» Retrieving the Most Frequent Occurrence for Each Category

Problem:
Each number in column B is designated to one of the categories A, B, or C. In different instances, the same number can be ascribed to any of the three categories.
Column A shows the category for each of the numbers in column B.
We want to find the number that occurs most frequently for each category.

Solution:

Use the MODE and IF functions as shown in the following Array formula:
{=MODE(IF($A$2:$A$12=D2,$B$2:$B$12))}