KEVOS® MAKEOS · Quality
Sample Size to Estimate a Mean
How many measurements or tests are needed to estimate the mean within this margin?
Minimum number of tests or measurements to estimate a mean within a chosen margin of error at a confidence level, with an optional finite-population correction.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Expected standard deviation | Estimate of the standard deviation from earlier data or a pilot study, in the units of the measurement. | |
| Required margin of error (±) | Half-width of the confidence interval you need, in the same units. | |
| Confidence level | choice | Confidence that the true mean lies within the margin. |
| Population size (0 = very large) | items | Total lot or population size for a finite-population correction; 0 if large or ongoing. |
Method and formulas
- n₀ = (z σ ÷ E)², with z = 1.645, 1.960 or 2.576 for 90, 95 and 99%.
- Finite population: n = n₀ ÷ (1 + (n₀ − 1) ÷ N).
- Round up to a whole number.
- Example: σ 0.05 and a ±0.02 margin at 95% need 25 measurements.
Limitations
- Uses the normal z value; for small samples with σ estimated from the same data, a t-based size is slightly larger.
- A poor σ estimate gives a poor sample size.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Plan how many test pieces to make
- Size a measurement study
- Justify an inspection sample
Who it is for
- Quality engineers
- Process engineers
- Test engineers
What you get
- Required sample size
- z value used
Interpreting the result
- If the sample is too large to afford, accept a wider margin or reduce variation first.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 130–132. Topic reference; no source tables or recommended settings are reproduced.
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