Exploratory data analysis I

Lecture 5

Dr. Mine Çetinkaya-Rundel

Duke University
STA 199 - Fall 2026

September 9, 2026

Warm up

While you wait: Participate 📱

Suppose you have a dataset df with 100 rows and 5 columns: x1, x2, x3, x4, and x5. x1 is a categorical variable with levels a and b. You run the following code:

x |>
  filter(x1 == "a") |>
  select(x1, x2, x5)

The resulting data frame will have:

• 3 columns, 50 rows
• 3 columns, 100 rows
• 3 columns, can’t tell how many rows
• 5 columns, 100 rows
• 5 columns, can’t tell how many rows

Go to wooclap.com and use the code KUCTINK.

Announcements

HW 1 is due tonight at 11:59 pm:

• Push all work to GitHub.

• Submit a PDF of your PDF file to Gradescope and mark your pages.

Getting to know you feedback: Questions

• Is the course designed for students with no prior coding or statistics background?
• What is the balance between learning statistical concepts and programming in R? How often will students code?
• How should students use readings, videos, and other materials—and which are essential?
• What should students expect from discussion projects, collaboration, and required uploads?
• What will exams look like, and what practice or study materials will be available?
• Where can students get help, and what kinds of collaboration are appropriate?
• How does the course compare to COMPSCI 216 (Everything Data) and STA 323 (Statistical Computing)?

Getting to know you feedback: Concerns

• Dominant concern: lack of prior coding experience—especially learning R, syntax, troubleshooting, and technical tools such as Git and GitHub
• Keeping pace: falling behind or being less prepared than classmates
• Workload: time management for labs, HW, projects, and other commitments
• Assessment: format of exams, details of grading, and effective study strategies
• Smaller themes: Group-project dynamics, large-lecture setting, and confidence with math/statistical terminology

From last time

In this class, you will…

Build cakes (ggplot)

Stack dolls (pipe |>)

Master these constructs, and everything will be A-Ok!

Source: Cake by Anirban Sengupta on Unsplash and Matryoshka dolls by Julia Kadel on Unsplash.

Exploratory data analysis

Packages

• For data wrangling and visualization: tidyverse
• For pretty axis labels: scales

library(tidyverse)
library(scales)

Data: gerrymander

gerrymander <- read_csv("data/gerrymander.csv")

What is gerrymandering?

https://www.washingtonpost.com/business/wonkblog/gerrymandering-explained/2016/04/21/e447f5c2-07fe-11e6-bfed-ef65dff5970d_video.html

Participate 📱💻

You are given a new dataset to analyze. What are some of the first things you would do to get to know the data?

Go to wooclap.com and use the code KUCTINK.

Data: gerrymander

glimpse(gerrymander)

Rows: 443
Columns: 14
$ district       <chr> "AK-00", "AL-01", "AL-02", "AL-03", "AL-04", "AL-05", "…
$ state_abb      <chr> "AK", "AL", "AL", "AL", "AL", "AL", "AL", "AL", "AR", "…
$ state          <chr> "Alaska", "Alabama", "Alabama", "Alabama", "Alabama", "…
$ house_rep_20   <chr> "Don Young", "Jerry Carl", "Barry Moore", "Mike Rogers"…
$ house_party_20 <chr> "Republican", "Republican", "Republican", "Republican",…
$ house_rep_22   <chr> "Mary Sattler Peltola", "Jerry L Carl", "Barry Moore", …
$ house_party_22 <chr> "Democrat", "Republican", "Republican", "Republican", "…
$ house_rep_24   <chr> "Nick Begich", "Barry Moore", "Shomari Figures", "Mike …
$ house_party_24 <chr> "Republican", "Republican", "Democrat", "Republican", "…
$ harris_24      <dbl> 41.41, 21.89, 53.52, 26.18, 15.96, 34.20, 29.68, 61.45,…
$ trump_24       <dbl> 54.54, 76.94, 45.31, 72.71, 83.02, 64.02, 68.47, 37.50,…
$ gerry_22       <chr> NA, "F", "F", "F", "F", "F", "F", "F", "C", "C", "C", "…
$ gerry_24       <chr> NA, "B", "B", "B", "B", "B", "B", "B", "C", "C", "C", "…
$ gerry_26       <chr> NA, "B", "B", "B", "B", "B", "B", "B", "C", "C", "C", "…

How many congressional districts are there in the United States? How many rows are there in the data? Do the number of rows in the data match your expectations?

