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Repeat readings: mean, half range and anomalies

Edexcel IAL Physics · WPH13 Practical Skills in Physics I

When readings are repeated, the spread of the values gives a better uncertainty than the resolution alone. These are some of the most reliable marks on the paper.

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The mean

Add the repeats and divide by how many there are. Give the mean to the same number of decimal places as the raw data, with a unit. Examiners penalise both extra digits and missing units. Watch the quantity: if each repeat is the time for 5 oscillations, the period is the mean divided by 5.

Uncertainty from repeats

The uncertainty in the mean is the half range:

uncertainty = (largest - smallest) / 2

The value furthest from the mean (its difference from the mean) is also accepted. The full range is not. Then:

percentage uncertainty = half range / mean x 100%, to 1 or 2 s.f.

If all the repeats are identical, use half the resolution instead.

Anomalous readings

An anomalous reading is one that does not fit the pattern of the others, often because of a mistake. During the experiment, the right response is to repeat that reading. When processing data, discount a value only if it is clearly far outside the others, name it, and say why; if in doubt, keep it. Never remove data just because it is inconvenient.

Worked example

Diameters of a wire, in mm: 0.46, 0.47, 0.45, 0.47, 0.46. Find the mean, the uncertainty and the percentage uncertainty.

  1. Mean = 2.31 / 5 = 0.462, given to 2 d.p. as 0.46 mm
  2. Half range = (0.47 - 0.45) / 2 = 0.010 mm
  3. Percentage uncertainty = 0.010 / 0.46 x 100 = 2.2%

Answer: d = 0.46 mm ± 2.2%

Key idea: Mean to the same decimal places as the data. Uncertainty = half the range (or furthest value from the mean). Percentage = half range / mean x 100. Repeat anomalous readings; discount only clear anomalies, and say so.

Check yourself

  1. Four times, in s: 2.31, 2.35, 2.28, 2.33. Calculate the mean time, to 2 d.p.
    Show answer

    2.32 s. Sum = 9.27; mean = 9.27 / 4 = 2.3175, so 2.32 s.

  2. For the times 2.31, 2.35, 2.28, 2.33 s, find the uncertainty using the half range, in s.
    Show answer

    0.035 s. (2.35 - 2.28) / 2 = 0.035 s.

  3. Using a mean of 2.32 s and a half range of 0.035 s, find the percentage uncertainty, to 2 s.f.
    Show answer

    1.5 %. 0.035 / 2.32 x 100 = 1.5%.

  4. Repeat readings of a fringe spacing, in mm: 82.1, 81.8, 84.4, 82.3. Which value is anomalous?
    • 82.1
    • 84.4
    • 81.8
    • 82.3
    Show answer

    84.4. 84.4 is about 2 mm above the others, which agree within 0.5 mm.

  5. Calculate the mean of 82.1, 81.8, 84.4, 82.3 mm after discounting the anomalous value, to 1 d.p.
    Show answer

    82.1 mm. (82.1 + 81.8 + 82.3) / 3 = 82.067, so 82.1 mm.

  6. During an experiment, a reading looks anomalous. What should the student do?
    • Delete it and carry on
    • Repeat that reading
    • Change the independent variable
    • Average it in without comment
    Show answer

    Repeat that reading. Repeating checks whether it was a mistake.

  7. A student records the time for 5 oscillations three times: 8.45 s, 8.52 s and 8.40 s. What is the mean period, in s, to 3 s.f.?
    Show answer

    1.69 s. Mean of 5T = 8.457 s; T = 8.457 / 5 = 1.6913 s.

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Last updated 8 November 2026. Spotted a mistake? Tell us.