To quickly get the median value of any given sequence is very important in many research fields. Some popular sort algorithms are discussed in this paper. Selection sort algorithm and bubble sort algorithm are redesigned as incomplete sort algorithms to quickly give the median value of randomly given sequence. In the new algorithms, only parts of the items in sequence need to be sorted to give the median value, then many data comparison and movement operation are reduced, and the speed of getting median value can be improved greatly. Besides, insertion sort algorithm and merge sort algorithm are analyzed thoroughly and found not suitable to be redesigned as incomplete sort algorithms for this purpose. At last, lots of experiments are done to compare the performance of incomplete selection sort algorithm and incomplete bubble sort algorithm. Experiment results and algorithm analysis show that incomplete selection sort algorithm perform very well in case of both short sequence and long sequence.