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# Percentage Fallacy - Adding percentages

Alum Member
3788 karma

When is it valid to add percentages of two different sets. I know that sometimes the two sets could be overlapping and their percentages can't be added together, but are there times when you could validly add them? For example, if we said 30% of dogs are brown and 40% of cats are brown, could we say that 70% of cats and dogs are brown?

• Alum Member Sage 7Sage Tutor
edited January 2018 10710 karma

Lets say there are a 100 dogs and 1000 cats.
If 30% of dogs are brown, then we can infer that 30 dogs are brown.
If we know 40% of cats are brown, then we can inter 400 cats are brown.

If we add the number of dogs and cats we get 1100. If we combine the number of dogs and cats that are brown we get 430. So what percent is 430 out of 1100?

That's about 39% and not 70%.

The problem with combining two sets is the percentage is dependent on the total size of the pie. 30% of 100 is vastly different from 30% of 1000. That's why you do not want to combine percentages of two different groups. The percent is only relevant to that particular set. Outside of that we need to know more information to conclude anything.

I hope this helped.

• Alum Member 🍌🍌
8673 karma

Excellent question.
If we have a group of 100 cats and 40% of them are gray=40 cats
and we have a group of 100 dogs and 30% of them are gray=30 dogs
then we have a group of 200 cats and dogs in which 70 are gray. That is not now 70%. That is 35%.

• Alum Member
edited January 2018 3788 karma

Thank you all! I was in work and I was running this through this problem and originally couldnt figure it out. It seems I need to consider the relative size of the pie for each set.

• Alum Member 🍌🍌
8673 karma

Consider looking at PT 48-1-24 when you get a chance. This argument is doing something similar to what you describe above (although not precisely the same.)

• Alum Member
3788 karma

@BinghamtonDave thanks! I will. It seems you have great memory