A diff in weighted average calculation?

[A.lau]

Hi guys,

Need some help here, I always assume:

weighted average of x & y multiply by the volume is equivalent to individual vol multiply by the respective x & y. But apparently this is not the case. Example as below:

700kg of palm kernel from origin A with a yield loss of 1.22 (or equivalent to 1/1.22)after processing
300kg of palm kernel from origin B with a yield loss of 1.27 (or equivalent to 1/1.27)after processing


Both origin will be mix together at 70% origin A to 30% origin B to produce crude palm oil.What is the expected crude palm oil output?

If I sum vol/yield individually for each origin A & B:
700/1.22 + 300/1.27 = 809.991

But if I take the weighted average of yield and take total vol./weighted average yield, I'll get:
Weighted average yield: (700*1.22 + 300*1.27)/1000 = 1.235
So, 1000/1.235 = 809.7166

There's a diff of 0.27436, which will be the correct answer?

Thanks!!
Adrian

 

[tkhunny]

Initial reaction: The weighted average makes no sense. Why would one yield loss have anything to do with the other substance? Is there a known interaction between the two yield losses? I'm thinking, like water and alcohol. The total isn't always the sum of the parts due to molecular interaction.

Haven't really thought that through, though.

 

[A.lau]

Sometimes producers will mix fruits (palm in this case) from different origin to produce a unique taste profile or a cheaper product. Using coffee as an example, a different composition of Arabica and Robusta bean will create different taste profile and of course cheaper than Arabica bean alone.

So if these beans have different yield loss and will be mixed together during production, how can we accurately calculate its output?

For me it make sense to use the weighted average of the yield as the fruits will be mixed together at a 70:30 ratio before production. However I'm equally puzzled why does the individual sum differ from the weighted average sum.

Thanks !