.large[Tangling is easy but untangling is hard]

# .large[Tangling is easy. Untangling is hard]

## Nicholas Tierney
## Telethon Kids Institute, Perth, Australia
## JSM, 8th/9th Aug, 2021

---

layout: true
<div class="my-footer"><span>bit.ly/njt-jsm21 • @nj_tierney</span></div>

---
class: middle, center, inverse

.huge[
How to make better spaghetti 🍝
]

---
class: middle, center, inverse

.huge[
~~How to make better spaghetti 🍝~~
]

.huge[
How to explore longitudinal data effectively
]

---
class: inverse, middle,

# What even **is** longitudinal data?

.huge[
> Individuals repeatedly measured through time
]

---

# What even **is** longitudinal data?

---

# What even **is** longitudinal data?

---

# What even **is** longitudinal data?

.large[
<table>
 <thead>
  <tr>
   <th style="text-align:left;"> country </th>
   <th style="text-align:right;"> year </th>
   <th style="text-align:right;"> height_cm </th>
  </tr>
 </thead>
<tbody>
  <tr>
   <td style="text-align:left;"> Australia </td>
   <td style="text-align:right;"> 1910 </td>
   <td style="text-align:right;"> 173 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Australia </td>
   <td style="text-align:right;"> 1920 </td>
   <td style="text-align:right;"> 173 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Australia </td>
   <td style="text-align:right;"> 1960 </td>
   <td style="text-align:right;"> 176 </td>
  </tr>
</tbody>
</table>
]

---

# What even **is** longitudinal data?

.large[
🎉 Individuals repeatedly measured through time
]

---

---

# All of Australia

---

# ...And New Zealand

---
# And the rest?

---
class: animated, heartBeat
# And the rest?

---
class: bg-black
background-image: url("gifs/noodle-explode.gif")
background-size: contain
background-position: 50% 50%
class: center, bottom, white

---

# Problems:

.large.pull-left[
<svg viewBox="0 0 512 512" style="height:1em;position:relative;display:inline-block;top:.1em;fill:#484878;" xmlns="http://www.w3.org/2000/svg">  <path d="M12.41 148.02l232.94 105.67c6.8 3.09 14.49 3.09 21.29 0l232.94-105.67c16.55-7.51 16.55-32.52 0-40.03L266.65 2.31a25.607 25.607 0 0 0-21.29 0L12.41 107.98c-16.55 7.51-16.55 32.53 0 40.04zm487.18 88.28l-58.09-26.33-161.64 73.27c-7.56 3.43-15.59 5.17-23.86 5.17s-16.29-1.74-23.86-5.17L70.51 209.97l-58.1 26.33c-16.55 7.5-16.55 32.5 0 40l232.94 105.59c6.8 3.08 14.49 3.08 21.29 0L499.59 276.3c16.55-7.5 16.55-32.5 0-40zm0 127.8l-57.87-26.23-161.86 73.37c-7.56 3.43-15.59 5.17-23.86 5.17s-16.29-1.74-23.86-5.17L70.29 337.87 12.41 364.1c-16.55 7.5-16.55 32.5 0 40l232.94 105.59c6.8 3.08 14.49 3.08 21.29 0L499.59 404.1c16.55-7.5 16.55-32.5 0-40z"></path></svg> Overplotting

🙈 We don't see the individuals

🤷 Looking at **144** plots doesn't really help
]

.pull-right.animated.shake[
<img src="figures/gg-heights-heights-again-1.png" width="90%" style="display: block; margin: auto;" />
]

---

# Answers: Transparency?

---

# Answers: Transparency + a model?

???

- This helps reduce the overplotting
- It's not that this is wrong, it is useful - but we lose the individuals
- We only get the overall average. We dont get the rest of the information
- How do we even get started?
---

# But we forget about the **individuals**

???

- The model might make some good overall predictions
- But it can be really _ill suited_ for some individual
- Exploring this is somewhat clumsy - we need another way to explore

---
class: inverse, middle

# Three problems in exploring longitudinal data

.large[
Problem #1: How do I look at **some** of the data?
]

.large[
Problem #2: How do I find **interesting** observations?
]

.large[
Problem #3: How do I **understand** a model?
]

---

# Introducing `brolgar`: [brolgar.njtierney.com](https://brolgar.njtierney.com)

.pull-left.mlarge[
**br**owsing <br>
**o**ver <br>
**l**ongitudinal data <br>
**g**raphically, and <br>
**a**nalytically, in <br>
**r**
]

.pull-right[
<img src="imgs/brolga-bird.jpg" width="90%" style="display: block; margin: auto;" />
]

???

