Some problems having array of numbers as input

Average
Input: array A of n numbers
Output: the average of the n numbers (sum divided by n)

Max
Input: array A of n numbers
Result: A is permuted so that A₁ ≤ A_i, for all i.

Min
Input: array A of n numbers
Result: A is permuted so that A_n ≥ A_i, for all i.

MaxMin
Input: array A of n numbers
Result: A is permuted so that A₁ ≤ A_i ≤ A_n, for all i.

Sort
Input: array A of n numbers
Result: A is permuted so that A_i ≤ A_i+1, for i = 1,2,...,n-1.

Median
Input: array A of n numbers
Output: element x of A such that, if A were sorted, x = A_⌈n/2⌉.

Select
Input: array A of n numbers and number k in 1..n
Output: element x of A such that, if A were sorted, x = A_k.

Equal Partition (subset sums to half)
Input: array A of n numbers
Output: true if and only if there is a subset of the entries whose sum is (1/2)Σⁿ_i=1 A_i.

Largest Increasing Sequence
Input: array A of n numbers
Output: length of a largest increasing subsequence of A (not necessarily adjacent).
Example: For A = (3,1,4,1,5,9,2,6,5,3,5), output is 4.

Which is hardest? Which is easiest? How should we measure hard and easy? How do we analyze and quantify correctness and performance of a solution (an algorithm)? Can we prove a solution is best possible?