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Distribution

Box-and-whisker plot

Summarises a distribution through median, quartiles, whiskers and optional outlier marks.

  • Plot
  • Distribution
  • Comparison

What it answers

How do centre, spread and potential outliers differ?

Shape
Quartile box, whiskers and points
What it shows
Median differences, spread and unusual values.

Example

The question

Which product type is delivered fastest and most reliably?

Days from order to delivery by product type (illustrative)

Days from order to delivery by product type (illustrative)Illustrative data, 13 orders per type. Catalogue: median 11; middle half 10 to 12; range 8 to 22; outlier 22. Built to order: median 27; middle half 24 to 32; range 18 to 41. Custom: median 36; middle half 34 to 41; range 30 to 45.Days from order to delivery01020304050CatalogueBuilt to orderCustom
Days from order to delivery by product type (illustrative)Illustrative data, 13 orders per type. Catalogue: median 11; middle half 10 to 12; range 8 to 22; outlier 22. Built to order: median 27; middle half 24 to 32; range 18 to 41. Custom: median 36; middle half 34 to 41; range 30 to 45.Days from order to delivery01020304050CatalogueBuilt to orderCustom
Illustrative data, 13 orders per type. Catalogue: median 11; middle half 10 to 12; range 8 to 22; outlier 22. Built to order: median 27; middle half 24 to 32; range 18 to 41. Custom: median 36; middle half 34 to 41; range 30 to 45.

Illustrative teaching data. It belongs to no company.

The misleading version

Same question, drawn badly

Boxes drawn from four values each

Boxes drawn from four values eachIllustrative data, 4 orders per type. Catalogue: median 11; middle half 9.75 to 14.5; range 9 to 22; outlier 22. Built to order: median 28; middle half 24.5 to 32.75; range 20 to 41. Custom: median 37.5; middle half 34 to 41.25; range 31 to 45.Days from order to delivery01020304050CatalogueBuilt to orderCustom
Boxes drawn from four values eachIllustrative data, 4 orders per type. Catalogue: median 11; middle half 9.75 to 14.5; range 9 to 22; outlier 22. Built to order: median 28; middle half 24.5 to 32.75; range 20 to 41. Custom: median 37.5; middle half 34 to 41.25; range 31 to 45.Days from order to delivery01020304050CatalogueBuilt to orderCustom
Illustrative data, 4 orders per type. Catalogue: median 11; middle half 9.75 to 14.5; range 9 to 22; outlier 22. Built to order: median 28; middle half 24.5 to 32.75; range 20 to 41. Custom: median 37.5; middle half 34 to 41.25; range 31 to 45.

What goes wrong. Each box rests on four values, but it looks as reliable as a box built from hundreds. With so few values, plot the points themselves.

When to use it

Use it when

Comparing numeric distributions across groups.

Avoid it when

When multimodal shape or individual values are essential without an additional layer.

How to read it

Read median, quartiles, whiskers and separately marked outliers.

Note

Quartile and whisker conventions differ across tools.

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
Value scale uses original units. Quartiles are positions in the sample distribution; whiskers depend on the chosen rule.
Example of the input layout: Long tableA long table: one row per observation, few columns. New data adds rows.GroupValueAABBC
A long table: one row per observation, few columns. New data adds rows.

Worked example

Sorted values 1,2,3,4,5. Under an inclusive quartile rule Q1=2, median=3, Q3=4. Draw the box and state whisker rules.

GroupValue
A10
A12
A18
B11
B23
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