* It's a crane, it fishes, and it's a native Australian bird

---
class: inverse, middle

# What is longitudinal data?

.huge[
> Individuals repeatedly measured through time
]

---
class: inverse, middle,

# What is longitudinal data?

.huge[
> Individuals **repeatedly** measured through time
]

---
class: inverse, middle,

# What is longitudinal data?

.huge[
> Individuals **repeatedly** measured through **time**
]

---

class: inverse, middle

# 🤔 longitudinal data as a **time series**?

.vlarge[
> Anything that is observed sequentially over time **is a time series**
]

.large[
[-- Rob Hyndman and George Athanasopolous,
Forecasting: Principles and Practice](https://otexts.com/fpp2/data-methods.html)
]

---

# Longitudinal data as a time series <img src="https://tsibble.tidyverts.org/reference/figures/logo.png" align="right" height=140/>

```r
heights <- as_tsibble(heights,
                      index = year,
                      key = country,
*                     regular = FALSE)
```

.medium[
1. **index**: Your time variable
2. **key**: Variable(s) defining individual groups (or series)

`1. +  2.` determine distinct rows in a tsibble.

(From Dr. Earo Wang's talk: [Melt the clock](https://slides.earo.me/rstudioconf19/#8))
]

---

.large[

```
## # A tsibble: 1,490 x 3 [!]
## # Key:       country [144]
##   country      year height_cm
##   <chr>       <dbl>     <dbl>
## 1 Afghanistan  1870      168.
## 2 Afghanistan  1880      166.
## 3 Afghanistan  1930      167.
## 4 Afghanistan  1990      167.
## 5 Afghanistan  2000      161.
## 6 Albania      1880      170.
## # … with 1,484 more rows
```
]

---

# Longitudinal data as a time series <img src="https://tsibble.tidyverts.org/reference/figures/logo.png" align="right" height=140/>

.large[
We add information about **index** + **key**:

📐 Index = Year
  
  🔑   Key = Country
  ]
  
--

.large[
Record important time series information **once**

Use it **many** times in other places

]

---
class: inverse, center, middle
# Problem #1: How do I look at **some** of the data?

# How do you **eat** spaghetti?

---

.pull-left[
<img src="gifs/full-house-spag.gif" width="90%" style="display: block; margin: auto;" />
]

.pull-right[
<img src="gifs/garfield-spaghetti.gif" width="90%" style="display: block; margin: auto;" />
]

.animated.rollIn.huge.center[
data indigestion
]

---

.pull-left[

<img src="gifs/cat-single-spag.gif" width="100%" style="display: block; margin: auto;" />
]

.pull-right[
<img src="gifs/rat-spaghetti.gif" width="100%" style="display: block; margin: auto;" />
]

---

# Portion out your spaghetti! 🍝 🍝 🍝 🍝

---

# Look at **one** set of subsamples 🍝

---

# Look at **many** subsamples 🍝 🍝 🍝 🍝 🍝 🍝

---
class: inverse

# **How** do I look at many subsamples? 🤔

.vlarge[
How many keys are there?
]
--

.vlarge[
How many facets do I want?
]

.vlarge[
How many keys per facet?
]

---
class: inverse

# **How** do I look at many subsamples? 🤔

.vlarge[
How to keep the same number of keys per plot?
]

.vlarge[
What is `rep`, `rep.int`, and `rep_len`?
]

.vlarge[
Do I want `length.out` or `times`?
]

---
background-image: url("imgs/what-year-is-it.jpg")
background-size: contain
background-position: 50% 50%
class: center, bottom, white

---

# Distraction threshold ⏲ 🐰 🕳

.large[

(Something I made up)
]

.large[
> If solving a problem requires solving **3+ smaller problems**

> Your focus shifts from the current goal to something else.

> You are distracted.

]

???

