A student measures the diameter of a wire five times using a micrometer. The results are: 0.52 mm, 0.51 mm, 0.52 mm, 0.53 mm and 0.52 mm. Explain how the student can use these repeat measurements to obtain a more reliable value for the diameter and describe ONE source of systematic error that could affect all five readings.
Written & reviewed by James Millett — Biology (Imperial College London), PGCE Science (University of Cambridge).
Model answer (5 marks)
The student should calculate the mean of the five readings:
(0.52+0.51+0.52+0.53+0.52)/5 = 0.522 mm.
A mean reduces the influence of random error because any positive and negative deviations tend to cancel out, giving a more reliable estimate of the true diameter.
The spread of the readings (0.51–0.53 mm) shows the size of the random error or uncertainty.
A possible systematic error is a zero error of the micrometer – if the instrument is not zeroed correctly, all five readings will be offset by the same amount.
Taking more repeats will not remove this systematic error; the mean will still be wrong because every measurement is affected in the same way.
(0.52+0.51+0.52+0.53+0.52)/5 = 0.522 mm.
A mean reduces the influence of random error because any positive and negative deviations tend to cancel out, giving a more reliable estimate of the true diameter.
The spread of the readings (0.51–0.53 mm) shows the size of the random error or uncertainty.
A possible systematic error is a zero error of the micrometer – if the instrument is not zeroed correctly, all five readings will be offset by the same amount.
Taking more repeats will not remove this systematic error; the mean will still be wrong because every measurement is affected in the same way.
Examiner tips
- Show the calculation of the mean with units; explain why averaging reduces random error; state the range to indicate uncertainty; give a clear example of systematic error; note that repeats cannot correct systematic error.
Common mistakes
- Calculating the mean incorrectly or omitting units; claiming that averaging removes systematic error; not recognising the spread as an indicator of random error.
Mark scheme (5 marks)
- Calculate the mean (average) of the five repeat measurements
- The mean reduces the effect of random error (accept: gives a more reliable/accurate result because random errors can be above or below the true value)
- Identify the range of the results (0.51–0.53 mm) or state that the spread of readings indicates the size of random error / uncertainty
- A systematic error affects all readings in the same direction / by the same amount (e.g. the micrometer is not zeroed correctly / zero error)
- Taking more repeats / increasing the number of measurements does NOT remove a systematic error — the mean will still be wrong (i.e. systematic error cannot be identified or removed by averaging alone)
Key terms in this question
Related
- All AQA A-Level Physics (7408) revision notes →
- How to answer a "Explain" question →
- Decode the mark scheme abbreviations →
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