Box Plot

WHAT IS A BOX PLOT?

A box plot (also called a box-and-whisker plot) provides a compact five-number summary: minimum, first quartile (Q1), median, third quartile (Q3), and maximum — with outliers shown as individual points. It is the most space-efficient way to compare distributions across multiple groups. Box plots answer "how does the spread and center of group A compare to group B?" They work well with 3-20 groups and are standard in scientific and statistical reporting. Note that box plots hide distribution shape (bimodality) — consider violin plots if shape matters. In ggplot2, use geom_boxplot().

HOW TO READ A BOX PLOT

The box spans the interquartile range: its lower edge is the 25th percentile, its upper edge the 75th, and the line inside is the median — not the mean. Half the observations fall inside the box, so its height is a direct read of spread. The whiskers extend to the most extreme point still within 1.5 times the IQR of the box, and anything beyond is drawn individually. That 1.5 is a convention, not a test: points outside it are candidates for investigation, not confirmed errors. A median sitting off-centre within the box indicates skew, and comparing notch overlap between groups gives a rough visual significance test. The critical limitation is that a box plot cannot show multimodality — two distributions with wildly different shapes can produce identical boxes, which is the single best argument for overlaying the raw points.

R + GGPLOT2 CODE EXAMPLE

ggplot(mtcars, aes(x = factor(cyl), y = mpg)) +
  geom_boxplot(fill = "#ff6a00", alpha = 0.7) +
  labs(title = "MPG by Cylinder Count", x = "Cylinders", y = "MPG")

BOX PLOT WITH JITTERED POINTS AND GROUP COUNTS

The version that fixes the box plot’s main weakness: raw points overlaid so distribution shape stays visible, and the sample size printed per group.

library(ggplot2)
library(dplyr)

counts <- mtcars |>
  count(cyl) |>
  mutate(label = paste0("n = ", n))

ggplot(mtcars, aes(x = factor(cyl), y = mpg)) +
  geom_boxplot(
    fill = "#ff6a00", alpha = 0.3,
    outlier.shape = NA, width = 0.55
  ) +
  geom_jitter(width = 0.12, alpha = 0.7, size = 2, colour = "#1c1c17") +
  stat_summary(
    fun = mean, geom = "point",
    shape = 23, size = 3, fill = "white"
  ) +
  geom_text(data = counts, aes(x = factor(cyl), y = 33, label = label),
            size = 3.2, colour = "grey40") +
  labs(
    title = "Fuel economy by cylinder count",
    subtitle = "Box shows median and IQR; diamond marks the mean",
    x = "Cylinders", y = "Miles per gallon"
  ) +
  theme_minimal(base_size = 12)

COMMON MISTAKES WITH THIS CHART

SIMILAR CHART TYPES