Measurement lab · RecallWeave

1. Set up a case

These starting readings are fictional. Use one quantity and the same unit throughout.

Readings in acquisition order

Enter 2–100 decimal readings, separated by commas, spaces or newlines. A comma marks a field; don't leave one empty.

Unit label

For example, mm or ms. This label does not convert values.

Additive calibration correction

Add this signed value to every reading. If readings are 0.04 too high, enter −0.04.

Shared calibration half-width, a

Assume the one shared correction is equally plausible anywhere within ±a of its stated value. Enter zero or a positive half-width, in the same unit.

Use decimal points, an ordinary minus sign, and optional e notation. For this teaching lab, nonzero magnitudes range from 1e-12 to 1e9; zero is allowed.

Try a fictional preset

A preset replaces all four inputs. Calculations stay in this tab; they are not uploaded or automatically saved.

2. Read the uncertainty budget

— observations

Corrected mean—

Raw mean plus the stated correction.

Combined standard uncertainty, u_c—

Independent repeatability and shared calibration components combined.

Repeatability of the mean, u_A—

Estimated single-reading scatter divided by √n.

Shared calibration, u_cal—

Rectangular half-width a divided by √3. Shared across all readings.

Raw mean: — · Applied correction: —
Sample standard deviation of readings, s: —

Budget and projection table values use six significant digits; chart ticks are abbreviated. Standard uncertainty is not a guaranteed bound or an automatic confidence percentage.

Look at the acquisition order

Each point is a recorded reading minus the raw mean. A shared correction shifts every reading equally, so it does not change this plot. A trend is a reason to investigate stability; the chart does not test independence.

Read every recorded value


Reading	Recorded	Corrected

3. Imagine more independent readings

This projection keeps the estimated single-reading scatter and calibration information fixed. It is a planning comparison, not additional observed data. Copying the existing rows does not create independent evidence.

Combined
Repeatability of mean
Shared calibration


Sample size	Repeatability	Calibration	Combined

What this model assumes

Repeat readings are independent observations of one stable quantity. Their scatter estimates repeatability.
A recognized additive calibration correction has been applied. Its remaining uncertainty is shared across every reading.
The correction's stated ±a range is modeled as rectangular, and its uncertainty is independent of the repeatability component.
Other effects are outside this two-component teaching model. A real uncertainty budget may need resolution, drift, correlations and other inputs.

u_A = s / √n
u_cal = a / √3
u_c = √(u_A² + u_cal²)

Type A and Type B describe evaluation methods. They do not mean “random” and “systematic,” and do not by themselves say what averaging will reduce.

Try it, then explain it

Compare the first two presets. Which uncertainty component changes even though every reading stays the same?
Change only the additive correction. What moves, and why does the scatter stay fixed?
Enter 9.8, 9.9, 10.0, 10.1, 10.2. What could their acquisition order suggest that a mean alone hides?

Check your reasoning

The calibration half-width changes the shared component and the combined result. An additive correction shifts the estimate, leaving deviations from the mean unchanged. The ordered readings may suggest drift; more evidence is needed before using an independent-repeatability model.

Keep the practice questions

Twelve original questions connect correction signs, sample scatter, shared uncertainty and experimental decisions. Download the JSON deck for a RecallWeave version that supports local course import.