Numerical Data

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

1 Introduction

  • 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.

2 Google Colab Setup

Copy the following code and put it in a code cell in Google Colab. Only do this if you are using a completely new notebook.

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


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

2.1 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")

2.2 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.

2.2.1 Quick replace checklist

  1. Swap DATA for your data frame (usually trashwheel).

  2. Swap VAR for your numerical column (e.g., PlasticBottles).

  3. For scatter plots, set VAR1 and VAR2.

  4. Adjust bins or binwidth for histograms/dot plots to show the distribution clearly.

3 Summary (descriptive) statistics

3.1 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

3.2 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.

3.3 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.

3.4 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

3.5 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

3.6 Quantiles

Template:

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

Example:

quantile(trashwheel$PlasticBottles, 
         probs = c(0.25, 0.5, 0.75), 
         na.rm = TRUE)
#>    25%    50%    75% 
#>  987.5 1900.0 2900.0

4 Data visualization

4.1 Histograms

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

Template (Frequency-based):

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()`).

Template (Density-based):

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

Example:

ggplot(trashwheel, aes(x = PlasticBottles, y = after_stat(density))) +
  geom_histogram(bins = 20)
#> Warning: Removed 1 row containing non-finite outside the scale range
#> (`stat_bin()`).

4.2 Density plot

A density plot is a way to visualize the distribution of a continuous variable — it shows where data values are concentrated (dense) and where they are sparse.

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()`).

4.3 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()`).

4.4 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()`).

4.5 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()`).

5 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.

6 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.

6.1 Basic Statistics

# Mean / Median / Var / SD
mean(DATA$VAR)
median(DATA$VAR)
var(DATA$VAR)
sd(DATA$VAR)
  • DATA → the name of your dataset (e.g., trashwheel).
  • VAR → a single categorical variable (e.g., PlasticBottles).
# Quantiles
quantile(DATA$VAR, probs = c(0.25, 0.5, 0.75))
  • DATA → the name of your dataset (e.g., trashwheel).
  • VAR → a single categorical variable (e.g., PlasticBottles).

6.2 Summary Statistics (csucistats)

num_stats(DATA$VAR)
  • DATA → the name of your dataset (e.g., trashwheel).
  • VAR → a single categorical variable (e.g., PlasticBottles).

6.3 Histogram (Frequency-based)

ggplot(DATA, aes(VAR)) + 
    geom_histogram()
  • DATA → the name of your dataset (e.g., trashwheel).
  • VAR → a single categorical variable (e.g., PlasticBottles).

6.4 Histogram (density-based)

ggplot(DATA, aes(x = VAR, y = after_stat(density))) +
  geom_histogram()
  • DATA → the name of your dataset (e.g., trashwheel).
  • VAR → a single categorical variable (e.g., PlasticBottles).

6.5 Histogram (Frequency-based) with bins

ggplot(DATA, aes(VAR)) + 
    geom_histogram(bins = X)
  • DATA → the name of your dataset (e.g., trashwheel).
  • VAR → a single categorical variable (e.g., PlasticBottles).
  • X → the number of bins (e.g., 15-30)

6.6 Histogram (Density-based) with bins

ggplot(DATA, aes(x = VAR, y = after_stat(density))) +
    geom_histogram(bins = X)
  • DATA → the name of your dataset (e.g., trashwheel).
  • VAR → a single categorical variable (e.g., PlasticBottles).
  • X → the number of bins (e.g., 15-30)

6.7 Density Plot

ggplot(DATA, aes(VAR)) + 
    geom_density()
  • DATA → the name of your dataset (e.g., trashwheel).
  • VAR → a single categorical variable (e.g., PlasticBottles).

6.8 Box plot

ggplot(DATA, aes(VAR)) + 
    geom_boxplot()
  • DATA → the name of your dataset (e.g., trashwheel).
  • VAR → a single categorical variable (e.g., PlasticBottles).

6.9 Dot plot

ggplot(DATA, aes(x = VAR)) + 
    geom_dotplot(binwidth = X)
  • DATA → the name of your dataset (e.g., trashwheel).
  • VAR → a single categorical variable (e.g., PlasticBottles).

6.10 Scatter Plot

ggplot(DATA, aes(x = VAR1, y = VAR2)) + 
    geom_point()
  • DATA → the name of your dataset (e.g., trashwheel).
  • VAR1 → a single categorical variable (e.g., PlasticBottles).
  • VAR2 → a single categorical variable (e.g., PlasticBags).

6.11 Scatter Plot + trend line

ggplot(DATA, aes(x = VAR1, y = VAR2)) + 
    geom_point() + 
    geom_smooth(method = "lm", se = TRUE)
  • DATA → the name of your dataset (e.g., trashwheel).
  • VAR1 → a single categorical variable (e.g., PlasticBottles).
  • VAR2 → a single categorical variable (e.g., PlasticBags).