"> 8.5 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;color: #7570B3 !important;color: #7570B3 !important;"> 1.0 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;color: #7570B3 !important;"> 12.1 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;color: #7570B3 !important;"> 8.2 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;color: #7570B3 !important;"> 9.8 </td>
   <td style="text-align:right;color: #7570B3 !important;"> 5.1 </td>
  </tr>
  <tr>
   <td style="text-align:left;color: white !important;background-color: #3F9F7A !important;width: 1cm; border-right:1px solid;"> g </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 19.8 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 26.4 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 24.8 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 20.6 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 8.1 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;color: #7570B3 !important;"> 8.5 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 0.0 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;color: #7570B3 !important;"> 7.6 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 20.6 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 16.0 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 18.4 </td>
   <td style="text-align:right;"> 13.6 </td>
  </tr>
  <tr>
   <td style="text-align:left;color: white !important;background-color: #3F9F7A !important;width: 1cm; border-right:1px solid;color: #7570B3 !important;"> h </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;color: #7570B3 !important;"> 13.4 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;color: #7570B3 !important;"> 19.1 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;color: #7570B3 !important;"> 18.0 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;color: #7570B3 !important;"> 13.5 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;color: #7570B3 !important;"> 2.2 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;color: #7570B3 !important;color: #7570B3 !important;"> 1.0 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;color: #7570B3 !important;"> 7.6 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;color: #7570B3 !important;color: #7570B3 !important;"> 0.0 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;color: #7570B3 !important;"> 13.0 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;color: #7570B3 !important;"> 9.2 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;color: #7570B3 !important;"> 10.8 </td>
   <td style="text-align:right;color: #7570B3 !important;"> 6.1 </td>
  </tr>
  <tr>
   <td style="text-align:left;color: white !important;background-color: #3F9F7A !important;width: 1cm; border-right:1px solid;"> i </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 9.2 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 8.2 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 10.2 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 5.8 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 13.0 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;color: #7570B3 !important;"> 12.1 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 20.6 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;color: #7570B3 !important;"> 13.0 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 0.0 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 7.6 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 2.2 </td>
   <td style="text-align:right;"> 7.2 </td>
  </tr>
  <tr>
   <td style="text-align:left;color: white !important;background-color: #3F9F7A !important;width: 1cm; border-right:1px solid;"> j </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 14.3 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 15.8 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 17.0 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 12.0 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 8.0 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;color: #7570B3 !important;"> 8.2 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 16.0 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;color: #7570B3 !important;"> 9.2 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 7.6 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 0.0 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 6.1 </td>
   <td style="text-align:right;"> 4.2 </td>
  </tr>
  <tr>
   <td style="text-align:left;color: white !important;background-color: #3F9F7A !important;width: 1cm; border-right:1px solid;"> k </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 8.9 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 9.8 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 11.0 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 6.1 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 10.8 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;color: #7570B3 !important;"> 9.8 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 18.4 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;color: #7570B3 !important;"> 10.8 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 2.2 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 6.1 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 0.0 </td>
   <td style="text-align:right;"> 5.0 </td>
  </tr>
  <tr>
   <td style="text-align:left;color: white !important;background-color: #3F9F7A !important;width: 1cm; border-right:1px solid;"> l </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 11.0 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 14.4 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 14.6 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 9.5 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 5.8 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;color: #7570B3 !important;"> 5.1 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 13.6 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;color: #7570B3 !important;"> 6.1 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 7.2 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 4.2 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 5.0 </td>
   <td style="text-align:right;"> 0.0 </td>
  </tr>
</tbody>
</table>
]]]
.column[.pad50px[.content[

Single: 13.0 or 13.4 `\(\rightarrow\)` .monash-orange2[13.0] <br>
Complete: 13.0 or 13.4 `\(\rightarrow\)` .monash-orange2[13.4] <br>
Average: (13.0 + 13.4)/2 = .monash-orange2[13.2] <br>
Centroid: .monash-orange2[13.2] <br>
mean of (f,h) is (5, 14.5) <br>
          mean of a (17,9) <br>
          `\(\sqrt{(5-17)^2 + (14.5-9)^2}\)` <br>
Wards: Your turn to calculate it 🤷

]]]

---
class: split-60
layout: false

]]]

