Errors, quadratic addition
From HandWiki
Let a measurement of the physical quantity yield the random variable X, and the deviation of X from
be due to N independent (uncorrelated) errors. Hypothetical measurements with only one of these errors present would yield the deviations
. If all these differences can be described by distributions with zero means and variances
then the difference
follows a distribution of zero mean and variance
( Convolution). Expressed in errors rather than variances, one has the rule of quadratic addition of errors:
which can also be written
For errors of normal distribution, the total error
will also have a normal distribution. For large N, the total error will have normal distribution for any distribution of the
( central limit theorem).