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A pencil balanced a ruler at one exact mark. Why?

This is Part II, Chapter 5, Tales by Dots and Lines.

What you will learn

• The balance point — the mean is the one spot where numbers balance.
• Above and below — the two sides of that spot always match.
• Moving one — change one number, and the mean moves too.
• Adding one — a new number can raise or lower the mean.
• Two groups — averaging two means is not always the right answer.
• A line over time — dots join when the order is real.
• Reading the line — how steep a stretch is, what a join hides.
• Drawing it honestly — the same numbers, two very different pictures.

Every idea has a lab. Move something yourself and watch the mean change.