PL/SQL :: Average In Tree With Partial Results

Oracle Database 11g Enterprise Edition Release 11.2.0.1.0 - 64bit Production
PL/SQL Release 11.2.0.1.0 - Production
"CORE     11.2.0.1.0     Production"
TNS for HPUX: Version 11.2.0.1.0 - Production
NLSRTL Version 11.2.0.1.0 - Production

I have a problem related with hierarchical queries, I have this tree.
-    a
    /
   b   c
/ |
d  e  fI need to calculate an average per node but using always the child's results for example: Only leafs will have values:

d = 10
e = 20
f = 30
c = 40So the expected result is:
d = 10
e = 20
f = 30
c = 40
b = (10(d) + 20(e) + 30(f)) / 3 (number of child nodes) = 20
a = (20(b) + 40(c)) / 2 (number of child nodes) = 30.

I have tried with recursive queries, hierarchical queries, I guess it's possible with model too but I can't produce the exact results that I need. Maybe in fact there is a very simple solution but I cannot figure it.

Here is an auxiliary WITH that you can use to start your tests:
WITH tree AS
(
     SELECT 'd' child, 'b' parent FROM dual UNION ALL
     SELECT 'e' child, 'b' parent FROM dual UNION ALL
     SELECT 'f' child, 'b' parent FROM dual UNION ALL
     SELECT 'b' child, 'a' parent FROM dual UNION ALL
     SELECT 'c' child, 'a' parent FROM dual UNION ALL
     SELECT 'a' child, null parent FROM dual
[code]....