As you will see below, due to correlations between various measurements, we need to evaluate the so-called covariance in order to establish a proper evaluation of the total variance and the thereby the standard deviation of a given expectation value.
The covariance however, leads to an evaluation of a double sum over the various stochastic variables. This becomes computationally too expensive to evaluate. Methods like the Bootstrap, the Jackknife and/or Blocking allow us to circumvent this problem.