Resolution tells you what the instrument can show. Spread tells you how much your repeated readings actually differ. The uncertainty you quote should be the larger of the two.
This lesson is part of uncertainty and practical-data reasoning. It extends reading measuring instruments and uncertainty.
How do you find each one?
Follow these steps for a set of repeated readings.
- Mean: add the readings and divide by the number of readings.
- Spread: half of (largest − smallest).
- Resolution: the smallest division or digit the instrument shows.
- Quote the larger of the spread and the resolution.
Worked example: timing 20 swings
An original pendulum experiment times 20 swings four times: 28.4 s, 28.9 s, 28.1 s and 28.6 s. The stopwatch resolution is 0.01 s.
Mean = (28.4 + 28.9 + 28.1 + 28.6) ÷ 4 = 114.0 ÷ 4 = 28.5 s.
Spread = (28.9 − 28.1) ÷ 2 = 0.8 ÷ 2 = 0.4 s.
Resolution = 0.01 s.
The spread is forty times the resolution, so the result should be written as 28.5 ± 0.4 s.
The mistake that costs marks
The common slip is to quote the stopwatch resolution, ±0.01 s, as the uncertainty. It looks precise, but the readings themselves differ by 0.4 s.
| Statement | Verdict |
|---|---|
| “Time = 28.50 ± 0.01 s” | Wrong: claims more certainty than the data show |
| “Time = 28.5 ± 0.4 s” | Right: uses the larger uncertainty |
Reaction time when timing by hand is the usual reason spread is bigger than resolution.
When is resolution the larger one?
If repeated readings agree exactly, the spread is zero, and resolution is the only visible uncertainty. A ruler reading 12.0 cm every time has a spread of zero but still has a resolution of 0.1 cm, so the uncertainty is governed by resolution.
Check yourself
Five readings of a length are 12.3, 12.5, 12.4, 12.6 and 12.2 cm. The ruler resolution is 0.1 cm. Find the mean, the spread and the uncertainty to quote.
Answer
Mean = (12.3 + 12.5 + 12.4 + 12.6 + 12.2) ÷ 5 = 62.0 ÷ 5 = 12.4 cm.
Spread = (12.6 − 12.2) ÷ 2 = 0.2 cm.
The spread (0.2 cm) is larger than the resolution (0.1 cm), so quote 12.4 ± 0.2 cm.
What to study next
Continue with explaining why a graph line should not join every dot. The units and significant-figure checker helps with presenting the result.
If you want a teacher to give you further data sets to practise on, see online one-to-one Physics tuition. The mistake log and paper-error review tool helps you track recurring slips.