Repeating a measurement several times reduces the effect of random errors and helps you spot anomalous readings.Step 1: look for anomalies. A reading that is clearly far from the others is anomalous. It should be excluded before calculating the mean (and, if possible, repeated).Step 2: find the mean. Add the remaining readings and divide by the number of readings. Quote the mean to the same resolution as the readings.Step 3: find the uncertainty. The absolute uncertainty in the mean is taken as half the range:uncertainty = (largest value − smallest value) ÷ 2 Worked example: The time for a ball to fall is measured five times: 0.61 s, 0.65 s, 0.62 s, 0.64 s and 0.80 s.
• 0.80 s is anomalous, so it is excluded.
• Mean = (0.61 + 0.65 + 0.62 + 0.64) ÷ 4 = 2.52 ÷ 4 = 0.63 s.
• Range = 0.65 − 0.61 = 0.04 s, so the uncertainty = 0.04 ÷ 2 = 0.02 s.
• Percentage uncertainty = 0.02 ÷ 0.63 × 100% = 3.2%.
Result: t = 0.63 ± 0.02 s.If all the repeated readings are identical, the range is zero; the uncertainty is then not zero but equals the uncertainty of a single reading (for example, the resolution of the instrument).Repeating does not reduce systematic errors: if every reading has the same zero error, the mean has it too.
• 0.80 s is anomalous, so it is excluded.
• Mean = (0.61 + 0.65 + 0.62 + 0.64) ÷ 4 = 2.52 ÷ 4 = 0.63 s.
• Range = 0.65 − 0.61 = 0.04 s, so the uncertainty = 0.04 ÷ 2 = 0.02 s.
• Percentage uncertainty = 0.02 ÷ 0.63 × 100% = 3.2%.
Result: t = 0.63 ± 0.02 s.If all the repeated readings are identical, the range is zero; the uncertainty is then not zero but equals the uncertainty of a single reading (for example, the resolution of the instrument).Repeating does not reduce systematic errors: if every reading has the same zero error, the mean has it too.