- Task one

- Task one being overshadowed slightly by minor task 1
- Task one being overshadowed slightly by minor task 2
- Task one being overshadowed slightly by minor task 3

---

# Avoiding the rabbit hole

.large[
We can blame ourselves when we are distracted for **not being better**.
]

.large[
It's not that we should be better, rather **with better tools we could be more efficient**. 
]

.large[
We need to make things **as easy as reasonable**, with the least amount of distraction.
]

---

# `facet_sample()`: See more individuals 👀

.large[

```r
ggplot(heights, aes(x = year, 
                    y = height_cm, 
                    group = country)) + 
  geom_line() 
```
]

---

# `facet_sample()`: See more individuals 👀

# `facet_sample()`: See more individuals 👀
---

# `facet_sample()`: See more individuals 👀

.large[

```r
ggplot(heights, aes(x = year,
                    y = height_cm,
                    group = country)) + 
  geom_line() + 
* facet_sample()
```
]

---

# `facet_sample()`: See more individuals 👀

---

# Remove distraction. Ask relevant questions

.large[
> How many keys per facet?

> How many plots do I want to look at?
]

.large[

```r
gg_heights +  
  facet_sample(
*   n_per_facet = 3,
*   n_facets = 9
  )
```
]

---

---

# How to see **all** individuals?

.huge[

```r
gg_heights +  
* facet_strata()
```
]

---

# `facet_strata()`: See **all** individuals

---

# 🤔 ... can we re-order these facets?

???

In asking these questions we can solve something else interesting

---

# We can re-order these facets?! 😄

---

# See all individuals **along** some variable

.huge[

```r
gg_heights + 
  facet_strata(
*   along = -year
    ) 
```
]

---

# See all individuals **along** some variable

---

# Magic facets: Focus on relevant questions instead of minutiae:

.pull-left[

**`facet_sample()`**

"How many lines per facet"

"How many facets?"

```r
gg_heights +  
  facet_sample(
*   n_per_facet = 10,
*   n_facets = 12
    ) 
```

]

.pull-right[

**`facet_strata()`**

"How many facets / strata?"

"**What** to arrange plots **along**?"

```r
gg_heights +  
  facet_strata(
*   n_strata = 10,
*   along = -year
    ) 
```

]

---

# `facet_strata()` & `facet_sample()`

.pull-left[
<img src="imgs/car-hood-small.jpg" width="100%" style="display: block; margin: auto;" />
]

.pull-right.large[
<svg viewBox="0 0 320 512" style="height:1em;position:relative;display:inline-block;top:.1em;fill:#484878;" xmlns="http://www.w3.org/2000/svg">  <path d="M296 160H180.6l42.6-129.8C227.2 15 215.7 0 200 0H56C44 0 33.8 8.9 32.2 20.8l-32 240C-1.7 275.2 9.5 288 24 288h118.7L96.6 482.5c-3.6 15.2 8 29.5 23.3 29.5 8.4 0 16.4-4.4 20.8-12l176-304c9.3-15.9-2.2-36-20.7-36z"></path></svg> with `sample_n_keys()` & `stratify_keys()`

You can still get at data and do manipulations
]

---

# Problem #1: How do I look at some of the data?

.left-code.large[

`as_tsibble()`

`facet_sample()`

`facet_strata()`

]

.right-plot.large[

Store useful information

View **many** subsamples

View **all** subsamples

]

---

# ~~Problem #1: How do I look at some of the data?~~

.left-code.large[

`as_tsibble()`

`facet_sample()`

`facet_strata()`

]

.right-plot.large[

Store useful information

View **many** subsamples

View **all** subsamples

]

---

## Problem #2: How do I find **interesting** observations?

---
class: inverse, center, middle

.huge[
A workflow
]

.huge[
**Define** what is interesting:
]

.huge.animated.bounceInLeft[
_maximum height_
]

---

## Identify features: one observation per **key**

---

## Identify features: one observation per **key**

---

## Identify features: one observation per **key**

---

## Identify **important features** and **decide** how to filter

---

## Identify **important features** and **decide** how to filter

---

## Join this feature back to the data

---

## Join this feature back to the data

---

## 🎉 Countries with smallest and largest max height

---
class: inverse, middle

.vhuge[
Let's see that **one more time**, but with the data
]

---

## Identify features: one observation per **key**

.large[

---

## Identify features: one observation per **key**

.large[

```
## # A tibble: 144 x 2
##   country       max
##   <chr>       <dbl>
## 1 Afghanistan  168.
## 2 Albania      170.
## 3 Algeria      171.
## 4 Angola       169.
## 5 Argentina    174.
## 6 Armenia      172.
## # … with 138 more rows
```
]

