A statistic becomes wisdom only when I understand
what disappeared while the world was being compressed into the number
Ask what the average is concealing
Statistics are tools for compression.
That is their great power.
It is also their danger.
An average summarizes many people.
A magnitude summarizes an earthquake.
A batting average summarizes hundreds of plate appearances.
A pain score compresses an entire subjective experience into one digit.
Compression is useful because reality is too complicated to carry around unedited.
But every summary throws information away.
So statistical thinking requires two complementary skills:
Know when to compress
and
Know when the variation matters more than the average