| Applications and Skills |
|---|
| Explaining how random and systematic errors can be identified and reduced |
| Collecting data that include absolute and/or fractional uncertainties and |
| stating these as an uncertainty range (expressed as: best estimate ± uncertainty range) |
| Propagating uncertainties through calculations involving addition, |
| subtraction, multiplication, division and raising to a power |
| Determining the uncertainty in gradients and intercepts |
| Understandings |
|---|
| Random and systematic errors |
| Absolute, fractional and percentage |
| uncertainties |
| Error bars |
| Uncertainty of gradient and intercepts |
$$ \text{Booklet}\\ _{ }\\ \bullet \text{ if } y = a \pm b \\\text{then } \Delta y = \Delta a + \Delta b\\\space\\ \bullet \text{ if } y = \frac{ab}{c} \\\text{then } \frac{\Delta y}{y} = \frac{\Delta a}{a} + \frac{\Delta b}{b} + \frac{\Delta c}{c} \\\space\\ \bullet \text{ if } y = a^n \\\text{then } \frac{\Delta y}{y} = |n\frac{\Delta a}{a}| $$
Systematic error is a consistent and repeatable error associated with faulty equipment or imperfect experiment design. These errors are usually caused by measuring instruments that are incorrectly calibrated or used incorrectly.
<aside> ❗ Systematic and random errors can interfere with your experiment from many sources and are difficult to detect.
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Some sources include, but are not limited to:
Random error has no pattern. One minute your readings might be too small. The next they might be too large.
You cannot predict random error and these errors are usually unavoidable.
Those errors are simply due to the imperfect nature of us and of measuring devices.
<aside> ❗ Random errors are due to the recorder rather than the instrument used: different people may measure the same line slightly differently.
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Example: What is the length of the blue line below?
One person might answer $11\text{mm} \pm 1\text{mm}$, while another might answer $12\text{mm} \pm 1\text{mm}$.