# Physics: Uncertainties and Errors

- This applies to both AS and A Level exams. You can find more examples in Appendix 10 in the Edexcel specification.

**A10i** Comparing results:

**Validity**: a measurement is valid if it measures what it's supposed to be measuring and if the measurement taken is only affected by one independent variable**True value**: this is the value that should've been obtained if there were no experimental flaws or sources of error**Accuracy**: a result is accurate if it is close to the*true value*- i.e. not influenced by random and systematic errors**Precision**: how close together values from multiple repeats are**Repeatability**: how similar results are when determined by different people with the same method**Reproducibility**: how similar results are when determined by different people using a different method/different apparatus

Test yourself

**A10ii** Uncertainties and errors:

**Uncertainty**: the interval that the true value should lie in with a high level of confidence. Every measurement will have an uncertainty, e.g. $\pm 0.5$\pm 0.5 $\mathrm{g}$\mathrm{g}

-**Absolute uncertainty**is the 'plus or minus' value

-**Percentage uncertainty**is the maximum percentage that the reading could be out by

percentage uncertainty $=$= $\frac{\mathrm{absolute\ uncertainty}}{\mathrm{measurement}}$\frac{\mathrm{absolute\ uncertainty}}{\mathrm{measurement}} $\times 100$\times 100 **Error**: the difference between the measurement result and the true value

-**Random errors**are caused by unpredictable variation in the method or equipment

-**Systematic errors**are caused by incorrectly calibrated equipment or an incorrect technique which is used throughout**Resolution**: the smallest measuring interval in a reading (e.g. a ruler measurement would have a resolution of $1\ \mathrm{mm}$1\ \mathrm{mm} )

Test yourself

## Compounding uncertainties:

**Addition/subtraction of two measurements**: add the absolute uncertainties**Multiplication/division of two measurements**: add the relative uncertainties**Multiplying a constant by a measurement**: multiply the absolute uncertainty by the constant. The relative uncertainty is not affected**Raising a measurement to a power**: multiply the relative uncertainty by the power