The percent change is often a much more informative value than the absolute change. Also, when something decreases by x% it requires more than an x% increase to get back where you started. Political discourse would greatly benefit from these two simple facts.

On the other hand, I came here to suggest that knowledge of Simpson's Paradox (https://en.wikipedia.org/wiki/Simpson's_paradox) could resolve a lot of political fights. And Simpson's paradox is only applicable when data is presented as percentages, so the key to unraveling the paradox is to show the absolute numbers and changes, instead of the percentages.

The real problem is that percentages hide the size of the groups, and even if you show the sizes of the groups separately, focusing on the percentages still obscures the reality unless this is called out explicitly.

Medians.

Average is last and first statistical measure that most people learn and it really isn't that useful. If we could just switch to medians and ban the average I would be really happy (and so would the world).

Median, mean, and mode are all types of averages. But yes, I was just reading Nassim Taleb today scolding the multitude for not recognizing the difference between median and mean.

Wrongful convictions: https://en.wikipedia.org/wiki/Prosecutor's_fallacy

Don't understand what your STD test really means: https://en.wikipedia.org/wiki/False_positive_paradox

Correlation/causation conflation.

Both are basically people not understanding Bayes' law. Or, equivalently, the difference between (posterior) probability and likelihood.

Backpressure. (Includes modeling something as producer/consumer in order to reason about it)

It boils down to learning how to say no, but in practice it smoothes out demand spikes and makes life much more predictable.

It can be applied to personal fines (only consume "wants" as fast as you can produce "surplus"), consulting (only consume "new clients" as fast as you produce "working fine") to maintain a decent work life balance, as well as many other areas.

Order of operations. Pains me how so much of the population can't do simple maths.

These two are not equivalent. A few missing parentheses isn't what causes people to be unable to do simple maths.

The scientific method itself.

The thought relates to going back and refining your original theory such that:

1. You create a hypothesis

2. Prove your theory

3. Publish your theory (and maybe discovery)

Most of the time it ends here. It should continue this way:

4. Practically apply your theory

5. Create a product or widget founded on your theory

6. Put this product into the hands of consumers

7. Make observations and watch how customers/consumers use it in ways you could never predict

8. Use this data to go back and refine your original theory and start the cycle over again.

Gravity (how it works with matter).