Exploratory data analysis I

Lecture 5

Author
Affiliation

Dr. Mine Çetinkaya-Rundel

Duke University
STA 199 - Fall 2026

Published

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

QR code for Wooclap

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

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?

QR code for Wooclap

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?

QR code for Wooclap

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)

QR code for Wooclap

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")