Percentage Fallacy - Adding percentages

Comments

• Sami Yearly + Live Member Sage ⭐ 7Sage Tutor

  January 2018 edited January 2018 10806 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.
• BinghamtonDave Alum Member ⭐ 🍌🍌

  January 2018 8711 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%.
• westcoastbestcoast Alum Member

  January 2018 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.
• 1 Like

  BinghamtonDave Alum Member ⭐ 🍌🍌

  January 2018 8711 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.)
• westcoastbestcoast Alum Member

  January 2018 3788 karma

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