Estimation, errors and uncertainty

Repair the common break

Common misconception: Extra decimal places remove measurement error.

Correct model: Separate random scatter from systematic offset, propagate the stated uncertainty and report only justified precision.

Worked transfer

For repeated times 1.42, 1.46, 1.44 and 1.48 s, the mean is 1.45 s and half-range uncertainty is 0.03 s, so report (1.45 ± 0.03) s. A zero offset would instead be a systematic error and is not reduced by averaging.

Guided practice

Explain why “Extra decimal places remove measurement error.” fails. Then construct one example that correctly applies estimation, errors and uncertainty.

Independent practice

Four diameter readings are 2.31, 2.35, 2.33 and 2.37 mm, while the micrometer has a +0.02 mm zero error. Calculate and report the corrected result with a justified uncertainty.

Return to the recorded repair plan when the explanation and application are secure enough to re-test.