---
class: split-60
layout: false

<table class="table table-striped" style="font-size: 24px; margin-left: auto; margin-right: auto;">
 <thead>
  <tr>
   <th style="text-align:left;color: white !important;background-color: #3F9F7A !important;">   </th>
   <th style="text-align:right;color: white !important;background-color: #3F9F7A !important;"> a </th>
   <th style="text-align:right;color: white !important;background-color: #3F9F7A !important;"> b </th>
   <th style="text-align:right;color: white !important;background-color: #3F9F7A !important;"> c </th>
   <th style="text-align:right;color: white !important;background-color: #3F9F7A !important;"> d </th>
   <th style="text-align:right;color: white !important;background-color: #3F9F7A !important;"> e </th>
   <th style="text-align:right;color: white !important;background-color: #3F9F7A !important;"> (f,h) </th>
   <th style="text-align:right;color: white !important;background-color: #3F9F7A !important;"> g </th>
   <th style="text-align:right;color: white !important;background-color: #3F9F7A !important;"> i </th>
   <th style="text-align:right;color: white !important;background-color: #3F9F7A !important;"> j </th>
   <th style="text-align:right;color: white !important;background-color: #3F9F7A !important;"> k </th>
   <th style="text-align:right;color: white !important;background-color: #3F9F7A !important;"> l </th>
  </tr>
 </thead>
<tbody>
  <tr>
   <td style="text-align:left;color: white !important;background-color: #3F9F7A !important;width: 1cm; border-right:1px solid;"> a </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 0.0 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 8.1 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 5.0 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 3.6 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 14.9 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;color: #7570B3 !important;"> 13.0 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 19.8 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 9.2 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 14.3 </td>
   <td style="text-align:right;"> 8.9 </td>
   <td style="text-align:right;"> 11.0 </td>
  </tr>
  <tr>
   <td style="text-align:left;color: white !important;background-color: #3F9F7A !important;width: 1cm; border-right:1px solid;"> b </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 8.1 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 0.0 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 4.5 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 5.8 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 19.8 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;color: #7570B3 !important;"> 18.4 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 26.4 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 8.2 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 15.8 </td>
   <td style="text-align:right;"> 9.8 </td>
   <td style="text-align:right;"> 14.4 </td>
  </tr>
  <tr>
   <td style="text-align:left;color: white !important;background-color: #3F9F7A !important;width: 1cm; border-right:1px solid;"> c </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 5.0 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 4.5 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 0.0 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 5.1 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 19.2 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;color: #7570B3 !important;"> 17.5 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 24.8 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 10.2 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 17.0 </td>
   <td style="text-align:right;"> 11.0 </td>
   <td style="text-align:right;"> 14.6 </td>
  </tr>
  <tr>
   <td style="text-align:left;color: white !important;background-color: #3F9F7A !important;width: 1cm; border-right:1px solid;"> d </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 3.6 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 5.8 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 5.1 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 0.0 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 14.4 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;color: #7570B3 !important;"> 12.8 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 20.6 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 5.8 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 12.0 </td>
   <td style="text-align:right;"> 6.1 </td>
   <td style="text-align:right;"> 9.5 </td>
  </tr>
  <tr>
   <td style="text-align:left;color: white !important;background-color: #3F9F7A !important;width: 1cm; border-right:1px solid;"> e </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 14.9 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 19.8 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 19.2 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 14.4 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 0.0 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;color: #7570B3 !important;"> 2.0 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 8.1 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 13.0 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 8.0 </td>
   <td style="text-align:right;"> 10.8 </td>
   <td style="text-align:right;"> 5.8 </td>
  </tr>
  <tr>
   <td style="text-align:left;color: white !important;background-color: #3F9F7A !important;width: 1cm; border-right:1px solid;color: #7570B3 !important;"> (f,h) </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;color: #7570B3 !important;"> 13.0 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;color: #7570B3 !important;"> 18.4 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;color: #7570B3 !important;"> 17.5 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;color: #7570B3 !important;"> 12.8 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;color: #7570B3 !important;"> 2.0 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;color: #7570B3 !important;color: #7570B3 !important;"> 0.0 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;color: #7570B3 !important;"> 7.6 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;color: #7570B3 !important;"> 12.1 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;color: #7570B3 !important;"> 8.2 </td>
   <td style="text-align:right;color: #7570B3 !important;"> 9.8 </td>
   <td style="text-align:right;color: #7570B3 !important;"> 5.1 </td>
  </tr>
  <tr>
   <td style="text-align:left;color: white !important;background-color: #3F9F7A !important;width: 1cm; border-right:1px solid;"> g </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 19.8 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 26.4 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 24.8 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 20.6 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 8.1 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;color: #7570B3 !important;"> 7.6 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 0.0 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 20.6 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 16.0 </td>
   <td style="text-align:right;"> 18.4 </td>
   <td style="text-align:right;"> 13.6 </td>
  </tr>
  <tr>
   <td style="text-align:left;color: white !important;background-color: #3F9F7A !important;width: 1cm; border-right:1px solid;"> i </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 9.2 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 8.2 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 10.2 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 5.8 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 13.0 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;color: #7570B3 !important;"> 12.1 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 20.6 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 0.0 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 7.6 </td>
   <td style="text-align:right;"> 2.2 </td>
   <td style="text-align:right;"> 7.2 </td>
  </tr>
  <tr>
   <td style="text-align:left;color: white !important;background-color: #3F9F7A !important;width: 1cm; border-right:1px solid;"> j </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 14.3 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 15.8 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 17.0 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 12.0 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 8.0 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;color: #7570B3 !important;"> 8.2 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 16.0 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 7.6 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 0.0 </td>
   <td style="text-align:right;"> 6.1 </td>
   <td style="text-align:right;"> 4.2 </td>
  </tr>
  <tr>
   <td style="text-align:left;color: white !important;background-color: #3F9F7A !important;width: 1cm; border-right:1px solid;"> k </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 8.9 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 9.8 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 11.0 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 6.1 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 10.8 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;color: #7570B3 !important;"> 9.8 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 18.4 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 2.2 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 6.1 </td>
   <td style="text-align:right;"> 0.0 </td>
   <td style="text-align:right;"> 5.0 </td>
  </tr>
  <tr>
   <td style="text-align:left;color: white !important;background-color: #3F9F7A !important;width: 1cm; border-right:1px solid;"> l </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 11.0 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 14.4 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 14.6 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 9.5 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 5.8 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;color: #7570B3 !important;"> 5.1 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 13.6 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 7.2 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 4.2 </td>
   <td style="text-align:right;"> 5.0 </td>
   <td style="text-align:right;"> 0.0 </td>
  </tr>
</tbody>
</table>
]]]
.column[.pad50px[.content[