---

## Identify important features and decide how to filter

```r
heights_five %>% 
  filter(max == max(max) | max == min(max))
```

```
## # A tibble: 2 x 2
##   country            max
##   <chr>            <dbl>
## 1 Denmark           183.
## 2 Papua New Guinea  161.
```

---

## Join summaries back to data

```r
heights_five %>% 
  filter(max == max(max) | max == min(max)) %>% 
  left_join(heights, by = "country")
```

```
## # A tibble: 21 x 4
##   country   max  year height_cm
##   <chr>   <dbl> <dbl>     <dbl>
## 1 Denmark  183.  1820      167.
## 2 Denmark  183.  1830      165.
## 3 Denmark  183.  1850      167.
## 4 Denmark  183.  1860      168.
## 5 Denmark  183.  1870      168.
## 6 Denmark  183.  1880      170.
## # … with 15 more rows
```

---

background-image: url("gifs/dog-solve-problem.gif")
background-size: contain
background-position: 50% 50%
class: center, bottom, white

---

.vhuge[
But Nick, how did you create those summaries?
]

---

## Identify features: one per **key** <img src="https://feasts.tidyverts.org/reference/figures/logo.png" align="right" height=140/>

```r
heights %>%
* features(height_cm, feat_five_num)
```

```
## # A tibble: 144 x 6
##   country       min   q25   med   q75   max
##   <chr>       <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 Afghanistan  161.  164.  167.  168.  168.
## 2 Albania      168.  168.  170.  170.  170.
## 3 Algeria      166.  168.  169   170.  171.
## 4 Angola       159.  160.  167.  168.  169.
## 5 Argentina    167.  168.  168.  170.  174.
## 6 Armenia      164.  166.  169.  172.  172.
## # … with 138 more rows
```

---

## What is the range of the data? `feat_ranges`

```r
heights %>%
  features(height_cm, feat_ranges)
```

```
## # A tibble: 144 x 5
##   country       min   max range_diff   iqr
##   <chr>       <dbl> <dbl>      <dbl> <dbl>
## 1 Afghanistan  161.  168.       7     3.27
## 2 Albania      168.  170.       2.20  1.53
## 3 Algeria      166.  171.       5.06  2.15
## 4 Angola       159.  169.      10.5   7.87
## 5 Argentina    167.  174.       7     2.21
## 6 Armenia      164.  172.       8.82  5.30
## # … with 138 more rows
```

---

## Does it only increase or decrease? `feat_monotonic`

```r
heights %>%
  features(height_cm, feat_monotonic)
```

```
## # A tibble: 144 x 5
##   country     increase decrease unvary monotonic
##   <chr>       <lgl>    <lgl>    <lgl>  <lgl>    
## 1 Afghanistan FALSE    FALSE    FALSE  FALSE    
## 2 Albania     FALSE    TRUE     FALSE  TRUE     
## 3 Algeria     FALSE    FALSE    FALSE  FALSE    
## 4 Angola      FALSE    FALSE    FALSE  FALSE    
## 5 Argentina   FALSE    FALSE    FALSE  FALSE    
## 6 Armenia     FALSE    FALSE    FALSE  FALSE    
## # … with 138 more rows
```

---

## What is the spread of my data? `feat_spread`

```r
heights %>%
  features(height_cm, feat_spread) 
```

```
## # A tibble: 144 x 5
##   country        var    sd   mad   iqr
##   <chr>        <dbl> <dbl> <dbl> <dbl>
## 1 Afghanistan  7.20  2.68  1.65   3.27
## 2 Albania      0.950 0.975 0.667  1.53
## 3 Algeria      3.30  1.82  0.741  2.15
## 4 Angola      16.9   4.12  3.11   7.87
## 5 Argentina    2.89  1.70  1.36   2.21
## 6 Armenia     10.6   3.26  3.60   5.30
## # … with 138 more rows
```

---

## features: MANY more features in `feasts` <img src="https://feasts.tidyverts.org/reference/figures/logo.png" align="right" height=140/>

.mlarge[

`feat_acf`: autocorrelation-based features

`feat_stl`: STL (Seasonal, Trend, and Remainder by LOESS) decomposition

[Create your own features](http://brolgar.njtierney.com/articles/finding-features.html#creating-your-own-features)

]

---

# ~~Problem #1: How do I look at **some** of the data?~~

# Problem #2: How do I find **interesting** observations?

---

# ~~Problem #1: How do I look at **some** of the data?~~

# ~~Problem #2: How do I find **interesting** observations?~~

# Problem #3: How do I **understand** a model?

.vhuge.center[
🤔
]

---

# Problem #3: How do I **understand** a model?

.medium[
Let's fit a mixed effects model.

