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Lesson 3.7 · AQA Combined Science

Measurements, means and uncertainty

Measurements have uncertainty

A measurement is not perfectly exact. The resolution of an instrument is the smallest change it can display or distinguish. Repeated measurements help reveal the spread of the readings, but repeating does not automatically remove a systematic error.

Find the mean and range

Example readings: 4.8 g, 5.0 g and 5.2 g.
Mean = (4.8 + 5.0 + 5.2) ÷ 3 = 5.0 g.
Range = highest − lowest = 5.2 − 4.8 = 0.4 g.

Estimate uncertainty from the spread

One common school estimate uses half the range: 0.4 ÷ 2 = 0.2 g. Report this example as 5.0 ± 0.2 g. This is an estimate based on repeated readings, not a guarantee of the true value. Follow the method stated in the question.

Spot precision and possible problems

A smaller spread means readings are more precise. Accuracy means closeness to the true value. Readings can be close together but all wrong because of a zero error.
An anomaly is a reading that does not fit the pattern. Investigate or repeat it; do not remove a result just because you dislike it.

Compare two sets fairly

SetReadings / gRange / g
A9.8, 10.0, 10.20.4
B9.9, 10.0, 10.10.2

Both means are 10.0 g. Set B has a smaller spread, so it is more precise. This alone does not prove it is more accurate.

Remember

Mean = total ÷ number. Range = highest − lowest. Repeats show spread; they do not automatically remove systematic errors.