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Random error
Intermediate
Unpredictable scatter that averages out with repeated readings.
Random errors vary unpredictably from reading to reading, due to reaction time, tiny fluctuations or reading estimates. They scatter above and below the true value, so averaging n readings reduces the uncertainty of the mean by about √n.
Ten timings of a swing might read 2.1, 2.3, 2.2, 2.0, 2.2 s. The mean 2.16 s is more reliable than any single value.
Averaging does not help if you keep making the same mistake, since that is systematic.
In more detail
Random errors vary unpredictably from one reading to the next, due to noise, reaction time or fluctuations. They can be reduced by taking more readings and averaging them.
Real-world uses
- Repeated timing of a falling object is averaged to reduce reaction-time scatter.
- Sensor noise in electronics is reduced by averaging many samples.
- When timing a falling object by hand, human reaction time varies from trial to trial, producing random scatter around the average.
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Frequently asked questions
Do random errors always average to zero?
Not exactly, but for many independent random errors the average tends towards the true value as the number of readings grows.
How many readings should I take?
Enough that the spread of the mean becomes small compared with the precision you need. Typically at least five to ten.
How many repeats make a random error small?
The uncertainty of the mean falls as one over the square root of the number of readings, so four readings halve it compared with one.
Related topics in Measurement & Math Tools
Rounding rules · Accuracy vs precision · Systematic error · Absolute error · Relative and percent error · Error in a sum or difference