Uncertainty, gradients and model testing
הוצג| English | משמעות |
|---|---|
| systematic error/ˌsɪstəˈmætɪk ˈerə/ | שגיאה שיטתית |
| uncertainty/ʌnˈsɜːtənti/ | אי־ודאות |
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?
רמת קושי 1/5 · 100 מטבעות + בונוס קטן בהשלמה הראשונה היום
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.
רמת קושי 2/5 · 140 מטבעות + בונוס קטן בהשלמה הראשונה היום
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?
רמת קושי 2/5 · 140 מטבעות + בונוס קטן בהשלמה הראשונה היום
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.
רמת קושי 2/5 · 140 מטבעות + בונוס קטן בהשלמה הראשונה היום
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 an uncertainty of 15 percent
- A 40 mm reading has an absolute uncertainty of 6 mm.
- Find the percentage uncertainty. For a quotient, add the percentage uncertainties.
Repeating a measurement always removes a calibration offset.
רמת קושי 1/5 · 100 מטבעות + בונוס קטן בהשלמה הראשונה היום
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.
רמת קושי 1/5 · 100 מטבעות + בונוס קטן בהשלמה הראשונה היום
uncertainty means A quantified limitation on a measured result.
A 40 mm reading has an absolute uncertainty of 6 mm. What is the percentage uncertainty, and how are two percentage uncertainties combined for a quotient?
6 divided by 40 is 0.15, which is 15 percent. Adding percentages is the maximum-uncertainty rule used here.
What is the percentage uncertainty?
רמת קושי 1/5 · 100 מטבעות + בונוס קטן בהשלמה הראשונה היום
6 divided by 40 is 15 percent.