Numerical Data

Descriptive stats & visualizations for quantitative variables (mean/median, spread, hist/box/scatter)

A student-friendly reference with concise explanations, runnable examples, and copy-paste templates for summarizing and visualizing numerical data in R.

1 Setup

2 Learning goals

Identify numerical (quantitative) variables and read their distributions.
Compute core descriptive statistics: min, Q1, median (Q2), mean, Q3, max, IQR, variance, sd.
Make and interpret histograms, box plots, dot plots, and scatter plots.
Recognize outliers and what they may indicate.
Use copy‑paste templates and replace placeholders with your data/columns.

Tip

Use the Copy button on each code chunk. Most topics have a template first and a worked example using the Mr. Trash Wheel dataset.

3 Google Colab Setup

# This code will load the R packages we will use
install.packages(c("csucistats"),
                 repos = c("https://inqs909.r-universe.dev", "https://cloud.r-project.org"))
library(csucistats)
library(tidyverse)

# Uncomment and run for categorical plots
# csucistats::install_plots()
# library(ggtricks)
# library(ggmosaic)
# library(waffle)

# Uncomment and run for themes
# csucistats::install_themes()
# library(ThemePark)
# library(ggthemes)

3.1 Data for this handout

We will use the Mr. Trash Wheel dataset from TidyTuesday.

Code

trashwheel <- read_csv(
  "https://raw.githubusercontent.com/rfordatascience/tidytuesday/master/data/2024/2024-03-05/trashwheel.csv")

3.2 Using the templates: what to change

Use this legend whenever you see a Template code block.

DATA → replace with your data frame/tibble name (e.g., trashwheel).
VAR → replace with the single numerical variable you want (e.g., PlasticBottles).
- In ggplot(DATA, aes(x = VAR)), write ggplot(trashwheel, aes(x = PlasticBottles)).
- In functions that take a vector (e.g., mean(DATA$VAR)), write mean(trashwheel$PlasticBottles).
VAR1 and VAR2 → replace with the x and y variables for scatter plots (e.g., PlasticBottles, PlasticBags).
bins = X, binwidth = X → choose a sensible number/width for your data scale.

3.2.1 Quick replace checklist

Swap DATA for your data frame (usually trashwheel).
Swap VAR for your numerical column (e.g., PlasticBottles).
For scatter plots, set VAR1 and VAR2.
Adjust bins or binwidth for histograms/dot plots to show the distribution clearly.

4 Summary statistics

4.1 What is numerical data?

Numerical (quantitative) variables record numbers for which arithmetic makes sense (e.g., items collected, weights, costs).

Example (first few values):

head(trashwheel$PlasticBottles)

#> [1] 1450 1120 2450 2380  980 1430

4.2 Central tendency

Central tendency summarizes a distribution with a representative value (mean or median).

Median (Q2) is the 50th percentile: half the data lie below it.
Mean is the arithmetic average: sensitive to outliers/skew.

4.3 Variation (spread)

Variation describes how far data tend to fall from the center.

Range = max − min
IQR = Q3 − Q1 (middle 50%)
Variance/SD measure average squared/root‑mean‑squared distance from the mean.

4.4 Summary Statistics

Template:

num_stats(DATA$VAR)           # five-number summary + mean

Example:

num_stats(trashwheel$PlasticBottles)

#>   min   q25     mean median  q75  max       sd     var    iqr missing
#> 1   0 987.5 2219.331   1900 2900 9830 1650.449 2723984 1912.5       1

Alternative:

summary(DATA$VAR)           # five-number summary + mean

4.5 Mean, median, variance, sd

Template:

mean(DATA$VAR)
median(DATA$VAR)
var(DATA$VAR)
sd(DATA$VAR)

With Missing Data:

mean(DATA$VAR, na.rm = TRUE)
median(DATA$VAR, na.rm = TRUE)
var(DATA$VAR, na.rm = TRUE)
sd(DATA$VAR, na.rm = TRUE)

Example:

mean(trashwheel$PlasticBottles, na.rm = TRUE)

#> [1] 2219.331

median(trashwheel$PlasticBottles, na.rm = TRUE)

#> [1] 1900

var(trashwheel$PlasticBottles, na.rm = TRUE)

#> [1] 2723984

sd(trashwheel$PlasticBottles, na.rm = TRUE)

#> [1] 1650.449

4.6 Quantiles

Template:

quantile(DATA$VAR, probs = c(0.25, 0.5, 0.75))

#> Error: object 'DATA' not found

Example:

quantile(trashwheel$PlasticBottles, probs = c(0.25, 0.5, 0.75), na.rm = TRUE)

#>    25%    50%    75% 
#>  987.5 1900.0 2900.0

5 Data visualization

5.1 Histograms

A histogram shows the distribution by binning values and counting how many fall in each bin.

