# Topic 11: Measurement and data processing - 11.1 Uncertainties and errors in measurement and results

Nature of science:

Making quantitative measurements with replicates to ensure reliability-precision, accuracy, systematic, and random errors must be interpreted through replication. 3.2  3.4

### Understandings

Essential idea: All measurement has a limit of precision and accuracy, and this must be taken into account when evaluating experimental results.

Qualitative data includes all non-numerical information obtained from observations not from measurement

Quantitative data are obtained from measurements, and are always associated with random errors/uncertainties, determined by the apparatus, and by human limitations such as reaction times.

Propagation of random errors in data processing shows the impact of the uncertainties on the final result.

Experimental design and procedure usually lead to systematic errors in measurement, which cause a deviation in a particular direction.

Repeat trials and measurements will reduce random errors, but not systematic errors.

### Applications and skills

Distinction between random errors and systematic errors.

Record uncertainties in all measurements as a range (±) to an appropriate precision.

Discussion of ways to reduce uncertainties in an experiment.

Propagation of uncertainties in processed data, including the use of percentage uncertainties.

Discussion of systematic errors in all experimental work, their impact on the results and how they can be reduced.

Estimation of whether a particular source of error is likely to have a major or minor effect on the final result.

Calculation of percentage error when the experimental result can be compared with a theoretical or accepted result.

Distinction between accuracy and precision in evaluating results.

### Guidance

The number of significant figures in a result is based on the figures given in the data. When adding or subtracting, the final answer should be given to the least number of decimal places. When multiplying or dividing the final answer is given to the least number of significant figures.

Note that the data value must be recorded to the same precision as the random error.

SI units should be used throughout the programme