# Random error

From AMS Glossary

## random error

The inherent imprecision of a given process of measurement; the unpredictable component of repeated independent measurements on the same object under sensibly uniform conditions.

It is found experimentally that, given sufficient refinement of reading, a series of independent measurements where μ (ordinarily the true value) is a numerical constant common to all members of the series and

*x*_{1},*x*_{2}, . . .,*x*_{n}will vary one from another even when conditions are most stringently controlled. Hence, any such measurement*x*_{i}may be regarded as composed of two terms:*v*_{i}, the random error, is an unpredictable deviation from μ. The principal conclusion of classical investigations of errors of measurement (by Gauss and Laplace) was that, as a consequence of the central limit theorem, repeated measurements under controlled conditions usually follow the normal distribution, and the corresponding distribution of the random error is known as the error distribution.