# Homework Help: How to combine percentages (Solely Simple Math Problem)

1. Aug 26, 2013

### Fisher92

1. The problem statement, all variables and given/known data

The problem was actually for a COMMS assignment that I have finished with the exception of the very last easiest part.

They wanted percentage of power spilled into gaurd bands - have calculated all the powers now need the percentage....

I have two frequency components modulating the carrier and I have calculated power components. I end up with the following:

f(Hz), P(W) - Channel 1
5, 1
10,5
15,2
20,3
25,4

f(Hz), P(W) - Channel 2
5, 1
15,5
20,2
25,3
30,4

Anything above 20kHz is spilled power and I want to know the percentage of spilled power (no thats no my actual results)

The problem is that if I work out the percentages for channel 1 and 2 separately (& then sum) I end up with a higher percentage than if I just summed everything... What is the correct way to do this.

******Example may be easier to follow then my explanation*****

Channel 1:
Total power = 1+5+2+3+4W=15W
Spilled Power (>20kHz)= 4W
Percentage = 4/15*100=26.67%

Channel 2:
Total power = 1+5+2+3+4W=15W
Spilled Power (>20kHz)= 3+4=7W
Percentage = 4/15*100=46.667%

CH1 + ch2 = 46.667+26.67=72% SPILLED

Combined
Total Power = 1+5+2+3+4+1+5+2+3+4=30W
Spilled Power (>20kHz)= 4+3+4=11W
Percentage = 11/30*100=37% SPILLED

Why is there a discrepancy? I get mathematically why this is giving me two different results but which 1 would be the power spilled?

2. Aug 27, 2013

### voko

Let's say you have 10 bucks and you lose all of it. Your loss is 100%.

I also have 10 bucks but I am lucky and I keep my stash. My loss is 0%.

Using your method #1, our total loss is 100% + 0% = 100%. Does this seem correct to you? (Note also that if my loss were anything > 0%, our total loss would be > 100%)

Using your method #2, our total loss is (10 + 0)/(10 + 10) = 50%. Does this seem correct to you?

3. Aug 27, 2013

### Fisher92

Thanks, I came to the same conclusion.