Distribution

Variable-width box plot

Adds group-size information by varying box width.

Plot
Distribution
Sample size

What it answers

How do distribution summaries and group sizes compare?

Shape: Boxes with different widths
What it shows: Spread, median and sample-size imbalance.

Example

The question

How do order values vary across stores of very different sizes?

Order value by store, box width shows number of orders (illustrative)

Box widths are in proportion to the square root of the number of orders. Big (400): median 39.6, middle half 33.9 to 46.2, range 10.5 to 75.9; Mid (100): median 50.8, middle half 40.5 to 60.4, range 16 to 83.5; Small (25): median 31.1, middle half 25.9 to 40.4, range 12.4 to 49.7.

Illustrative data. It belongs to no company.

When to use it

Use it when

Comparing distributions while showing unequal sample sizes.

Avoid it when

When width encoding is unexplained or masks small groups.

How to read it

Read each box's statistics, then width using the sample-size key.

Note

State whether width follows sample size or its square root.

The data you need

Layout: Long table
Fields: Group: text; Value: number
One row is: One raw observation belonging to a group. What is the grain?
Rules: Retain individual observations and group labels. State weighting and missing-data rules.
Optional: For box plots only, some tools accept Group,Q1,Median,Q3,WhiskerLow,WhiskerHigh plus separate outliers. Other distributions usually need raw data.
Preparation: Keep raw numeric observations, group them if needed and handle missingness explicitly. Choose bins, bandwidth or summary conventions as appropriate to this specific plot.
Units: The value axis uses original units; box width encodes sample size or a stated transformation of it.

A long table: one row per observation, few columns. New data adds rows.

Worked example

Groups A: n 25 and B: n 100. If width follows square root of n, B is twice as wide as A, not four times.

Group	Value
A	10
A	12
A	18
B	11
B	23

All charts in the library