» Finding Specified Items in a List and Averaging their Associated Values

Problem:

We want to look up List1 (column A) for each of the values in column C. For each lookup, we want to calculate the average of all the numbers from List2 (column B) that correspond to matches in List1.

Solution:

Use the AVERAGE and IF functions in the following Array formula:
{=AVERAGE(IF($A$2:$A$7=C2,$B$2:$B$7))}