Backwards Percentages – The Idea
Consider the following situation:
- 33% of all people are Democrats (the rest are Independents or Republicans)
- 78% of Democrats disapprove of Trump’s handling healthcare (the rest either approve or have no opinion)
- 33% of non-Democrats disapprove of Trump’s handling of healthcare.
(These bullet points are in the order of logic applied in the video below.)
Consider the following question and its relationship to the second bullet point:
What percentage of those who disapprove of Trump’s handling of healthcare are Democrats?
This question is asking for the backwards percentage of the percentage given in the second bullet point. Here is the abstract form of a pair of backwards percentages:
The percent of A that are B
The percent of B that are A
Backwards Percentages – A Beginner Calculation
The easiest way to calculate the situation described above is to describe the situation in terms of a population of 10,000 people and fill in the table as demonstrated in the video below. (Please make sure the sound is on as the explanation is spoken word.)
As demonstrated in the video, the following two percentages are a pair of backwards percentages – given the entire situation as described.
The percentage of Democrats who disapprove is 78%
The percentage of disapprovers who are democrats is 54%
We also see that the calculation of one from the other is holistic; that is, it depends upon the whole situation.
In future posts, we will look into this more and more. Eventually, we will understand how to compute the following pairs of backwards percentages.