Data: gerrymander

• Rows: Congressional districts in the 2020, 2022, and 2024 elections

• Columns:

  • Congressional district, state abbreviation, and state name

  • Name and party of the House candidate who won in 2020, 2022, and 2024

  • 2024 election: % for Harris, % for Trump

  • Gerrymandering score for 2022, 2024, and 2026 (A: Good, B: Better than average with some bias, C: Average, D/F: Poor)

Variable types: district

Variable	Type
district	categorical, ID
state_abb
state
house_rep_20
house_party_20
house_rep_22
house_party_22
house_rep_24
house_party_24
harris_24
trump_24
gerry_22
gerry_24
gerry_26

gerrymander |>
  select(district)

# A tibble: 443 × 1
   district
   <chr>   
 1 AK-00   
 2 AL-01   
 3 AL-02   
 4 AL-03   
 5 AL-04   
 6 AL-05   
 7 AL-06   
 8 AL-07   
 9 AR-01   
10 AR-02   
# ℹ 433 more rows

Variable types: state_abb

Variable	Type
district	categorical, ID
state_abb	categorical
state
house_rep_20
house_party_20
house_rep_22
house_party_22
house_rep_24
house_party_24
harris_24
trump_24
gerry_22
gerry_24
gerry_26

gerrymander |>
  select(district, state_abb)

# A tibble: 443 × 2
   district state_abb
   <chr>    <chr>    
 1 AK-00    AK       
 2 AL-01    AL       
 3 AL-02    AL       
 4 AL-03    AL       
 5 AL-04    AL       
 6 AL-05    AL       
 7 AL-06    AL       
 8 AL-07    AL       
 9 AR-01    AR       
10 AR-02    AR       
# ℹ 433 more rows

Variable types: state

Variable	Type
district	categorical, ID
state_abb	categorical
state	categorical
house_rep_20
house_party_20
house_rep_22
house_party_22
house_rep_24
house_party_24
harris_24
trump_24
gerry_22
gerry_24
gerry_26

gerrymander |>
  select(district, state)

# A tibble: 443 × 2
   district state   
   <chr>    <chr>   
 1 AK-00    Alaska  
 2 AL-01    Alabama 
 3 AL-02    Alabama 
 4 AL-03    Alabama 
 5 AL-04    Alabama 
 6 AL-05    Alabama 
 7 AL-06    Alabama 
 8 AL-07    Alabama 
 9 AR-01    Arkansas
10 AR-02    Arkansas
# ℹ 433 more rows

Variable types: House representatives

Variable	Type
district	categorical, ID
state_abb	categorical
state	categorical
house_rep_20	categorical, ID
house_party_20
house_rep_22	categorical, ID
house_party_22
house_rep_24	categorical, ID
house_party_24
harris_24
trump_24
gerry_22
gerry_24
gerry_26

gerrymander |>
  select(district, starts_with("house_rep"))

# A tibble: 443 × 4
   district house_rep_20                   house_rep_22             house_rep_24
   <chr>    <chr>                          <chr>                    <chr>       
 1 AK-00    "Don Young"                    "Mary Sattler Peltola"   "Nick Begic…
 2 AL-01    "Jerry Carl"                   "Jerry L Carl"           "Barry Moor…
 3 AL-02    "Barry Moore"                  "Barry Moore"            "Shomari Fi…
 4 AL-03    "Mike Rogers"                  "Mike Rogers"            "Mike Roger…
 5 AL-04    "Robert B Aderholt"            "Robert B Aderholt"      "Robert B. …
 6 AL-05    "Mo Brooks"                    "Dale Strong"            "Dale W. St…
 7 AL-06    "Gary J Palmer"                "Gary J Palmer"          "Gary J. Pa…
 8 AL-07    "Terri A Sewell"               "Terri A Sewell"         "Terri A. S…
 9 AR-01    "Eric A \\\"Rick\\\" Crawford" "Eric A Â\u0080\u009cRi… "Eric A. \\…
10 AR-02    "J French Hill"                "J French Hill"          "J. French …
# ℹ 433 more rows

