01 · Purpose
Why and when to use it
Use it to compare location and spread across groups, while recognising that the summary hides individual values and distribution detail.
Who takes part?
The measurement owner works with people who understand the process and the recorded data. Statistical or measurement-system decisions should involve someone able to check the assumptions and study design.
02 · Application
How to apply it
Start with an agreed measurement purpose, explicit units and trustworthy observations. Identify missing cases and assumptions before calculating.
- Define comparable groups and units.
- Choose and report a quartile convention.
- Calculate Q1, median, Q3 and IQR = Q3 − Q1.
- Set whiskers using an explicit convention and show observations beyond them.
- Compare group sizes and investigate differences with process context.
03 · Example
A worked measurement example
Original fictional teaching example. Small datasets illustrate the method; they are not proposed as sufficient study sizes. Supplied parameters are assumptions, not estimates from a real process.
| Summary for 2, 4, 4, 6, 9 minutes | Value (linear-interpolated quantiles) |
|---|---|
| Q1 / median / Q3 | 4 / 4 / 6 |
| IQR | 6 − 4 = 2 |
| Lower / upper fences | 1 / 9 |
| Whiskers | 2 and 9; no values beyond the fences |
04 · Interpretation
What the result tells you
The box covers the central half under this quantile convention. Other software conventions can give different quartiles in a tiny sample; record the method.
Completion check: A labelled group distribution summary with stated quantile and whisker conventions.
05 · Judgement
Mistakes and limitations
An outlying point is a flag for investigation, not proof of an error. A box plot can conceal multimodality and does not show process stability.
07 · Reading
Sources and further reading
The tool list follows the accepted LeanTrainingLab overview and its reference to Six Sigma+Lean Toolset, second edition (Lunau, editor; Springer, 2013). The book chapters were not available for direct review during this build. Explanations, examples and worksheets are original teaching material. Further reading supplies professional background; local conventions are stated explicitly.