01 · Purpose
Why and when to use it
Use a central quantile span when a measure less dominated by extreme observations is useful. Do not compare results labelled “span” until their definitions match.
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.
- Choose the percentile pair based on the purpose.
- Specify the quantile calculation convention.
- Calculate the lower and upper quantiles.
- Subtract the lower from the upper.
- Report the pair, unit, sample size and excluded-tail implications.
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.
| 2, 4, 4, 6, 9 minutes; linear interpolation | Result |
|---|---|
| Q1 / Q3 | 4 / 6 minutes |
| Interquartile span (IQR) | 6 − 4 = 2 minutes |
| Full observed range | 9 − 2 = 7 minutes; a different definition |
04 · Interpretation
What the result tells you
The central-half span is two minutes under this convention. It says little about the worst delays outside the central half.
Completion check: A named quantile-spread measure with its exact definition.
05 · Judgement
Mistakes and limitations
This local definition is explicit because the book’s chapter-specific terminology has not been verified. Use the named percentile-distance guide for P90 − P10 and avoid an unqualified “span” label.
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.