A student measures the time for a pendulum to complete one full swing. She repeats the measurement five times and gets the following results: 1.4 s, 1.5 s, 1.4 s, 1.9 s, 1.4 s. Describe how the student should identify and deal with any anomalous result, and explain how repeating measurements improves the reliability of the final value.
Written & reviewed by James Millett — Biology (Imperial College London), PGCE Science (University of Cambridge).
A student measures the time for a pendulum to complete one full swing. She repeats the measurement five times and gets the following results: 1.4 s, 1.5 s, 1.4 s, 1.9 s, 1.4 s.
Model answer (5 marks)
1. The value 1.9 s is clearly an outlier compared with the other four results.
2. The student should remove the 1.9 s measurement from the data set.
3. The mean of the remaining four values (1.4, 1.5, 1.4, 1.4 s) is calculated: (1.4+1.5+1.4+1.4)/4 = 1.425 s.
4. Repeating the measurement reduces the influence of random error, because random errors are unlikely to repeat in the same direction.
5. Taking the mean of many repeated measurements gives a value that is more reliable and closer to the true value, as the random errors cancel out.
2. The student should remove the 1.9 s measurement from the data set.
3. The mean of the remaining four values (1.4, 1.5, 1.4, 1.4 s) is calculated: (1.4+1.5+1.4+1.4)/4 = 1.425 s.
4. Repeating the measurement reduces the influence of random error, because random errors are unlikely to repeat in the same direction.
5. Taking the mean of many repeated measurements gives a value that is more reliable and closer to the true value, as the random errors cancel out.
Examiner tips
- Use the word ‘outlier’ or ‘anomalous’ to identify 1.9 s. State explicitly that it is excluded before calculating the mean. Show the arithmetic for the mean. Explain that random error is reduced by repetition. Mention that the mean is a more accurate estimate of the true value.
Common mistakes
- Including the 1.9 s in the mean. Failing to calculate the mean after exclusion. Not explaining why repetition improves reliability. Using the median instead of the mean without justification.
Mark scheme (5 marks)
- Identifies 1.9 s as the anomalous result / outlier
- States that the anomalous result should be excluded / not included when calculating the mean
- States that the mean (average) of the remaining results should be calculated
- Explains that repeating measurements reduces the effect of random error
- Explains that calculating a mean from repeated results gives a more reliable / accurate value
Key terms in this question
anomalous result · reliability
Related
- All AQA A-Level Physics (7408) revision notes →
- How to answer a "Describe" question →
- Decode the mark scheme abbreviations →
More Limitations of Physical Measurements questions
- A student measures the resistance of a resistor five times using an ohmmeter. Hi…
- A student measures the acceleration of a toy car rolling down a ramp. She times …
- A student measures the focal length of a converging lens by finding the distance…
- A student measures the mass of a metal block five times using a digital balance.…
- A student measures the density of a liquid by recording its volume and mass. He …
- A student measures the voltage across a battery using a voltmeter. He takes five…