01 · Purpose
Why and when to use it
Use it to quantify spread and as a building block for statistical models and variance-component studies.
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.
- Decide whether a sample or complete-population calculation is intended.
- Calculate the mean.
- Square each deviation and add the squared deviations.
- Divide by the appropriate denominator.
- Report the denominator convention and squared units.
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.
| Sample 2, 4, 4, 6, 9 minutes | Calculation |
|---|---|
| Mean | 5 |
| Squared deviations | 9 + 1 + 1 + 1 + 16 = 28 |
| Sample variance | 28 / 4 = 7 min² |
| Finite-population descriptive variance | 28 / 5 = 5.6 min² |
04 · Interpretation
What the result tells you
Seven square minutes and 5.6 square minutes use different denominator conventions for the same values. Neither should be reported simply as “seven minutes”.
Completion check: A variance calculation with explicit convention and units.
05 · Judgement
Mistakes and limitations
At least two values are required for sample variance. Extreme values and mixed process populations affect it; spread alone does not establish 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.