This entry is part of the Chart Index, the reference library for the Chart Design Field Guide.
The box plot is Tukey's invention, and one of the most efficient chart types ever designed. In a single glyph the size of a postage stamp it shows median, quartiles, range, and outliers — five summary statistics, encoded as length and position. The form scales linearly: ten box plots side by side compare ten distributions in the space a single histogram would occupy.
The trade-off is summary versus shape. A box plot reduces a distribution to five numbers; subtle features — bimodality, skewness, irregular tails — disappear behind the box. For comparing many groups, that compression is the chart's superpower. For looking carefully at one distribution, the histogram or violin remains preferable.
What it is
A box plot encodes a distribution as a rectangle (the box) bounded by the first quartile (Q1) and third quartile (Q3), with a line inside the box at the median. From the box, whiskers extend to the most extreme values within 1.5× the interquartile range; observations beyond the whiskers are plotted individually as outliers. The whole composition fits comfortably in a thin vertical strip.
Five service tiers, five box plots aligned to a shared scale. The eye reads each tier's median (the central line), the spread (box height), and the tail behaviour (whiskers and outlier dots). Comparison across tiers happens in a single sweep.
When to use it
Box plots are the right choice when:
- You are comparing distributions across many groups (5–30 groups is comfortable).
- The reader's question is "how do these distributions differ?" in terms of centre, spread, and tail.
- The data is continuous with enough observations per group (typically ≥30) for quartiles to be meaningful.
- You have outliers worth surfacing — the form makes them explicit.
- The display needs to be dense — a row of box plots fits easily where a row of histograms would not.
When not to use it
- Small samples. With fewer than 20 observations per group, quartiles become noisy. Show the raw points (strip or bee swarm) instead.
- Subtle distribution shape. A bimodal distribution and a unimodal distribution can have identical five-number summaries. Use a histogram, violin, or density plot.
- Audiences unfamiliar with the form. Non-statistical audiences may not recognise the box's encoding. Either add a small legend or use a simpler form.
- One distribution. A single box plot is unremarkable. Use a histogram or density plot, which carry richer detail.
Design principles
Show the data behind the box
Tukey's modern advocates — particularly Hadley Wickham — argue for jittered points overlaid on the box. The box gives the summary; the points show the actual observations. Together they preserve both the abstraction and the raw evidence.
Use the right whisker rule
Tukey's 1.5×IQR is the default but not the only choice. For data with heavy tails, use percentile-based whiskers (e.g., 5th–95th). For small samples, use the actual min and max. Document the choice; a box plot without a stated whisker rule is unreadable.
Align scales across panels
When comparing multiple box plots, every plot must share the same y-axis (or x-axis for horizontal). Independent scales destroy comparability; the form is then doing more harm than good.
Use log scale when distributions span orders of magnitude
API latencies, file sizes, transaction values — these often span three or four orders of magnitude. A linear y-axis squashes nearly everything into a narrow band at the bottom. A log scale spreads the distribution and lets the boxes have real height.
Annotate the n per box
A box plot summary is only as good as its sample. Add a small annotation under each box showing the count: n = 1,420. This guards against the reader weighting boxes with twelve observations equally with boxes built on twelve thousand.
Quiet the box fill
The box's fill is decoration, not data. Use a low-saturation pastel — perhaps 15–25% opacity of the accent colour — and let the box outline and median line carry the visual weight.
Highlight the median, not the mean
Box plots are quartile-based; the mean is not part of the form. If the mean matters, add a small marker (a diamond or asterisk) inside the box, but do not let it replace the median line. Tukey's resistance to non-resistant statistics is the chart's philosophical foundation.
Anatomy
A multi-box-plot panel is a row of vertical glyphs, each summarising one distribution. Shared scale, consistent box widths, consistent whisker rule — these are the design choices that keep the comparison fair.
Related types
- Violin plot — replaces the box with a density curve. Shows shape; harder to read precise quartiles.
- Strip / jitter plot — every point shown; better for small samples. Often combined with a box plot.
- Bee swarm — strip plot with collision avoidance.
- Histogram / density plot — for one distribution at a time; shows shape that box plots hide.
- Range plot — encodes minimum and maximum only, no quartiles or median.
Reading list
- Tukey, J. (1977). Exploratory Data Analysis. The original box plot.
- McGill, R., Tukey, J. & Larsen, W. (1978). Variations of Box Plots. The notched variant.
- Wickham, H. & Stryjewski, L. (2011). 40 Years of Boxplots. A retrospective and modern variants.
- Cleveland, W. (1993). Visualizing Data. On the comparative use of box plots.