Findind The n/lgn intermidiate values in an unsorted array with asymptotic run time of $\Theta(n)$ SELECT algorithm
You can find a $k$-th order statistic of an array using a selection algorithm in $\Theta(n)$ time. It means that you can also find the $k$ least (and the $k$ greatest) elements of an array in $\Theta(n)$ time by first finding the $k$-th ordering statistic and then comparing it with each element of an array.
So in your case we can find $n / 2$ (median) and $n/2 + n / \log(n)$ order statistics and then find all suitable elements by scanning an array and comparing its elements with both statistics.