Data Summary

I'm not sure how to average certain data in a column
while ignoring 'blank' lines? I tried the command
SUMIF($B$1:$B$5,"a",C$1:C$5)/COUNTIF($B$1:$B$5,"a").

The SUMIF gives me 9 which is OK, but the COUNTIF
gives me 3 which is not OK!

COL B COL C
1 a 5
2 b 4
3 a
4 a 4
5 d 6

I only want to average non-blank numbers relating to
'a' values. Example: I want above average to give
me (5+4)/2=4.5 and not (5+4)/3=3!!!

Can anyone help?