Repeated Measurement Statistics

Worked example and next step

The default readings 10, 12, 14, 16 and 18 have mean 14, squared deviations summing to 40, sample variance 40/4 = 10, and sample standard deviation √10 ≈ 3.162278. The standard error is √10/√5 = √2 ≈ 1.414214, in the same unit as the readings.

For the uncertainty propagation calculator, an estimate based on this mean would use 14 and, if the assumptions apply and this is the only component, standard uncertainty 1.414214. Review other uncertainty components before combining inputs. See the worked uncertainty guide.

Method and assumptions

All readings have equal weight and use the same unit. Mean = Σx/n; sample variance = Σ(x − mean)²/(n − 1). Median is the middle ordered reading, or the average of the middle pair.

Interpreting s/√n as Type A standard uncertainty of the mean requires independent observations obtained under the same measurement conditions. Independence is not tested here. Drift, correlated readings and changing conditions require a suitable measurement model.

Sample standard deviation describes observed spread; standard error describes the estimated spread of the mean under the stated assumptions. No confidence interval, outlier removal, normality test or calibration uncertainty is supplied. Identical readings do not prove zero total measurement uncertainty.

Uses shifted, compensated sums and scaled deviations. Decimal input is stored as floating-point numbers; digits lost on input cannot be recovered. Numerical overflow or underflow is rejected. Limit: 2–1,000 readings.

API

POST a JSON object to /api/statistics/sample. The values field is an array of numbers, for example:

{"values":[10,12,14,16,18]}

References

• NIST Engineering Statistics Handbook: Run-sequence plotAccessed 2026-09-08
• NIST: Evaluating uncertainty components, Type AAccessed 2026-09-08
• NIST: Univariate Summary Statistics, numerical accuracyAccessed 2026-09-08
• NIST StRD NumAcc1: benchmark data and exact resultsAccessed 2026-09-08