Variable types: winning parties

Variable	Type
district	categorical, ID
state_abb	categorical
state	categorical
house_rep_20	categorical, ID
house_party_20	categorical
house_rep_22	categorical, ID
house_party_22	categorical
house_rep_24	categorical, ID
house_party_24	categorical
harris_24
trump_24
gerry_22
gerry_24
gerry_26

gerrymander |>
  select(district, starts_with("house_party"))

# A tibble: 443 × 4
   district house_party_20 house_party_22 house_party_24
   <chr>    <chr>          <chr>          <chr>         
 1 AK-00    Republican     Democrat       Republican    
 2 AL-01    Republican     Republican     Republican    
 3 AL-02    Republican     Republican     Democrat      
 4 AL-03    Republican     Republican     Republican    
 5 AL-04    Republican     Republican     Republican    
 6 AL-05    Republican     Republican     Republican    
 7 AL-06    Republican     Republican     Republican    
 8 AL-07    Democrat       Democrat       Democrat      
 9 AR-01    Republican     Republican     Republican    
10 AR-02    Republican     Republican     Republican    
# ℹ 433 more rows

Variable types: harris_24 and trump_24

Variable	Type
district	categorical, ID
state_abb	categorical
state	categorical
house_rep_20	categorical, ID
house_party_20	categorical
house_rep_22	categorical, ID
house_party_22	categorical
house_rep_24	categorical, ID
house_party_24	categorical
harris_24	numerical, continuous
trump_24	numerical, continuous
gerry_22
gerry_24
gerry_26

gerrymander |>
  select(district, harris_24, trump_24)

# A tibble: 443 × 3
   district harris_24 trump_24
   <chr>        <dbl>    <dbl>
 1 AK-00         41.4     54.5
 2 AL-01         21.9     76.9
 3 AL-02         53.5     45.3
 4 AL-03         26.2     72.7
 5 AL-04         16.0     83.0
 6 AL-05         34.2     64.0
 7 AL-06         29.7     68.5
 8 AL-07         61.4     37.5
 9 AR-01         26.4     71.7
10 AR-02         41.0     56.6
# ℹ 433 more rows

Variable types: Gerrymandering level

Variable	Type
district	categorical, ID
state_abb	categorical
state	categorical
house_rep_20	categorical, ID
house_party_20	categorical
house_rep_22	categorical, ID
house_party_22	categorical
house_rep_24	categorical, ID
house_party_24	categorical
harris_24	numerical, continuous
trump_24	numerical, continuous
gerry_22	categorical, ordinal
gerry_24	categorical, ordinal
gerry_26	categorical, ordinal

gerrymander |>
  select(district, starts_with("gerry"))

# A tibble: 443 × 4
   district gerry_22 gerry_24 gerry_26
   <chr>    <chr>    <chr>    <chr>   
 1 AK-00    <NA>     <NA>     <NA>    
 2 AL-01    F        B        B       
 3 AL-02    F        B        B       
 4 AL-03    F        B        B       
 5 AL-04    F        B        B       
 6 AL-05    F        B        B       
 7 AL-06    F        B        B       
 8 AL-07    F        B        B       
 9 AR-01    C        C        C       
10 AR-02    C        C        C       
# ℹ 433 more rows

Based on the Gerrymandering Project’s Redistricting Report Card. (A: Good, B: Better than average with some bias, C: Average, D/F: Poor)

Univariate analysis

Univariate analysis

Analyzing a single variable:

• Numerical: histogram, box plot, density plot, etc.

• Categorical: bar plot, pie chart, etc.

Focus: 2024 Elections

gerrymander_24 <- gerrymander |>
  filter(!is.na(house_rep_24))

dim(gerrymander_24)

[1] 435  14

Histogram - Step 1

ggplot(gerrymander_24)

Histogram - Step 2

ggplot(gerrymander_24, aes(x = trump_24))

Histogram - Step 3

ggplot(gerrymander_24, aes(x = trump_24)) +
  geom_histogram()

`stat_bin()` using `bins = 30`. Pick better value `binwidth`.

Participate 📱💻

Which of the following has the most appropriate binwidth for visualizing the distribution of trump_24?

Go to wooclap.com and use the code KUCTINK.

