, 
. From a sample 
of size N, e.g.the results of a series of N measurements, one can construct functions Si = Si
with which are called estimators of the parameters , and can be used to determine the .
An estimator is unbiased if its expectation value E(Si) is equal to the parameter in question ( ). Otherwise it has the
bias
An estimator is consistent if its bias and variance both vanish for infinite sample size
An estimator is called efficient if its variance attains the minimum variance bound ( 
Cramer-Rao Inequality), which is the smallest possible variance.
For the estimators of the parameters of
the more important distributions e.g. Binomial Distributione.g. Binomial Distribution, Normal Distribution. Uncertainties of estimators with unknown statistical properties can be studied using subsamples ( Bootstrap).
Quite independent of the type of distribution, unbiased estimators of the expectation value variance are the sample mean and the sample variance :
The practical implementation of this formula seems to necessitate two passes through the sample, one for finding the sample mean, a second one for finding 
. A one-pass formula is
where C has been introduced as a first guess of the mean,
to avoid numerical difficulties clearly given if 
. Usually, C = X1 is a sufficiently accurate guess, if C = 0 is not adequate.