The Average Hides the Shape
Is the average person in your data anywhere near average?
The idea
A mean describes the centre and says nothing about how the values are spread or whether the centre is typical.
In the real world
A mean salary pulled far above what almost everyone earns by a few very high ones.
Going deeper
A mean is one number standing in for an entire distribution, and it discards everything about spread and shape. Where the data has a long tail, the mean sits somewhere almost nobody occupies.
A 400ms average response time with constant complaints is the standard case: most requests are fast, a tail is very slow, and the tail is what people experience and remember. The mean compresses that tail into the centre and makes it disappear. Reporting a percentile alongside — the 95th, say — exposes the experience the average was concealing, at no extra cost.
Where it stops applying
Means are the right summary for roughly symmetric data and are what most statistical methods assume. The problem is defaulting to one without looking at the shape.
Why it matters
It stops a single number standing in for a distribution you have never looked at.
Try this today
For one average you rely on, find the median and the range as well.
Test yourself
A team reports a mean response time of 400ms and users complain constantly. How can both be true?
Show the answer
Most requests are fast and a tail is very slow, and the tail is what people notice and remember. A mean compresses the tail into the centre; the 95th percentile would show the experience the average is concealing.
Learn this in the feed Answering from memory, then again days later, is what makes it stick.