Histogram - Step 4

ggplot(gerrymander_24, aes(x = trump_24)) +
  geom_histogram(binwidth = 5) +
  scale_x_continuous(labels = label_percent(scale = 1))

Histogram - Step 5

ggplot(gerrymander_24, aes(x = trump_24)) +
  geom_histogram(binwidth = 5) +
  scale_x_continuous(labels = label_percent(scale = 1)) +
  labs(
    title = "Percent of vote received by Trump in 2024 Presidential Election",
    subtitle = "From each Congressional District",
    x = "Percent of vote",
    y = "Count"
  )

Box plot - Step 1

ggplot(gerrymander_24)

Box plot - Step 2

ggplot(gerrymander_24, aes(x = trump_24))

Box plot - Step 3

ggplot(gerrymander_24, aes(x = trump_24)) +
  geom_boxplot()

Box plot - Alternative Step 2 + 3

ggplot(gerrymander_24, aes(y = trump_24)) +
  geom_boxplot()

Box plot - Step 4

ggplot(gerrymander_24, aes(x = trump_24)) +
  geom_boxplot() +
  labs(
    title = "Percent of vote received by Trump in 2024 Presidential Election",
    subtitle = "From each Congressional District",
    x = "Percent of vote",
    y = NULL
  )

Density plot - Step 1

ggplot(gerrymander_24)

Density plot - Step 2

ggplot(gerrymander_24, aes(x = trump_24))

Density plot - Step 3

ggplot(gerrymander_24, aes(x = trump_24)) +
  geom_density()

Density plot - Step 4

ggplot(gerrymander_24, aes(x = trump_24)) +
  geom_density(color = "firebrick")

Density plot - Step 5

ggplot(gerrymander_24, aes(x = trump_24)) +
  geom_density(color = "firebrick", fill = "firebrick1")

Density plot - Step 6

ggplot(gerrymander_24, aes(x = trump_24)) +
  geom_density(color = "firebrick", fill = "firebrick1", alpha = 0.5)

Density plot - Step 7

ggplot(gerrymander_24, aes(x = trump_24)) +
  geom_density(
    color = "firebrick",
    fill = "firebrick1",
    alpha = 0.5,
    linewidth = 1
  )

Density plot - Step 8

ggplot(gerrymander_24, aes(x = trump_24)) +
  geom_density(
    color = "firebrick",
    fill = "firebrick1",
    alpha = 0.5,
    linewidth = 2
  ) +
  labs(
    title = "Percent of vote received by Trump in 2024 Presidential Election",
    subtitle = "From each Congressional District",
    x = "Percent of vote",
    y = "Density"
  )

Summary statistics

gerrymander_24 |>
  summarize(
    mean = mean(trump_24),
    sd = sd(trump_24),
    min = min(trump_24),
    q25 = quantile(trump_24, 0.25),
    median = median(trump_24),
    q75 = quantile(trump_24, 0.75),
    max = max(trump_24),
  )

# A tibble: 1 × 7
   mean    sd   min   q25 median   q75   max
  <dbl> <dbl> <dbl> <dbl>  <dbl> <dbl> <dbl>
1  49.2  15.2  10.6  37.9   50.3  61.0  83.0

Distribution of votes for Trump in the 2024 election

Describe the distribution of percent of vote received by Trump in 2024 Presidential Election from Congressional Districts.

• Shape: The distribution of votes for Trump in the 2024 election from Congressional Districts is unimodal and left-skewed.

• Center: The percent of vote received by Trump in the 2024 Presidential Election from a typical Congressional Districts is 50.3%.

• Spread: In the middle 50% of Congressional Districts, 37.9% to 61% of voters voted for Trump in the 2024 Presidential Election.

• Unusual observations: -

Bivariate analysis

Bivariate analysis

Analyzing the relationship between two variables:

• Numerical + numerical: scatterplot

• Numerical + categorical: side-by-side box plots, violin plots, etc.

• Categorical + categorical: stacked bar plots

• Using an aesthetic (e.g., fill, color, shape, etc.) or facets to represent the second variable in any plot

Side-by-side box plots

ggplot(
  gerrymander_24,
  aes(
    x = trump_24,
    y = gerry_24
  )
) +
  geom_boxplot()

Participate 📱💻

What goes in the [blank] in the code below to do the following step for each level of gerry_24?

gerrymander_24 |>
  # [blank]
  summarize(
    min = min(trump_24),
    q25 = quantile(trump_24, 0.25),
    median = median(trump_24),
    q75 = quantile(trump_24, 0.75),
    max = max(trump_24),
  )

• filter(gerry_24)
• group_by(gerry_24)
• mutate(gerry_24)
• select(gerry_24)

Go to wooclap.com and use the code KUCTINK.

