What's in a percentage?

 

The question of the day is:
What is X in X - 68% = 1%?
.. And how is this linked to presidential elections?

I came across this "puzzle" on the side of a milk carton that stated that the 1% fat containing milk has 68% less fat than whole milk. And it reminded me of the numerous times I've tried to help people understand percentage.

One reason this struck me was that I was nearly fooled for a fraction of a second. Reading the text one could think that whole milk has 69% of fat in it - which is obviously not the right answer. Whole milk has about 3% of fat and taking out 68%, about two thirds that is, leaves 1%.

The reason people get confused with percentages is that they are thinking adding and subtracting. And in percentages it's about dividing and multiplying (and some adding or subtracting). That is, unless you'd say: 1% reduced fat milk has two percentage points less fat than full milk.

And to wrap up this uninteresting windy blabber about percentages I wanna link this to the presidential elections - the reason I was probably open to think about this in the first place.

The thing is that people don't think about the difference between percentages and percentage points when they think about election results, which makes them misunderstand the vote differences between candidates.

See, for example in the Obama-McCain race Obama got some 52.5% of all votes and McCain got got 46.2% (reports Pollster.com my favorite poll site). And while the difference between the two was 6.3 percentage points Obama got 13.2% more votes than McCain [(52.5-46.2)/46.2]*100%.