Uncertainty & measurement
Repeated measurements & timing
Summarize repeated readings and timing uncertainty.
Your measurements
Number formats & units
Use decimal dots in datasets. Single values also accept decimal commas and scientific notation such as 1.2e-3 or 1.2 × 10⁻³.
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Result & working
ExampleThe calculator is loading. You can read the worked example below.
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Interpretation & assumptions
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Formula & example
The relationship
What the variables mean
| Symbol | Meaning |
|---|---|
| Number of repeated readings. | |
| Exact cycle/item count per reading, a positive integer. | |
| Floor | An explicitly supplied lower bound for uncertainty. It is not estimated from the data. |
Worked example
- Repeated readings / total times
- 20.1, 20.3, 20.2, 20.0
- Absolute instrument / method uncertainty floor
- 0.1
- Exact number of cycles or items per reading
- 10
- Reading and result unit
- s
(2.02 ± 0.02) s
Follow the example steps
- Mean = 80.6 / 4 = 20.15 s.
- Range = 20.3 − 20 = 0.3; half-range = 0.15 s.
- Chosen uncertainty = max(0.15, 0.1) = 0.15 s.
- Value per cycle/item = 20.15/10 = 2.015; uncertainty = 0.15/10 = 0.015 s.
- Final reported value: (2.02 ± 0.02) s.
Common mistakes
Half-range and standard error are different methods.
Incorrect approach
9, 10, 11: Δx = 1/√3
Correct approach
9, 10, 11: Δx = (11 − 9)/2 = 1
More checks before you submit
- Do not divide the half-range by √n; that produces neither the half-range nor sample SEM.
- Distinguish repeats n from cycles per timing N.
- Do not remove an extreme value without investigating and explaining it.
Method notes
Use half the range when that is the convention requested in a school experiment. This tool applies the larger of half-range and the supplied floor; this is a stated reporting convention, not an IB rule for every instrument or a universal statistical formula.
Timing several cycles can reduce the relative effect of a fixed start/stop uncertainty. Count complete oscillations and keep the cycle count exact. The tool also displays sample SD and SEM for comparison, without substituting them for the half-range.
Identical repeated readings do not prove zero uncertainty. Resolution, calibration and method limits still matter. A systematic offset is not removed by repetition.