Question

Let S be an array with n distinct integers. Similar to the selection algorithm, we partition S into n / 11 sub-arrays, each of which contains 11 numbers. Let x be the median of the medians of the LaTeX: n/11n / 11 sub-arrays. How many numbers in LaTeX: SS are guaranteed to be less than LaTeX: xx?

Answer 1

The answer is "
`\bold{(3n)/(11)}`"

Step-by-step explanation:

The value x was its
`(n)/(11)` average array median. Almost every other median is less than 6 elements, because the total of 11 components is all mediums of its arrays i.e.
`(n)/(22)` it's less than half x. Its at least x is also less than:

`\to 6 * (n)/(22) \\\\ \to (3n)/(11)`