01 · Purpose
Why and when to use it
Use it to describe spread without letting the sample minimum and maximum dominate, while examining tails separately.
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 and name the percentile pair.
- Sort the data and state the quantile method.
- Calculate lower and upper percentiles.
- Subtract the lower percentile from the upper.
- Report units, sample size and tail observations separately.
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 |
|---|---|
| Position convention | h = (n − 1)p on zero-based ordered indices |
| P10 / P90 | 2.8 / 7.8 minutes |
| P90 − P10 | 5.0 minutes |
04 · Interpretation
What the result tells you
The example interpolates between observations. The five-minute span is not the full observed range of seven minutes and is a poor basis for precise population-tail claims with only five observations.
Completion check: A named percentile distance with a reproducible calculation method.
05 · Judgement
Mistakes and limitations
Quantiles from different software can disagree. Do not use a central span to conceal critical extreme delays; customer requirements may concern an upper percentile or maximum.
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.