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How to combine percentages (Solely Simple Math Problem)

  1. Aug 26, 2013 #1
    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. jcsd
  3. Aug 27, 2013 #2
    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?
     
  4. Aug 27, 2013 #3
    Thanks, I came to the same conclusion.
     
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