More on confidence intervals for the median of a single sample
The empirical cumulative distribution function (ecdf) and a confidence interval for the ecdf at a single point
The ecdf (x) = = the proportion of observations <= x . Since the number of observations less than x is a binomial random variable with parameter p = F(x), we can calculate the standard deviation of ecdf(x) and develop a confidence interval for F evaluated at x, using either the binomial distribution or (in large samples) a normal approximation to the binomial distribution.
Confidence intervals for percentiles of a single sample