Order-statistic confidence interval for a median
= Order-statistic confidence interval for a median
{title2=$(X_{(j)},X_{(n-j+1)}]$}
For a sample of size $n$ from a <continuous probability distribution>, this interval covers the <median> $F^{-1}(1/2)$ with probability $1-2\sum_{r=0}^{j-1}\binom nr2^{-n}$, for $1\leq j<n/2$. Count observations below the <median>: their number has the <binomial distribution> with parameters $n,1/2$. No strict increase of the <distribution function> is needed.