A precise estimate of the average can coexist with widely varying individual fills. State which quantity the summary describes.
Two quantities answer different questions
The sample standard deviation describes spread among observations. For independent observations under the usual common-distribution model, the estimated standard error of their mean is s divided by the square root of n. The latter enters a confidence interval for the mean. It is not a replacement for the spread of individual fills.
A hypothetical spreadsheet trap
Imagine a trial table with 100 independent observations and sample standard deviation 2 g. Its estimated standard error of the mean is 0.2 g. Reporting only “variation 0.2 g” would make the individual-fill spread look ten times smaller. The arithmetic did not improve the machine; it changed the quantity being reported.
Conversely, increasing the number of observations can refine an estimated mean without reducing the existing unit-to-unit spread. This example concerns interpretation only. It provides no proposed HM filling limit, measurement uncertainty budget or universal sample-size rule.
Keep both the raw data and the named statistic
Use separate columns for observation count, sample mean, sample standard deviation and standard error of the mean. Identify units and the data grouping. Repeated readings of one container do not automatically supply 100 independent filling outcomes. Check what the experimental unit actually was.
Before comparing summaries from two suppliers, confirm that both use the same named statistic. Ask which process conditions and time span their samples represent. If the buyer needs evidence about individual fills, retain the individual readings and the relevant distribution or acceptance analysis; a narrow mean interval answers a narrower question.
Trial discussion worksheet
This blank worksheet is for your own project. It contains no H M machine trial result.
| Review question | Reference or observation to retain |
|---|---|
| Which statistic is reported? | SD or SE of a specified mean |
| What does n count? | Independent experimental units |
| What decision is being made? | Average estimate or individual outcome |
Customer Questions
Is standard error a filling accuracy specification?
No. It describes uncertainty of a statistical estimate under its model.
Does a larger sample make individual fills less variable?
Collecting more data alone does not alter the process spread.
Should the original readings be retained?
Yes. A summary cannot reveal every grouping or time pattern.
Primary References
These references support the technical principles discussed in this guide. The worked examples and review questions are educational.
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