3.4 Measurements and uncertainty
How to find the mean of repeat measurements, identify anomalous results, estimate uncertainty from the range, and understand resolution, accuracy and precision.
AQA
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Repeat measurements
Key terms
- Mean: the sum of the repeat results divided by the number of results.
- Anomalous result: a result that does not fit the pattern of the others.
- Range: the spread of the repeat results, from the smallest to the largest.
- Uncertainty: the amount by which a result could be different from the true value.
Every measurement has some uncertainty. Repeating a measurement and calculating a mean gives a more reliable value.
Example: five times were recorded for a reaction.
- Ignore anomalous results. 26.1 s is much bigger than the others, so leave it out.
- Calculate the mean: (24.2 + 24.6 + 24.4 + 24.8) ÷ 4 = 98.0 ÷ 4 = 24.5 s
- Find the range: 24.8 − 24.2 = 0.6 s
- Uncertainty = half the range: 0.6 ÷ 2 = 0.3 s
So the result is written as 24.5 ± 0.3 s.
Resolution, accuracy and precision
- Resolution: the smallest change a measuring instrument can show. A balance reading to 0.01 g has a higher resolution than one reading to 0.1 g.
- Accurate: close to the true value.
- Precise: repeat results are close together (a small range).
Reducing uncertainty
- Use equipment with a higher resolution, such as a burette instead of a measuring cylinder.
- Repeat measurements and calculate a mean, ignoring anomalies.
- Measure larger quantities, so the uncertainty is a smaller proportion of the reading.
| Measuring | Lower resolution | Higher resolution |
|---|---|---|
| Volume of liquid | measuring cylinder | burette or pipette |
| Mass | balance to 0.1 g | balance to 0.01 g |
| Temperature | thermometer to 1 °C | thermometer to 0.1 °C |
Test yourself on this lesson
5 exam questions · 8 marks · with mark schemes and model answers
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