🤔 Now which .monash-orange2[distance is the smallest]?

<br>

]]]

---
class: split-60
layout: false

<table class="table table-striped" style="font-size: 24px; margin-left: auto; margin-right: auto;">
 <thead>
  <tr>
   <th style="text-align:left;color: white !important;background-color: #3F9F7A !important;">   </th>
   <th style="text-align:right;color: white !important;background-color: #3F9F7A !important;"> a </th>
   <th style="text-align:right;color: white !important;background-color: #3F9F7A !important;"> b </th>
   <th style="text-align:right;color: white !important;background-color: #3F9F7A !important;"> c </th>
   <th style="text-align:right;color: white !important;background-color: #3F9F7A !important;"> d </th>
   <th style="text-align:right;color: white !important;background-color: #3F9F7A !important;"> e </th>
   <th style="text-align:right;color: white !important;background-color: #3F9F7A !important;"> (f,h) </th>
   <th style="text-align:right;color: white !important;background-color: #3F9F7A !important;"> g </th>
   <th style="text-align:right;color: white !important;background-color: #3F9F7A !important;"> i </th>
   <th style="text-align:right;color: white !important;background-color: #3F9F7A !important;"> j </th>
   <th style="text-align:right;color: white !important;background-color: #3F9F7A !important;"> k </th>
   <th style="text-align:right;color: white !important;background-color: #3F9F7A !important;"> l </th>
  </tr>
 </thead>
<tbody>
  <tr>
   <td style="text-align:left;color: white !important;background-color: #3F9F7A !important;width: 1cm; border-right:1px solid;"> a </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 0.0 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 8.1 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 5.0 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 3.6 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 14.9 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;color: #7570B3 !important;"> 13.4 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 19.8 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 9.2 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 14.3 </td>
   <td style="text-align:right;"> 8.9 </td>
   <td style="text-align:right;"> 11.0 </td>
  </tr>
  <tr>
   <td style="text-align:left;color: white !important;background-color: #3F9F7A !important;width: 1cm; border-right:1px solid;"> b </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 8.1 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 0.0 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 4.5 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 5.8 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 19.8 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;color: #7570B3 !important;"> 19.1 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 26.4 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 8.2 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 15.8 </td>
   <td style="text-align:right;"> 9.8 </td>
   <td style="text-align:right;"> 14.4 </td>
  </tr>
  <tr>
   <td style="text-align:left;color: white !important;background-color: #3F9F7A !important;width: 1cm; border-right:1px solid;"> c </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 5.0 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 4.5 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 0.0 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 5.1 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 19.2 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;color: #7570B3 !important;"> 18.0 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 24.8 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 10.2 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 17.0 </td>
   <td style="text-align:right;"> 11.0 </td>
   <td style="text-align:right;"> 14.6 </td>
  </tr>
  <tr>
   <td style="text-align:left;color: white !important;background-color: #3F9F7A !important;width: 1cm; border-right:1px solid;"> d </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 3.6 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 5.8 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 5.1 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 0.0 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 14.4 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;color: #7570B3 !important;"> 13.5 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 20.6 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 5.8 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 12.0 </td>
   <td style="text-align:right;"> 6.1 </td>
   <td style="text-align:right;"> 9.5 </td>
  </tr>
  <tr>
   <td style="text-align:left;color: white !important;background-color: #3F9F7A !important;width: 1cm; border-right:1px solid;"> e </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 14.9 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 19.8 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 19.2 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 14.4 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 0.0 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;color: #7570B3 !important;"> 2.2 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 8.1 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 13.0 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 8.0 </td>
