This is Bad Math

Blog Posts
August 4, 2019

Every so often, we stumble upon a realization that we’ve discovered something larger than ourselves. In this instance, what seemed to be a simple question about fruit preference grew into a far greater question about statistics than I ever thought I’d give mind to. I barely remember my statistics class from college, though I did take one at some point.

A google search of 'are blueberries berries'
Are blueberries berries? I didn’t learn the answer, but apparently bananas are berries

The Statement

The average blueberry is better than the average raspberry, but the best raspberry is better than the best blueberry.


I spent a while trying to figure out if this is already something that’s defined by some mathematical relation: given a set A and a set B, what is the law where max(A) > max(B) but mean(B) > mean(A)?

Example: the set { 4, 1, 0} and { 2, 2, 2} adhere to this principle. Imagine that set A is of the rating of 3 raspberries, while set B is the rating of 3 blueberries.

The Two Big Questions

1. Is there a math term for what those two sets are? I want to call them something fun, where, like, a ‘Raspberry Set’ is one where this holds true. I’m guessing this exists but it has a name like “The average relativity principle” or it’s named after a dead guy.

2. What other things does this hold true for? Some ideas:

The average Instagram post is higher quality than the average Twitter post, but the best Twitter post is better than the best Instagram post.

The average summer day is better than the average winter day, but the best winter day is better than the best summer day.

How to use this Math
Get your group of friends to find a statement in this form that they agree on. It doesn’t count if you aren’t on the same page!

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