Template (choose either bins OR binwidth):

ggplot(DATA, aes(x = VAR)) +
  geom_histogram(bins = X)

Example:

ggplot(trashwheel, aes(x = PlasticBottles)) +
  geom_histogram(bins = 20)

#> Warning: Removed 1 row containing non-finite outside the scale range
#> (`stat_bin()`).

5.2 Kernel density plot

Template:

ggplot(DATA, aes(x = VAR)) +
  geom_density()

Example:

ggplot(trashwheel, aes(x = PlasticBottles)) +
  geom_density()

#> Warning: Removed 1 row containing non-finite outside the scale range
#> (`stat_density()`).

5.3 Box plots

A box plot summarizes median, quartiles, and potential outliers.

Template:

ggplot(DATA, aes(VAR)) +
  geom_boxplot()

Example:

ggplot(trashwheel, aes(PlasticBottles)) +
  geom_boxplot()

#> Warning: Removed 1 row containing non-finite outside the scale range
#> (`stat_boxplot()`).

5.4 Dot plots

A dot plot stacks dots within bins to show distribution.

Template:

ggplot(DATA, aes(x = VAR)) +
  geom_dotplot(binwidth = X)  # choose a sensible binwidth

Example:

ggplot(trashwheel, aes(x = PlasticBottles)) +
  geom_dotplot(binwidth = 100)

#> Warning: Removed 1 row containing missing values or values outside the scale range
#> (`stat_bindot()`).

6 Scatter plots (two numerical variables)

A scatter plot reveals association, trend direction, and form.

Template:

ggplot(DATA, aes(x = VAR1, y = VAR2)) +
  geom_point()

Example:

ggplot(trashwheel, aes(x = PlasticBottles, y = PlasticBags)) +
  geom_point()

#> Warning: Removed 1 row containing missing values or values outside the scale range
#> (`geom_point()`).

Add a trend line (optional):

ggplot(trashwheel, aes(x = PlasticBottles, y = PlasticBags)) +
  geom_point() +
  geom_smooth(method = "lm", se = TRUE)

#> `geom_smooth()` using formula = 'y ~ x'

#> Warning: Removed 1 row containing non-finite outside the scale range
#> (`stat_smooth()`).

#> Warning: Removed 1 row containing missing values or values outside the scale range
#> (`geom_point()`).

7 Quick troubleshooting

Lots of NAs? Add na.rm = TRUE where available or filter rows with drop_na(VAR).
Histogram looks too blocky/smooth? Tune bins or binwidth.
Weird axis or units? Check for unit conversions or outliers dominating the scale.
Outliers change the mean a lot. Consider reporting median or using robust summaries.

8 Appendix: minimal templates (copy‑paste)

Each template below has placeholders in ALL CAPS (e.g., DATA, VAR, VAR1, VAR2). Replace them with your dataset name and variable names.

# Mean / Median / Var / SD
mean(DATA$VAR)
median(DATA$VAR)
var(DATA$VAR)
sd(DATA$VAR)

# Quantiles
quantile(DATA$VAR, probs = c(0.25, 0.5, 0.75))

# One-liner (csucistats)
num_stats(DATA$VAR)

# Histogram
ggplot(DATA, aes(VAR)) + 
    geom_histogram(bins = X)

# Density
ggplot(DATA, aes(VAR)) + 
    geom_density()

# Box plot
ggplot(DATA, aes(VAR)) + 
    geom_boxplot()

# Dot plot
ggplot(DATA, aes(x = VAR)) + 
    geom_dotplot(binwidth = X)

# Scatter
ggplot(DATA, aes(x = VAR1, y = VAR2)) + 
    geom_point()

# Scatter + trend line
ggplot(DATA, aes(x = VAR1, y = VAR2)) + 
    geom_point() + 
    geom_smooth(method = "lm", se = TRUE)