Grouped summary statistics

gerrymander_24 |>
  group_by(gerry_24) |>
  summarize(
    min = min(trump_24),
    q25 = quantile(trump_24, 0.25),
    median = median(trump_24),
    q75 = quantile(trump_24, 0.75),
    max = max(trump_24),
  )

# A tibble: 6 × 6
  gerry_24   min   q25 median   q75   max
  <chr>    <dbl> <dbl>  <dbl> <dbl> <dbl>
1 A         10.8  36.7   47.0  57.7  81.3
2 B         10.6  32.8   44.0  52.4  83.0
3 C         39.3  59.7   65.5  70.7  77.0
4 D         22.1  43.0   51.3  61.5  73.4
5 F         13.5  45.9   57.7  62.2  78.4
6 <NA>      32.6  37.8   43.6  61.2  72.3

NA for gerrymandering?

gerrymander_24 |>
  filter(is.na(gerry_24)) |>
  select(district, starts_with("state"), starts_with("gerry"))

# A tibble: 10 × 6
   district state_abb state        gerry_22 gerry_24 gerry_26
   <chr>    <chr>     <chr>        <chr>    <chr>    <chr>   
 1 AK-00    AK        Alaska       <NA>     <NA>     <NA>    
 2 DE-00    DE        Delaware     <NA>     <NA>     <NA>    
 3 HI-01    HI        Hawaii       <NA>     <NA>     <NA>    
 4 HI-02    HI        Hawaii       <NA>     <NA>     <NA>    
 5 ND-00    ND        North Dakota <NA>     <NA>     <NA>    
 6 RI-01    RI        Rhode Island <NA>     <NA>     <NA>    
 7 RI-02    RI        Rhode Island <NA>     <NA>     <NA>    
 8 SD-00    SD        South Dakota <NA>     <NA>     <NA>    
 9 VT-00    VT        Vermont      <NA>     <NA>     <NA>    
10 WY-00    WY        Wyoming      <NA>     <NA>     <NA>    

Density plots

gerrymander_24 |>
  filter(!is.na(gerry_24)) |>
  ggplot(aes(x = trump_24, color = gerry_24)) +
  geom_density()

Filled density plots

gerrymander_24 |>
  filter(!is.na(gerry_24)) |>
  ggplot(aes(x = trump_24, color = gerry_24, fill = gerry_24)) +
  geom_density()

Better filled density plots

gerrymander_24 |>
  filter(!is.na(gerry_24)) |>
  ggplot(aes(x = trump_24, color = gerry_24, fill = gerry_24)) +
  geom_density(alpha = 0.5)

Better colors

gerrymander_24 |>
  filter(!is.na(gerry_24)) |>
  ggplot(aes(x = trump_24, color = gerry_24, fill = gerry_24)) +
  geom_density(alpha = 0.5) +
  scale_color_viridis_d() +
  scale_fill_viridis_d()

Violin plots

gerrymander_24 |>
  filter(!is.na(gerry_24)) |>
  ggplot(aes(x = trump_24, y = gerry_24, color = gerry_24)) +
  geom_violin() +
  scale_color_viridis_d()

Multiple geoms

gerrymander_24 |>
  filter(!is.na(gerry_24)) |>
  ggplot(aes(x = trump_24, y = gerry_24, color = gerry_24)) +
  geom_violin() +
  geom_point() +
  scale_color_viridis_d()

Multiple geoms

gerrymander_24 |>
  filter(!is.na(gerry_24)) |>
  ggplot(aes(x = trump_24, y = gerry_24, color = gerry_24)) +
  geom_violin() +
  geom_jitter() +
  scale_color_viridis_d()

Remove legend

gerrymander_24 |>
  filter(!is.na(gerry_24)) |>
  ggplot(aes(x = trump_24, y = gerry_24, color = gerry_24)) +
  geom_violin() +
  geom_jitter() +
  scale_color_viridis_d() +
  theme(legend.position = "none")