Uncertainty, gradients and model testing
Введено| English | Значение |
|---|---|
| systematic error/ˌsɪstəˈmætɪk ˈerə/ | систематическая ошибка |
| uncertainty/ʌnˈsɜːtənti/ | неопределённость |
What would explain this observation?
- A line passing near every data point is useful, but its gradient can still be uncertain. A graph is evidence for a model within the measurement range.
Build the model
- Random variation makes repeated readings differ.
- Systematic error 系统误差 shifts results consistently.
- Absolute uncertainty 不确定度 has the measured unit; relative or percentage uncertainty compares uncertainty with the measured value.
- uncertainty: A quantified limitation on a measured result.
- systematic error: A consistent measurement bias.
Which is most likely a systematic error?
Сложность 1/5 · 100 монет + небольшой бонус за первое выполнение сегодня
A balance reading 0.20 g when empty shifts EVERY reading the same way - that is a systematic zero error. Fluctuations either side of the mean and variable reaction times scatter randomly and shrink with repeats; an offset does not.
Match each technical term to its precise meaning.
Сложность 2/5 · 140 монет + небольшой бонус за первое выполнение сегодня
Use the definitions to distinguish related quantities and processes.
Choose evidence that can test it
- For a product or quotient, adding fractional uncertainties is a common maximum-uncertainty approximation.
- For a difference, add absolute uncertainties.
- A nonzero intercept can reveal an offset or an incomplete model.
In the lab: Show units on axes and choose a sensible scale. Plot uncertainty bars where justified, draw a best-fit line rather than joining every point, and estimate steepest and shallowest plausible gradients when the course method calls for them.
Which two habits make the investigation or model in this case more defensible?
Сложность 2/5 · 140 монет + небольшой бонус за первое выполнение сегодня
Stating the conditions and assumptions lets others repeat the work exactly, and recording the supporting evidence lets them check the conclusion. Hiding disagreeing results removes the evidence that could challenge a wrong conclusion, and one measurement can never establish a wider claim.
Work from known quantities
- Known: length = 50.0 mm with uncertainty 1.0 mm.
- Percentage uncertainty = absolute uncertainty/value ×100 = 1.0/50.0×100 = 2.0%.
- For a quotient of two independently measured quantities with maximum percentage uncertainties 2% and 3%, the summed maximum estimate is 5%.
Your turn: A 40 cm reading has an absolute uncertainty of 1 cm. Find percentage uncertainty.
A 40 cm reading has an absolute uncertainty of 1 cm. Find percentage uncertainty.
Сложность 2/5 · 140 монет + небольшой бонус за первое выполнение сегодня
The result is 2.5 %. Known: reading 40 cm; absolute uncertainty 1 cm. Use percentage uncertainty = absolute uncertainty / value x 100. Percentage uncertainty = 1/40 x 100 = 2.5%. Smaller measured values carry larger percentage uncertainties for the same absolute uncertainty.
Check the conclusion and its limits
- Repeating readings reduces random uncertainty in a mean but does not automatically remove a zero error.
- Do not quote more decimal places than your measurement can support.
Not true: Repeating a measurement always removes a calibration offset. Repeating and averaging reduces RANDOM scatter in the mean. A calibration offset shifts every reading identically, so repeats land on the same wrong value; only recalibration removes it.
- Random variation makes repeated readings differ.
- For a product or quotient, adding fractional uncertainties is a common maximum-uncertainty approximation.
- Watch for: repeating readings reduces random uncertainty in a mean but does not automatically remove a zero error.
Write from a percentage uncertainty of 4 percent
- A 50 cm reading has an absolute uncertainty of 2 cm.
- Find the percentage uncertainty. Repeating the reading does not remove a calibration offset.
Repeating a measurement always removes a calibration offset.
Сложность 1/5 · 100 монет + небольшой бонус за первое выполнение сегодня
Repeating and averaging reduces RANDOM scatter in the mean. A calibration offset shifts every reading identically, so repeats land on the same wrong value; only recalibration removes it.
A quantified limitation on a measured result: write the technical term.
Сложность 1/5 · 100 монет + небольшой бонус за первое выполнение сегодня
uncertainty means A quantified limitation on a measured result.
A 50 cm reading has an absolute uncertainty of 2 cm. What is the percentage uncertainty, and why does repeating the measurement not remove a calibration offset?
Percentage uncertainty is the absolute uncertainty divided by the reading, times 100. Random and systematic effects are reduced in different ways.
What is the percentage uncertainty?
Сложность 1/5 · 100 монет + небольшой бонус за первое выполнение сегодня
2 divided by 50 is 0.04, so the percentage uncertainty is 4 percent. Other options — 2.5 percent (the lesson reading of 40 cm with an uncertainty of 1 cm); 2 cm (the absolute uncertainty).