# Adding and averaging

Authored explanation; editorial review pending.

Imagine four equally sized containers holding 3, 1, 1 and 3 units. Combining them gives 8 units. Sharing the total equally between the four containers gives 2 in each. Two is the average; the original containers were not all equal.

The number of observations and the sum of their values are different quantities. Doubling the number of repeated observations doubles the sum but leaves the average unchanged.

## Worked example

1. Add 3 + 1 + 1 + 3 to obtain 8.
2. Count four values.
3. Divide 8 by 4 to obtain 2.
4. Repeating the list gives 16 divided by 8, still 2.

An average is a total shared equally among the number of observations.