Distribution
Boxen / letter-value plot
Uses progressively more extreme quantiles to reveal distribution tails in large samples.
- Plot
- Distribution
- Comparison
What it answers
What happens in the distribution tails?
- Shape
- Nested quantile boxes
- What it shows
- Tail asymmetry and extreme quantile structure.
Example
The question
What do the tails of a large set of response times look like?
Response times for 5,000 requests, letter-value plot (illustrative)
Illustrative data. It belongs to no company.
When to use it
Use it when
Large datasets where tail detail matters.
Avoid it when
Small samples or audiences unfamiliar with letter-value summaries.
How to read it
Read nested boxes from central to increasingly extreme quantiles.
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 measurement axis retains its original unit. Frequency uses observations; normalised frequency divides by group sample size; density also depends on interval width.
Worked example
Example supplied intervals: central 50%=8-12, next 75%=6-15. Draw nested boxes; wider outer bounds reveal tail extension.
| Group | Value |
|---|---|
| A | 10 |
| A | 12 |
| A | 18 |
| B | 11 |
| B | 23 |