Everything is a distribution

Any phenomenon you measure is not a single value. It is a spread of possible outcomes generated by an underlying process. Treating it as a point estimate throws away most of the information.

Take your commute. You say it's twenty-eight minutes. It isn't. Your commute is a different number every day, drawn from a distribution. Twenty-eight is the average of that distribution. The average is a summary, not the thing.

Each dot is one day. The pile sits near the middle, the dashed line is the average, and off to the right are the bad days. The average hides all of this. If you only know the average, you don't know the commute.

Leave twenty-eight minutes early, the average, and you're late half the time. To be on time most days, you have to plan for a bad day, not an average one. The average was never a plan. It was a summary of a shape you chose not to look at.

Salary, response time, customer spend, feature estimate, deploy frequency. Each quoted number sits on top of a shape you aren't being shown. The shape is usually lopsided. The tail is usually where the surprises come from.

The practical rule: when someone hands you a number, ask two follow-ups. What's the spread? What's the shape? If they can answer, you have information. If they can't, you have a rumor.

One number is always a lie about something that varies. Mean plus spread is the minimum. Mean plus shape is better. The distribution itself is best.

A distribution is the trace a process leaves behind. Different processes leave different shapes. Steady independent arrivals leave Poisson shapes. Independent multiplicative factors leave lognormal shapes. Feedback loops leave power-law shapes. If you learn to read the shapes, you can read the processes underneath, which is usually what you actually wanted to know.