A student measures the extension of a spring when a 500 g mass is hung from it. She takes five measurements using a ruler and records the following extensions: 42 mm, 43 mm, 42 mm, 58 mm, 43 mm. Describe how the student should process these results to obtain a reliable value for the extension, and explain why one of the readings should be treated differently from the others.

AQA A-Level Physics (7408) — 3.1.2 Limitations of Physical Measurements · Describe · 5 marks · View as Markdown

Written & reviewed by James Millett — Biology (Imperial College London), PGCE Science (University of Cambridge).

Model answer (5 marks)

1. Identify 58 mm as an outlier.
2. Exclude the 58 mm reading from further analysis.
3. Calculate the mean of the remaining four values: (42+43+42+43)/4 = 42.5 mm.
4. State that using the mean reduces the influence of random errors and gives a more reliable estimate.
5. Explain that the 58 mm result is likely due to a random error such as a mis‑reading of the ruler or the mass swinging during measurement.

Examiner tips

  • Use the word ‘outlier’ to show you recognise the anomalous value. Show the calculation of the mean and include units. Link the mean to ‘reliability’ and ‘random error’ as the scheme expects.
  • Mention that the excluded reading is probably caused by a random error like a mis‑reading or a swing of the mass.

Common mistakes

  • Including the 58 mm value in the mean. Failing to show the calculation of the mean. Not explaining why the 58 mm reading is anomalous.

Mark scheme (5 marks)

  1. Identifies 58 mm as an anomalous result / outlier
  2. States that the anomalous result should be excluded / not included in the mean calculation
  3. States that the mean (average) of the remaining values should be calculated
  4. Links calculating the mean to improving reliability / reducing the effect of random error
  5. Explains that the anomalous result is likely caused by a random error (e.g. misreading the ruler / the mass swinging)

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