Averageif

I am currently trying to figure out if the averageif formula will work or if I need something else.

I am trying to find the average of a column based on if another column meets a reference columns needs.

Here is kind of how it looks

Name Number Original List
A 1 A
c 2 B
A 3 C
B 2 D
C 1 E
E 4 F
F 1 G
D 2 E

What I need is for each letter on the original list, is to check the name column for the letter in the original list and then average all the numbers that match the name of the letter to the one being referenced in the original list.

Ask any questions for clarifications!
Thanks

So if your list starts in A2 through C9, in D2 try:
=IFERROR(AVERAGEIFS($B$2:$B$9,$A$2:$A$9,C2),"")
and copy down