   <td style="text-align:right;"> 10.8 </td>
   <td style="text-align:right;"> 5.8 </td>
  </tr>
  <tr>
   <td style="text-align:left;color: white !important;background-color: #3F9F7A !important;width: 1cm; border-right:1px solid;color: #7570B3 !important;"> (f,h) </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;color: #7570B3 !important;"> 13.4 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;color: #7570B3 !important;"> 19.1 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;color: #7570B3 !important;"> 18.0 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;color: #7570B3 !important;"> 13.5 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;color: #7570B3 !important;"> 2.2 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;color: #7570B3 !important;color: #7570B3 !important;"> 0.0 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;color: #7570B3 !important;"> 8.5 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;color: #7570B3 !important;"> 13.0 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;color: #7570B3 !important;"> 9.2 </td>
   <td style="text-align:right;color: #7570B3 !important;"> 10.8 </td>
   <td style="text-align:right;color: #7570B3 !important;"> 6.1 </td>
  </tr>
  <tr>
   <td style="text-align:left;color: white !important;background-color: #3F9F7A !important;width: 1cm; border-right:1px solid;"> g </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 19.8 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 26.4 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 24.8 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 20.6 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 8.1 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;color: #7570B3 !important;"> 8.5 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 0.0 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 20.6 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 16.0 </td>
   <td style="text-align:right;"> 18.4 </td>
   <td style="text-align:right;"> 13.6 </td>
  </tr>
  <tr>
   <td style="text-align:left;color: white !important;background-color: #3F9F7A !important;width: 1cm; border-right:1px solid;"> i </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 9.2 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 8.2 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 10.2 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 5.8 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 13.0 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;color: #7570B3 !important;"> 13.0 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 20.6 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 0.0 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 7.6 </td>
   <td style="text-align:right;"> 2.2 </td>
   <td style="text-align:right;"> 7.2 </td>
  </tr>
  <tr>
   <td style="text-align:left;color: white !important;background-color: #3F9F7A !important;width: 1cm; border-right:1px solid;"> j </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 14.3 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 15.8 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 17.0 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 12.0 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 8.0 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;color: #7570B3 !important;"> 9.2 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 16.0 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 7.6 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 0.0 </td>
   <td style="text-align:right;"> 6.1 </td>
   <td style="text-align:right;"> 4.2 </td>
  </tr>
  <tr>
   <td style="text-align:left;color: white !important;background-color: #3F9F7A !important;width: 1cm; border-right:1px solid;"> k </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 8.9 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 9.8 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 11.0 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 6.1 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 10.8 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;color: #7570B3 !important;"> 10.8 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 18.4 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 2.2 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 6.1 </td>
   <td style="text-align:right;"> 0.0 </td>
   <td style="text-align:right;"> 5.0 </td>
  </tr>
  <tr>
   <td style="text-align:left;color: white !important;background-color: #3F9F7A !important;width: 1cm; border-right:1px solid;"> l </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 11.0 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 14.4 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 14.6 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 9.5 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 5.8 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;color: #7570B3 !important;"> 6.1 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 13.6 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 7.2 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 4.2 </td>
   <td style="text-align:right;"> 5.0 </td>
   <td style="text-align:right;"> 0.0 </td>
  </tr>
</tbody>
</table>
]]]
.column[.pad50px[.content[

🤔 Now which .monash-orange2[distance is the smallest]?

