The mean is a balance point
A pencil under a ruler balances at one exact spot. Nowhere else works.
The ruler is a beam. The pencil is the pivot, the point it rests on. Level means flat.
Loading lab…
- Pivot on 20. The beam tips right.
- Pivot on 24. The beam is level.
Add up, then check the distances
You know the mean: add, then share the total. Five weights lie at 20, 22, 24, 26 and 28. Each number is a reading. The total is 120. Shared five ways, 120 ÷ 5 = 24. So the mean is 24.
Now check each weight's distance from 24. Below 24 is minus. Above 24 is plus. The distances are −4, −2, 0, +2 and +4. They add to 0: the minus distances cancel the plus ones. So the beam is level only where the distances cancel.
The mean is the balance point of the readings.
Watch out!
The middle reading is not always the balance point. For 2, 4 and 9, the middle one is 4. The mean is 5. At 5 the distances are −3, −1 and +4. They add to 0.