A crazy deterministic, linear-time algorithm for approximately finding this value was authored by the powerhouse team of Blum, Floyd, Pratt, Rivest, and Tarjan.
Cormen's Introduction to Algorithms introduces the so-called "post-office location problem", i.e. the problem of efficiently locating a post office, to which a weighted example of this value is the solution. A crazy deterministic, linear-time algorithm for approximately finding this value was authored by the powerhouse team of Blum, Floyd, Pratt, Rivest, and Tarjan. That algorithm begins by splitting an n length array into n over five groups of five elements, finding this value for each group, then finding this order statistic of the values. Randomly selecting three entries from an array, then selecting this value from them, is a decent way to choose a pivot for quicksort and is called the this-value-of-three partition. For an array of length odd n, a naïve algorithm to find this value is simply sorting the array, then selecting the value at n plus one all over two. For 10 points, name this value that separates the upper and lower halves of an array or data set.
Cormen's Introduction to Algorithms introduces the so-called "post-office location problem", i.e. the problem of efficiently locating a post office, to which a weighted example of this value is the solution.
median [or middle]