  The goal of this paper is to apply statistical methods to determine electrons
densities and their errors from measurements of density-sensitive line
intensities in the quiet Sun. Three methods are employed. The first is the use
of L-function plots to provide a quick visual assessment of the likelihood that
a set of line intensities can provide a robust estimate of these quantities. A
second methods involves a chi-squared minimization together with a prescription
for determining the regions of statistical confidence in addition to the
best-fitting value. A third method uses a Bayesian inference technique that
employs a Monte-Carlo Markov-chain (MCMC) calculation from which an analysis of
the posterior distributions provide estimates of the mean and regions of high
probability density. Using these three methods, observations of
extreme-ultraviolet spectral lines originating from regions of the quiet Sun
have been analyzed. The quantitative chi-squared minimization and MCMC sampling
provide results that are generally in good agreement, especially for sets of
lines of ions that have L-function plots that suggest that a robust analysis
might be possible.