Fixed effect of year + Random intercept for country
]

```r
heights_fit <- lmer(height_cm ~ year + (1|country), heights)

heights_aug <- heights %>%
  add_predictions(heights_fit, var = "pred") %>%
  add_residuals(heights_fit, var = "res")
```

---

# Problem #3: How do I **understand** a model?

.large[

```
## # A tsibble: 1,490 x 5 [!]
## # Key:       country [144]
##   country      year height_cm  pred    res
##   <chr>       <dbl>     <dbl> <dbl>  <dbl>
## 1 Afghanistan  1870      168.  164.  4.59 
## 2 Afghanistan  1880      166.  164.  1.52 
## 3 Afghanistan  1930      167.  166.  0.823
## 4 Afghanistan  1990      167.  168. -1.04 
## 5 Afghanistan  2000      161.  169. -7.10 
## 6 Albania      1880      170.  168.  2.39 
## # … with 1,484 more rows
```
]

---

# Problem #3: How do I **understand** a model?

---

# Look at **many** subsamples? `facet_sample()`

```r
gg_heights_fit + facet_sample()
```

---

# Look at **all** subsamples? `facet_strata()`

```r
gg_heights_fit + facet_strata()
```

---

# Look at **all** subsamples **along** residuals?

```r
gg_heights_fit + facet_strata(along = -res)
```

---

# Look at the predictions with the data?

```r
set.seed(2020-01-21)
heights_sample <- 
heights_aug %>%
* sample_n_keys(size = 9) %>%
  ggplot(aes(x = year,
             y = pred,
             group = country)) + 
  geom_line() +
  facet_wrap(~country)

heights_sample
```

---

# Look at the predictions with the data?

---

# Look at the predictions with the data?

```r
heights_sample + geom_point(aes(y = height_cm))
```

---

# Take homes

## Problem #1: How do I look at **some** of the data?

.mlarge[
1. Longitudinal data as a time series 💹
2. Specify structure, get a free lunch. 🥪
3. Look at as much of the raw data as possible  🍣
4. Use `facet_sample()` / `facet_strata()`
]

---

# Take homes

## Problem #2: How do I find **interesting** observations?

.mlarge[
1. Decide what features are interesting
2. Summarise down to one observation per key
3. Decide how to filter
4. Join this feature back to the data
]

---

# Take homes

## Problem #3: How do I **understand** a model?

.mlarge[
1. Look at (one, more or all!) subsamples
1. Arrange subsamples
1. (actually use similar approaches to earlier!)
]

---

# Future Directions

.large[
<svg viewBox="0 0 512 512" style="height:1em;position:relative;display:inline-block;top:.1em;fill:#484878;" xmlns="http://www.w3.org/2000/svg">  <path d="M501.54 60.91c17.22-17.22 12.51-46.25-9.27-57.14a35.696 35.696 0 0 0-37.37 3.37L251.09 160h151.37l99.08-99.09zM496 192H16c-8.84 0-16 7.16-16 16v32c0 8.84 7.16 16 16 16h16c0 80.98 50.2 150.11 121.13 178.32-12.76 16.87-21.72 36.8-24.95 58.69-1.46 9.92 6.04 18.98 16.07 18.98h223.5c10.03 0 17.53-9.06 16.07-18.98-3.22-21.89-12.18-41.82-24.95-58.69C429.8 406.11 480 336.98 480 256h16c8.84 0 16-7.16 16-16v-32c0-8.84-7.16-16-16-16z"></path></svg> More features (summaries)

---

# Thanks

.large.pull-left[
- Di Cook
- Tania Prvan
- Stuart Lee
- Mitchell O'Hara Wild
- Earo Wang
- Rob Hyndman
- Nick Golding
]

.large.pull-right[
- Miles McBain
- Hadley Wickham
- Garrick Aden-Buie
- Monash University
- ACEMS
- Telethon Kids Institute
]

