# Adding and averaging

Add the values, then divide by how many there are. The average keeps the total and the count, and loses the individual values.

Written for this edition, not translated from Einstein.

## What does an average keep, and what does it lose?

Four jars hold 3, 1, 1 and 3 marbles. Pour them together and there are 8. Share the 8 equally between the four jars and each holds 2. Two is the average, although no jar held 2 to begin with.

The average keeps the total and the count and nothing else, so 3, 1, 1, 3 and 2, 2, 2, 2 have the same average. Listing every value twice doubles both the total and the count, and the average stays at 2.

## Worked example: Three mornings with the same average

1. One morning the four jars hold 3, 1, 1 and 3 marbles. Add them: 8. Divide by the four jars: an average of 2.
2. Another morning they hold 8, 0, 0 and 0. Add them: 8 again. Divide by four: 2 again, and now three jars are empty.
3. A third morning every jar holds 2, which is the average itself. Add them: 8. Divide by four: 2.
4. Write any of those three lists out twice over. The total doubles to 16 and the count doubles to 8 jars, and 16 divided by 8 is still 2.
5. Four descriptions and one average. It keeps the total and the count, and the differences between the mornings are what it leaves behind.

## Where this lesson stops

An average is the total shared equally among the observations, and two very different lists can have the same one.