randomerror

Random error, often written as randomerror in informal text or in code, design documents, and data logs, refers to the unpredictable component of measurement error that arises from inherently variable processes and limits of instruments.

Unlike systematic error, which biases measurements in a consistent direction, random error fluctuates around the true value without a fixed pattern. With many independent sources, it is commonly modeled as a random variable with zero mean and finite variance, frequently approximated by a normal distribution under general measurement conditions. The extent of random error is described by a standard deviation (sigma); the precision of a measurement improves as more observations are combined. The standard error of the mean is σ divided by the square root of the number of measurements.

Common sources include electronic noise, environmental fluctuations (temperature, humidity), timing inaccuracies, detector sensitivity, and intrinsic variability of the measured quantity. In practice, random error determines the limit of precision; although it can be reduced by improving instruments or procedures, it cannot be completely eliminated. Reducing its impact often involves repeating measurements, averaging results, proper calibration, and robust statistical analysis.

Researchers and practitioners distinguish random error from systematic error, which arises from bias in measurement methods or equipment.