Before generation
Use this diagnostic after a repeated classroom measurement when learners need to separate center, spread, reference agreement, and displayed resolution. It supports a first review of repeatability and possible bias and keeps every trial visible. The summary is not a calibration certificate, uncertainty budget, control chart, outlier test, or proof of accuracy. Decisions about exclusion, equipment fitness, or corrective action require the approved laboratory method and accountable review.
Worked example
Five fictional measurements of a 50.00 g reference are 49.98, 50.01, 50.00, 49.99, and 50.02 g with 0.01 g resolution. Their mean is exactly 50.00 g, the sample standard deviation is about 0.0158 g, and the range is 0.04 g or four resolution intervals. Mean percent error is zero, but the nonzero spread remains visible, demonstrating why agreement of the average does not make every trial identical or remove uncertainty.
Formula or methodology
Mean equals the sum of readings divided by n. Sample standard deviation equals the square root of the sum of squared deviations from the mean divided by n minus one. Range equals maximum minus minimum. Bias equals mean minus reference. For a nonzero reference, percent error equals absolute bias divided by absolute reference times 100. Relative spread equals sample standard deviation divided by absolute mean times 100 when mean is nonzero.
How to interpret the result
A small reference error describes the mean under this entered comparison; a small sample standard deviation describes repeatability in these trials. Either can be small while the other is large. Range in resolution intervals indicates how observed variation compares with displayed increments but does not identify its cause. Examine drift, sequence, technique, zero offset, environment, calibration history, and whether the reference value and instrument range suit the question.
Common mistakes
Do not call precision accuracy, calculate population standard deviation when the required method uses a sample estimate, hide trials behind an average, delete a value only because it looks unusual, report percent error against a zero reference, or claim resolution equals complete uncertainty. Preserve raw data, graph readings in collection order, document exclusions, check calibration and units, and round the reported result in line with the measurement and required uncertainty convention.
