I recently came across the book: “A Mathematician Reads the Newspaper”

It’s a paperback from 1997 by John Allen Paulos, a professor of mathematics at Temple University.

It shines a light on how statistics, probability, and logic are often misused or misunderstood in media reporting.

In it, it references the “potato paradox”. The potato paradox is a mathematical calculation that has a result which seems counterintuitive to many people.

The scenario goes like this:

You buy 100 kg of potatoes and are told that they are 99% water. After leaving them outside, you discover that they are now 98% water. What is the weight of the dehydrated potatoes?

If a 100kg potatoes sack is 99% water, the dry mass is 1%. This means that the 100 kg of potatoes contains 1 kg of dry mass. Regardless of the water content this mass does not change.

Leaving the sack outside, the water content goes from 99% to 98%.

In order to make the potatoes 98% water, the dry mass must become 2% of the total weight, double what it was before. The amount of dry mass, 1 kg, remains unchanged, so this can only be achieved by reducing the total mass of the potatoes sack. Since the proportion that is dry mass must be doubled, the total mass of the potatoes sack must be halved, answering 50 kg

The apparent paradox lies in showing the change in percentage of the water which is relatively small, but this hides the large change in the quantity of solid part.

According to Quine’s classification of paradoxes, this is a veridical paradox.

The potato paradox was a “Puzzler” on the Car Talk radio show in 2017.

Statistics can, and sometimes are, misleading. As someone recently proposed: Statistics are a means to change people’s mind. Indeed, they are often used to provide proof for a point of view, rather than be just one of the ingredients from which an opinion is baked.