<br>

]]]

---
class: split-60
layout: false

<table class="table table-striped" style="font-size: 24px; margin-left: auto; margin-right: auto;">
 <thead>
  <tr>
   <th style="text-align:left;color: white !important;background-color: #3F9F7A !important;">   </th>
   <th style="text-align:right;color: white !important;background-color: #3F9F7A !important;"> a </th>
   <th style="text-align:right;color: white !important;background-color: #3F9F7A !important;"> b </th>
   <th style="text-align:right;color: white !important;background-color: #3F9F7A !important;"> c </th>
   <th style="text-align:right;color: white !important;background-color: #3F9F7A !important;"> d </th>
   <th style="text-align:right;color: white !important;background-color: #3F9F7A !important;"> e </th>
   <th style="text-align:right;color: white !important;background-color: #3F9F7A !important;"> (f,h) </th>
   <th style="text-align:right;color: white !important;background-color: #3F9F7A !important;"> g </th>
   <th style="text-align:right;color: white !important;background-color: #3F9F7A !important;"> i </th>
   <th style="text-align:right;color: white !important;background-color: #3F9F7A !important;"> j </th>
   <th style="text-align:right;color: white !important;background-color: #3F9F7A !important;"> k </th>
   <th style="text-align:right;color: white !important;background-color: #3F9F7A !important;"> l </th>
  </tr>
 </thead>
<tbody>
  <tr>
   <td style="text-align:left;color: white !important;background-color: #3F9F7A !important;width: 1cm; border-right:1px solid;"> a </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 0.0 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 8.1 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 5.0 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 3.6 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 14.9 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;color: #7570B3 !important;"> 13.0 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 19.8 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 9.2 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 14.3 </td>
   <td style="text-align:right;"> 8.9 </td>
   <td style="text-align:right;"> 11.0 </td>
  </tr>
  <tr>
   <td style="text-align:left;color: white !important;background-color: #3F9F7A !important;width: 1cm; border-right:1px solid;"> b </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 8.1 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 0.0 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 4.5 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 5.8 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 19.8 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;color: #7570B3 !important;"> 18.4 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 26.4 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 8.2 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 15.8 </td>
   <td style="text-align:right;"> 9.8 </td>
   <td style="text-align:right;"> 14.4 </td>
  </tr>
  <tr>
   <td style="text-align:left;color: white !important;background-color: #3F9F7A !important;width: 1cm; border-right:1px solid;"> c </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 5.0 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 4.5 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 0.0 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 5.1 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 19.2 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;color: #7570B3 !important;"> 17.5 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 24.8 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 10.2 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 17.0 </td>
   <td style="text-align:right;"> 11.0 </td>
   <td style="text-align:right;"> 14.6 </td>
  </tr>
  <tr>
   <td style="text-align:left;color: white !important;background-color: #3F9F7A !important;width: 1cm; border-right:1px solid;"> d </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 3.6 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 5.8 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 5.1 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 0.0 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 14.4 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;color: #7570B3 !important;"> 12.8 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 20.6 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 5.8 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 12.0 </td>
   <td style="text-align:right;"> 6.1 </td>
   <td style="text-align:right;"> 9.5 </td>
  </tr>
  <tr>
   <td style="text-align:left;color: white !important;background-color: #3F9F7A !important;width: 1cm; border-right:1px solid;"> e </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 14.9 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 19.8 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 19.2 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 14.4 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 0.0 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;color: #7570B3 !important;"> 2.0 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 8.1 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 13.0 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 8.0 </td>
   <td style="text-align:right;"> 10.8 </td>
   <td style="text-align:right;"> 5.8 </td>
  </tr>
  <tr>
   <td style="text-align:left;color: white !important;background-color: #3F9F7A !important;width: 1cm; border-right:1px solid;color: #7570B3 !important;"> (f,h) </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;color: #7570B3 !important;"> 13.0 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;color: #7570B3 !important;"> 18.4 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;color: #7570B3 !important;"> 17.5 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;color: #7570B3 !important;"> 12.8 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;color: #7570B3 !important;"> 2.0 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;color: #7570B3 !important;color: #7570B3 !important;"> 0.0 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;color: #7570B3 !important;"> 8.5 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;color: #7570B3 !important;"> 12.1 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;color: #7570B3 !important;"> 8.2 </td>
   <td style="text-align:right;color: #7570B3 !important;"> 9.8 </td>
   <td style="text-align:right;color: #7570B3 !important;"> 5.1 </td>
  </tr>
  <tr>
   <td style="text-align:left;color: white !important;background-color: #3F9F7A !important;width: 1cm; border-right:1px solid;"> g </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 19.8 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 26.4 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 24.8 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 20.6 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 8.1 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;color: #7570B3 !important;"> 8.5 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 0.0 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 20.6 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 16.0 </td>
   <td style="text-align:right;"> 18.4 </td>
   <td style="text-align:right;"> 13.6 </td>
  </tr>
  <tr>
   <td style="text-align:left;color: white !important;background-color: #3F9F7A !important;width: 1cm; border-right:1px solid;"> i </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 9.2 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 8.2 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 10.2 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 5.8 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 13.0 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;color: #7570B3 !important;"> 12.1 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 20.6 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 0.0 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 7.6 </td>
   <td style="text-align:right;"> 2.2 </td>
   <td style="text-align:right;"> 7.2 </td>
  </tr>
  <tr>
   <td style="text-align:left;color: white !important;background-color: #3F9F7A !important;width: 1cm; border-right:1px solid;"> j </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 14.3 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 15.8 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 17.0 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 12.0 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 8.0 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;color: #7570B3 !important;"> 8.2 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 16.0 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 7.6 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 0.0 </td>
   <td style="text-align:right;"> 6.1 </td>
   <td style="text-align:right;"> 4.2 </td>
  </tr>
  <tr>
   <td style="text-align:left;color: white !important;background-color: #3F9F7A !important;width: 1cm; border-right:1px solid;"> k </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 8.9 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 9.8 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 11.0 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 6.1 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 10.8 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;color: #7570B3 !important;"> 9.8 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 18.4 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 2.2 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 6.1 </td>
   <td style="text-align:right;"> 0.0 </td>
   <td style="text-align:right;"> 5.0 </td>
  </tr>
  <tr>
   <td style="text-align:left;color: white !important;background-color: #3F9F7A !important;width: 1cm; border-right:1px solid;"> l </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 11.0 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 14.4 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 14.6 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 9.5 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 5.8 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;color: #7570B3 !important;"> 5.1 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 13.6 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 7.2 </td>
   <td style="text-align:right;width: 1cm; border-right:1px solid;"> 4.2 </td>
   <td style="text-align:right;"> 5.0 </td>
   <td style="text-align:right;"> 0.0 </td>
  </tr>
</tbody>
</table>
]]]
.column[.pad50px[.content[