---

# Resources

.large[
<svg viewBox="0 0 640 512" style="height:1em;position:relative;display:inline-block;top:.1em;fill:#484878;" xmlns="http://www.w3.org/2000/svg">  <path d="M425.7 256c-16.9 0-32.8-9-41.4-23.4L320 126l-64.2 106.6c-8.7 14.5-24.6 23.5-41.5 23.5-4.5 0-9-.6-13.3-1.9L64 215v178c0 14.7 10 27.5 24.2 31l216.2 54.1c10.2 2.5 20.9 2.5 31 0L551.8 424c14.2-3.6 24.2-16.4 24.2-31V215l-137 39.1c-4.3 1.3-8.8 1.9-13.3 1.9zm212.6-112.2L586.8 41c-3.1-6.2-9.8-9.8-16.7-8.9L320 64l91.7 152.1c3.8 6.3 11.4 9.3 18.5 7.3l197.9-56.5c9.9-2.9 14.7-13.9 10.2-23.1zM53.2 41L1.7 143.8c-4.6 9.2.3 20.2 10.1 23l197.9 56.5c7.1 2 14.7-1 18.5-7.3L320 64 69.8 32.1c-6.9-.8-13.5 2.7-16.6 8.9z"></path></svg> [feasts](http://feasts.tidyverts.org/)

---

# Colophon

.medium[
<svg viewBox="0 0 512 512" style="height:1em;position:relative;display:inline-block;top:.1em;fill:#484878;" xmlns="http://www.w3.org/2000/svg">  <path d="M12.41 148.02l232.94 105.67c6.8 3.09 14.49 3.09 21.29 0l232.94-105.67c16.55-7.51 16.55-32.52 0-40.03L266.65 2.31a25.607 25.607 0 0 0-21.29 0L12.41 107.98c-16.55 7.51-16.55 32.53 0 40.04zm487.18 88.28l-58.09-26.33-161.64 73.27c-7.56 3.43-15.59 5.17-23.86 5.17s-16.29-1.74-23.86-5.17L70.51 209.97l-58.1 26.33c-16.55 7.5-16.55 32.5 0 40l232.94 105.59c6.8 3.08 14.49 3.08 21.29 0L499.59 276.3c16.55-7.5 16.55-32.5 0-40zm0 127.8l-57.87-26.23-161.86 73.37c-7.56 3.43-15.59 5.17-23.86 5.17s-16.29-1.74-23.86-5.17L70.29 337.87 12.41 364.1c-16.55 7.5-16.55 32.5 0 40l232.94 105.59c6.8 3.08 14.49 3.08 21.29 0L499.59 404.1c16.55-7.5 16.55-32.5 0-40z"></path></svg> Slides made using [xaringan](https://github.com/yihui/xaringan)

---

# Learning more

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class: animated, heartBeat

.vhuge[
BONUS ROUND
]

---

---

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# What about interactive graphics?

.vlarge[
> if you make a tooltip or rollover, **assume no one will ever see it**"
-- Archie Tse, NYT
]

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# What if we grabbed a sample of those who have the best, middle, and worst residuals?

.medium[

```r
summary(heights_aug$res)
```

```
##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
## -8.1707 -1.6202 -0.1558  0.0000  1.3545 12.1729
```
]

.mlarge[
Which countries are **nearest** to these statistics?
]

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# use `keys_near()`

.pull-left[

```r
keys_near(heights_aug, 
          var = res)
```

```
## # A tibble: 6 x 5
##   country       res stat  stat_value stat_diff
##   <chr>       <dbl> <fct>      <dbl>     <dbl>
## 1 Ireland    -8.17  min       -8.17   0       
## 2 Azerbaijan -1.62  q_25      -1.62   0.000269
## 3 Laos       -0.157 med       -0.156  0.00125 
## 4 Mongolia   -0.155 med       -0.156  0.00125 
## 5 Egypt       1.35  q_75       1.35   0.000302
## 6 Poland     12.2   max       12.2    0
```
]

.pull-right[

> 🔑 🔑 🔑 that best match the 5 number summary.

]

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# Join data back and explore

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.vhuge.left-code[
**End.**
]

.right-plot[
<img src="imgs/explorer.jpg" width="100%" style="display: block; margin: auto;" />

]