🤔 Now which .monash-orange2[distance is the smallest]?

<br>

]]]

---

---

## Dendrogram

<br>

- Each .monash-orange2[leaf] of the dendrogram represents one observation
- Leaves .monash-orange2[fuse] into branches and branches fuse, either with leaves or other branches.	
- Fusions .monash-orange2[lower in the tree] mean the groups of observations are more similar to each other. 
<br>
<br>

---

---

## Pros and cons

<br>
- Single linkage tends to "chain" the data into long stringy clusters, can avoid confusion from nuisance variables but gets confused by "inliers" (outliers between clusters)
- Complete linkage tends to be confused by nuisance variables, but not by inliers
- Wards tends to create spherical homogeneously shaped clusters, a little similar to `\(k\)`-means

No one perfect method for all problems, but Wards tends to be a good starting point.

---

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class: title-slide
background-image: url("images/bg-02.png")

<a rel="license" href="http://creativecommons.org/licenses/by-sa/4.0/"><img alt="Creative Commons License" style="border-width:0" src="https://i.creativecommons.org/l/by-sa/4.0/88x31.png" /></a><br />This work is licensed under a <a rel="license" href="http://creativecommons.org/licenses/by-sa/4.0/">Creative Commons Attribution-ShareAlike 4.0 International License</a>.

.bottom_abs.width100[

Lecturer: *Professor Di Cook*

Department of Econometrics and Business Statistics

<i class="fas fa-envelope"></i>  ETC3250.Clayton-x@monash.edu

<i class="fas fa-calendar-alt"></i> Week 10a

<br>

]